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Report Overview
Summary of Alignment & Usability: Open Up Resources K-5 Math | Math
Product Notes
Imagine Learning Illustrative Mathematics K-5 Math, Kendall Hunt's Illustrative Mathematics K-5, and Open Up Resources K-5 Math draw upon the same mathematics content and therefore the scores and evidence for Gateways 1 and 2 are the same in all three programs, albeit with differences in navigation. There are differences in usability as Imagine Learning Illustrative Mathematics K-5 Math, Kendall Hunt's Illustrative Mathematics K-5, and Open Up Resources K-5 Math do not have the same delivery platforms for the instructional materials.
Math K-2
The materials reviewed for Open Up Resources K-2 Math 2022 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for usability including Teacher Supports and Student Supports; the materials partially meet expectations for Assessment.
Kindergarten
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
1st Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
2nd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Math 3-5
The materials reviewed for Open Up Resources 3-5 Math 2022 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for usability including Teacher Supports and Student Supports; the materials partially meet expectations for Assessment.
3rd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
4th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
5th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 1st Grade
Alignment Summary
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and meet expectations for practice-content connections.
1st Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.
Gateway 1
v1.5
Criterion 1.1: Focus
Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.
Indicator 1A
Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.
The curriculum is divided into eight units, and each unit contains a written End-of-Unit Assessment for individual student completion. The Unit 8 Assessment is an End-of-Course Assessment and includes problems from across the grade. Examples from End-of-Unit Assessments include:
Unit 2, Addition and Subtraction Story Problems, End-of-Unit Assessment, Problem 2, “After recess, Tyler collected 6 footballs. Then he collected some baseballs. Altogether, Tyler collected 10 balls. How many baseballs did Tyler collect? Show your thinking with drawings, numbers, or words. Write an equation to match the story problem.” (1.OA.1, 1.OA.6)
Unit 4, Numbers to 99, End-of-Unit Assessment, Problem 4, “a. Circle the number that is greater. 41 or 29, b. Circle the number that is greater. 77 or 75. c. Write to compare the numbers. 67___ 81, 31___ 31.” (1.NBT.3)
Unit 5, Adding Within 100, End-of-Unit Assessment, Problem 1, “Find the value of each sum. a. . b. . c. .” (1.NBT.4, 1.NBT.5)
Unit 7, Geometry and Time, End-of-Unit Assessment, Problem 6, “a. What time is shown on the clock? b. Draw the clock hands to show the time.” The clock hands show 4:30, and the digital clock shows 8:00. (1.MD.3)
Unit 8, Putting It All Together, End-of-Course Assessment and Resources, Problem 10, “Find the number that makes each equation true. Show your thinking using drawings, numbers, or words. a. ___, b. ___, c. ___.” (1.NBT.2b, 1.OA.8)
Indicator 1B
Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The instructional materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The instructional materials provide extensive work in Grade 1 as students engage with all CCSSM standards within a consistent daily lesson structure. Per the Grade 1 Course Guide, “A typical lesson has four phases: a Warm-up, one or more instructional activities, the lesson synthesis, a Cool-down. In grade 1, some lessons do not have Cool-downs. During these lessons, checkpoints are used to formatively assess understanding of the lesson.” Examples of extensive work include:
Unit 1, Adding, Subtracting, and Working with Data, Section C, Lessons 11, 13, and 15 engage students in extensive work with 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another). Lesson 11, Class Pet Surveys, Warm-up: Notice and Wonder: Tally Marks, Launch, students work with tally marks organized in groups of five, like the 5-frame, “Groups of 2. Display the image. ‘What do you notice? What do you wonder?’” Lesson 13, Questions About Data, Activity 1, Student Work Time, students determine whether or not a question about data can be answered with a given data representation, “Read the task statement. ‘If the question can be answered, circle ‘thumbs up’. If it can’t be answered, circle ‘thumbs down’.’ 3 minutes: independent work time. 3 minutes: partner work time.” Lesson 15, Animals in the Jungle, Activity 3, Launch, students use data collected in Activity 1 and their analysis of the data from Activity 2 to decide what findings to share and make choices about how to represent them, “Give each group tools for creating a visual display and access to their data and questions from the previous activities. ‘Think of at least two things about your survey you want to share.’ 1 minute: quiet think time. 2 minutes: partner discussion. If students need ideas, invite students to share some examples, such as: how many people took your survey, a fact about how many ____, an interesting discovery you made.”
Unit 2, Addition and Subtraction Story Problems, Section B, Lesson 8; Unit 4, Numbers to 99, Section D, Lesson 19; and Unit 8, Putting It All Together, Section C, Lesson 7 engage students in extensive work with 1.NBT.1 (Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral). In Unit 2, Lesson 8, Shake, Spill, and Cover, Warm-up: Choral Count: Count on from 10, Launch and Student Work Time, students count on from numbers other than 1, In Launch, “‘Count by 1, starting at 10.’ Record as students count. Stop counting and recording at 40.” In Student Work Time, “‘What patterns do you see?’” In Unit 4, Lesson 19, Make Two-digit Numbers, Activity 3, Launch and Student Work Time, students choose from activities that offer practice working with two-digit numbers. In Launch, “Groups of 2. ‘Now you are going to choose from centers we have already learned.’ Display the center choices in the student book.’Think about what you would like to do.’ 30 seconds: quiet think time” In Student Work Time, “Invite students to work at the center of their choice. 10 minutes: center work time, Student Facing, Choose a center. Greatest of Them All (71, 75). Get Your Numbers in Order. 14, 36, 82. Grab and Count.” In Lesson Synthesis, “‘Today we made two-digit numbers in different ways. We used different amounts of tens and ones to make the same number.’ Display 3 tens and 7 ones, 2 tens and 17 ones, 1 ten and 27 ones, 37 ones. ‘Which do you think best matches the two-digit number 37? Why do you think it matches the number best?’ (3 tens and 7 ones matches best because the digits in the number tell us that there are 3 tens and 7 ones. 37 ones matches best because the number is read ‘thirty-seven.’).” In Unit 8, Lesson 7, Count Large Collections, Warm-up, Launch and Student Work Time, students show multiple ways to represent a number using tens and ones. In Launch, “Display the number. ‘What do you know about 103?’ 1 minute: quiet think time.” In Student Work Time, “Record responses. ‘How could we represent the number 103?’” In Activity 1, Launch, students count within 120 starting at a number other than 1, “Display chart with ‘start’ and 'stop’ numbers. ‘Today we are playing a new game called Last Number Wins. In this game your group will count from the ‘start’ number to the ‘stop’ number. The person to say the last number wins. Let’s play one round together. Our ‘start’ number will be 1 and our ‘stop’ number will be 43.’ Arrange students in a circle and explain that each student says one number. Count to 43. The person who says ‘43’ wins.”
Unit 3, Adding and Subtracting Within 20, Section A, Lesson 3 and Section C, Lesson 16 engage students in extensive work with 1.OA.3 (Apply properties of operations as strategies to add and subtract). Lesson 3, Are the Expressions Equal? Activity 1, Launch and Student Work Time, students sort addition expressions by their value. In Launch, “Groups of 2. Give students their addition expression cards. ‘Sort the cards into groups with the same value.’ Display an addition expression card, such as . ‘I know the value of this sum is seven. It is a sum that I just know. I will start a pile for sums of seven.’” In Student Work Time, “‘Work with your partner. Make sure that each partner has a chance to find the value before you place the card in a group. If you and your partner disagree, work together to find the value of the sum.’ 12 minutes: partner work time.” In Activity 2,Student Work Time, students determine whether equations are true or false. Student Facing, “Determine whether each equation is true or false. Be ready to explain your reasoning in a way that others will understand. a. . b. . c. d. . e. .” True, or thumbs up, and False, or thumbs down, are included with each equation. Lesson 16, Add Three Numbers, Warm-up: Number Talk: Related Expressions, Launch and Student Work Time, students use strategies and understandings for adding on to ten. In Launch, “Display one expression. ‘Give me a signal when you have an answer and can explain how you got it.’ 1 minute: quiet think time” In Student Work Time, “Record answers and strategy. Keep expressions and work displayed. Repeat with each expression. Student Facing, Find the value of each expression mentally. , , , .”
The instructional materials provide opportunities for all students to engage with the full intent of Grade 1 standards through a consistent lesson structure. According to the Grade 1 Course Guide, A Typical Lesson, “The first event in every lesson is a Warm-up. Every Warm-up is an Activity Narrative. The Warm-up invites all students to engage in the mathematics of the lesson… After the Warm-up, lessons consist of a sequence of one to three instructional activities. The activities are the heart of the mathematical experience and make up the majority of the time spent in class… After the activities for the day, students should take time to synthesize what they have learned. This portion of class should take 5-10 minutes before students start working on the Cool-down…The Cool-down task is to be given to students at the end of the lesson. Students are meant to work on the Cool-down for about 5 minutes independently and turn it in…In grade 1, some lessons do not have Cool-downs. During these lessons, checkpoints are used to formatively assess understanding of the lesson.” Examples of meeting the full intent include:
Unit 2, Adding and Subtracting within 100 Story Problems, Section C, Lesson 14 and Section D, Lesson 17 engage students with the full intent of 1.OA.7 (Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false). Lesson 14, Compare with Addition and Subtraction, Warm-up: True or False: Equal Sign, Launch and Student Work Time students develop and deepen their understanding of the equal sign. In Launch, “Display one statement. ‘Give me a signal when you know whether the statement is true and can explain how you know.’ 1 minute: quiet think time.” In Student Work Time, “Share and record answers and strategy. Repeat with each equation. Student Facing, Decide if each statement is true or false. Be prepared to explain your reasoning. , , .” Lesson 17, How Do the Stories Compare?, Warm-up: Which One Doesn’t Belong: Equations, Student Work Time, students analyze and compare equations. “Discuss your thinking with your partner.’ 2–3 minutes: partner discussion, Record responses. Student Facing, Which one doesn’t belong? A. , B. , C. , D. .”
Unit 3, Adding and Subtracting Within 20, Section C, Lesson 15 and Unit 4, Numbers to 99, Section B, Lesson 12 engage students with the full intent of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten [e.g., ]; decomposing a number leading to a ten [e.g., ]; using the relationship between addition and subtraction [e.g., knowing that, one knows that , one knows ]; and creating equivalent but easier or known sums [e.g., adding by creating the known equivalent ]). Unit 3, Lesson 15, Solve Story Problems with Three Numbers, Warm-up: How Many Do You See: 10-frames, Launch, students subitize or use grouping strategies to describe the images they see, “Groups of 2. ‘How many do you see? How do you see them?’ Flash the image. 30 seconds: quiet think time.” Unit 4, Lesson 12, Mentally Add and Subtract Tens, Warm-up: Number Talk: Add and Subtract 10, Launch and Student Work TIme, students develop understanding and fluency using different strategies for adding and subtracting 10. In Launch, “Display one expression. ‘Give me a signal when you have an answer and can explain how you got it.’ 1 minute: quiet think time” In Student Work Time, “Record answers and strategy. Keep expressions and work displayed. Repeat with each expression. Student facing, , , , .”
Unit 7, Geometry and Time, Section B, Lessons 9, 10 and 11 engage students with the full intent of 1.G.3 (Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares). Lesson 9, Equal Pieces, Activity 2, Student Work Time, students are given a circle and a square blackline master and asked to fold the shapes into equal pieces, “Read the task statement. 10 minutes; independent work time. Monitor for students who line up the edges and fold the square horizontally, vertically, or diagonally, and a student who folds the circle.” Student Facing, a. Cut out one circle and one square. Fold each shape so that there are 2 equal pieces. Be ready to explain how you know your shape has 2 equal pieces. b. Cut out one circle and one square. Fold each shape so that there are 4 equal pieces. Be ready to explain how you know your shape has 4 equal pieces.” Lesson 10, One of the Pieces, All of the Pieces, Activity 1,Student Work Time, students continue to work with partitioning shapes into halves and fourths, using the correct fractional terminology, “Read the task statement. 2 minutes: independent work time. 2 minutes: partner discussion. Monitor for a range of ways to describe the amount shaded such as ‘some is shaded,’ ‘one piece of the square is shaded,’ ‘one out of two pieces is shaded,’ or ‘a half is shaded.’ Student facing, “Problem 1. a. Split the square into halves. Color in one of the halves. b. How much of the square is colored in? Problem 2. a. Split the circle into fourths. Color in one of the fourths. b. How much of the circle is colored in?” Lesson 11, A Bigger Piece, Activity 2, Student Work Time, students generalize that partitioning the same-size shape into fourths creates smaller pieces than partitioning it into halves. Students are shown a picture of roti and given a circle to help them solve the problem, “Read the task statement. 5 minutes: partner work time. Monitor for a student who shows and can explain that a half is bigger than a fourth. Student facing, Priya and Han are sharing roti. Priya says, ‘I want half of the roti because halves are bigger than fourths.’ Han says, ‘I want a fourth of the roti because fourths are bigger than halves because 4 is bigger than 2.’ Who do you agree with? Show your thinking using drawings, numbers, or words. Use the circle if it helps you.”
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.
Indicator 1C
When implemented as designed, the majority of the materials address the major clusters of each grade.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The instructional materials devote at least 65% of instructional time to the major clusters of the grade:
The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 7 out of 8, approximately 88%.
The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 142 out of 154, approximately 92%. The total number of lessons devoted to major work of the grade include: 136 lessons plus 6 assessments for a total of 142 lessons.
The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 152 out of 155, approximately 98%.
A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each unit. As a result, approximately 92% of the instructional materials focus on major work of the grade.
Indicator 1D
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers on a document titled “Lessons and Standards” found within the Course Guide tab for each unit. Connections are also listed on a document titled “Scope and Sequence”. Examples of connections include:
Unit 1, Adding, Subtracting, and Working with Data, Section C, Lesson 11, Cool-down connects the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the major work of 1.OA.5 (Relate counting to addition and subtraction). Students look at data and then make observations about the data including the total number of votes collected. Student Facing states, “Another class answered the question ‘Which animal would make the best class pet?’ Their responses are shown below. Write 1 true statement about the data.” A hamster, fish, and frog are shown with tally marks, grouped by fives, for students to count.
Unit 2, Addition and Subtraction Story Problems, Section C, Lesson 13, Activity 1, Student Work TIme, connects the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the major work of 1.OA.1 (Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions). Students determine whether comparison statements about data are true or false and explain how they know. The activity states, “Read the task statement. ‘Priya and Han made some statements about their data. Your job is to decide whether you agree or disagree. Once you decide, circle it on your paper.’” A chart titled “Favorite Art Supply” is displayed. Student Facing states, “A group of students was asked, ‘What is your favorite art supply?’ Their responses are shown in this chart. a. More students voted for crayons than markers. b. Fewer students voted for crayons than paint. c. Three more students voted for markers than crayons. Show your thinking using drawings, numbers, or words. d. One more student voted for paint than crayons. Show your thinking using drawings, numbers, or words. e. One fewer student voted for paint than markers. Show your thinking using drawings, numbers, or words. If you have time: Change the false statements to make them true.”
Unit 7, Geometry and Time, Section C, Lesson 15, Activity 1, Student Work Time, connects the supporting work of 1.MD.3 (Tell and write time in hours and half-hours using analog and digital clocks.) to the major work of 1.NBT.1 (Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral). Students tell and write time in hours and half-hours using analog and digital clocks. In the Student Facing materials, students see a clock. Directions state, “Start at 12. Count the minutes around the clock until you get to half the clock. Circle where you stop.”
Indicator 1E
Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
The instructional materials for Open Up Resources K–5 Math Grade 1 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
Materials are coherent and consistent with the Standards. These connections can be listed for teachers in one or more of the four phases of a typical lesson: instructional activities, lesson synthesis, or Cool-down. Examples of connections include:
Unit 2, Addition and Subtraction Story Problems, Section A, Lesson 2, Activity 1, Student Work Time, connects the major work of 1.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 1.OA.D (Work with addition and subtraction equations). Students make sense of addition and subtraction story problems as they make equations to represent them. Student Facing states, “a. 7 people were working on the computers. 3 more people came to the computers. Now 10 people are working on the computers. Equation: ____ b. A group of kids was using 10 puppets to act out a story. They put 5 of the puppets away. Now they have 5 puppets left. Equation: ____ c. 5 people came to story time. Then 4 more people joined. Now there are 9 people at story time. Equation: ____ d. 8 students were doing homework at a table. 3 of the students finished their homework and left the table. Now there are 5 students at the table. Equation: ____.”
Unit 4, Numbers to 99, Section B, Lesson 8, Activity 2, Launch and Student Work Time, connects the major work of 1.NBT.A (Extend the counting sequence) to the major work of 1.NBT.B (Understand place value). Students match cards that show different base-ten representations. The Launch states, “Groups of 2–4, Give each group a set of cards and access to connecting cubes in towers of 10 and singles. Display the student workbook page. ‘Today we are going to sort cards into groups that show the same two-digit number. For example, look at these three cards. Which two representations show the same two-digit number? Why doesn’t the other one belong?’ (The first two cards both show 4 tens and 1 one or 41. The last card isn't the same because it only shows 1 ten. It has the same digits, but they mean something different.).” In Student Work Time, Student Facing states, ”Your teacher will give you a set of cards that show different representations of a two-digit number. Find the cards that match. Be ready to explain your reasoning.“ Three representations are provided: An image of four 4 tens and one connecting cube, (as an expression) and 1 ten and 4 ones (written in words).
Unit 6, Length Measurements Within 120 Units, Section C, Lesson 11, Activity 1, Launch and Student Work Time, connects the major work of 1.MD.A (Measure lengths indirectly and by iterating length units) to the major work of 1.OA.A (Represent and solve problems involving addition and subtraction). Students measure the length of their shoe using connecting cubes and solve a Put Together, Result Unknown problem and a Compare, Difference Unknown problem about their measurements. The Launch states, “Groups of 2, Give each group connecting cubes in towers of 10 and singles and paper. ‘A few days ago we measured the length of the biggest foot in the world. Today we are each going to measure the length of our own shoe and solve some problems using the length. First we will trace our shoe on a piece of paper and then use connecting cubes to measure the length of our shoe.’ Demonstrate tracing or have a student trace your shoe and measure the length. ‘Record the length of my shoe in your book. Now your partner will trace your shoe on a piece of paper and then you will use connecting cubes to measure the length of your own shoe. Measure from the tip of the toe to the back of the heel. Your shoe might not line up with the end of a connecting cube. Find the closest number of cubes to the length of your shoe. Record the length of your shoe and your partner’s shoe.’ 5 minutes: partner work time” In Student Work Time, Student Facing states, “1. My teacher's shoe is ___ connecting cubes long. My shoe is ___ connecting cubes long. My partner’s shoe is ___ connecting cubes long. 2. Solve these problems about the length of your group’s shoes. Show your thinking using drawings, numbers, words, or equations. a. What is the length of your shoe and your partner’s shoe together? b. Whose shoe is longer, yours or your partner’s? How much longer? c. Whose shoe is shorter, your teacher’s shoe or your shoe? How much shorter?”
Unit 7, Geometry and Time, Section C, Lesson 17, , Launch and Student Work Time, connects the supporting work of 1.MD.B (Tell and write time) to the supporting work of 1.G.A (Reason with shapes and their attributes). Students tell time to the hour and half hour using their knowledge of circles and its fractional pieces. The Launch states, “Groups of 2, Display image. ‘Pick one that doesn’t belong. Be ready to share why it doesn’t belong.’ 1 minute: quiet think time” Student Work Time states, “‘Discuss your thinking with your partner.’ 2–3 minutes: partner discussion, Share and record responses.” Student facing shows four different clocks, one in digital mode, and the student must select the one that doesn’t belong.
Indicator 1F
Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The instructional materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
Prior and Future connections are identified within materials in the Course Guide, Scope and Sequence Section, within the Dependency Diagrams which are shown in Unit Dependency Diagram and Section Dependency Diagram. An arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section. While future connections are all embedded within the Scope and Sequence, descriptions of prior connections are also found within the Preparation tab for specific lessons and within the notes for specific parts of lessons.
Examples of connections to future grades include:
Unit 2, Addition and Subtraction Story Problems, Section B, Lesson 9, Preparation connects the work of 1.OA.1 (Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions), 1.OA.3 (Apply properties of operations as strategies to add and subtract), and 1.OA.7 (Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false) to work with representing story problems in Grade 2. Lesson Narrative states, “Students write equations that match the story problem, identifying where the answer to the question is in the equation. Students should have access to connecting cubes or two-color counters. In Activity 1, students work with partners to solve a story problem and write an equation. During Activity 2, students do a gallery walk within their group and compare story problems, methods for solving the problems, and equations that represent the problems. Students do not need to master representing and solving these problem types until the end of grade 2, so the important part of this lesson is that students can make sense of the story problem and explain how their equation matches the problem.”
Unit 6, Length Measurements Within 120 Units, Section B, Lesson 9, Warm-up connects 1.NBT.1 (Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral) to work with understanding three-digit numbers in Grade 2. The Narrative states, “The purpose of this Choral Count is to invite students to practice counting by 1 from 90 to 120 and notice patterns in the count. Keep the record of the count displayed for students to reference throughout the lesson. When students notice the patterns in the digits after counting beyond 99 and explain the patterns based on what they know about the structure of the base-ten system, they look for and express regularity in repeated reasoning (MP7, MP8). Students will develop an understanding of a hundred as a unit and three-digit numbers in grade 2.”
Unit 8, Putting It All Together, Section A, Lesson 3, Preparation connects 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums) and 1.OA.8 (Determine the unknown whole number in an addition or subtraction equation relating three whole numbers) to work with addition and subtraction in 2nd Grade. Lesson Narrative states, “In previous lessons, students practiced adding and subtracting within 10. In this lesson, students use the methods that make the most sense to them to add and subtract within 20. The lesson activities encourage students to use methods such as using known facts, making 10 to add, decomposing a number to lead to a 10 to subtract, and using the relationship between addition and subtraction. This lesson helps students practice adding and subtracting with 20 and apply their fluency within 10 in preparation for their work with addition and subtraction in grade 2.”
Examples of connections to prior knowledge include:
Grade 1 Course Guide, Scope and Sequence, Unit 1, Adding, Subtracting, and Working with Data, Unit Learning Goals connect 1.OA.5 (Relate counting to addition and subtraction) and 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on, making ten, decomposing a number leading to a ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums) working sorting objects by attributes from Kindergarten. Lesson Narrative states, “Students also build on the work in kindergarten as they engage with data. Previously, they sorted objects into given categories such as size or shape. Here, students use drawings, symbols, tally marks, and numbers to represent categorical data. They go further by choosing their own categories, interpreting representations with up to three categories, and asking and answering questions about the data.”
Unit 3, Adding and Subtracting Within 20, Section B, Lesson 8, Preparation connects 1.NBT.2a (10 can be thought of as a bundle of ten ones - called a “ten”) and 1.NBT.2b (The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones) to work decomposing numbers from K.NBT.1. Lesson Narrative states, “In this lesson, students build on their work from kindergarten where they composed and decomposed teen numbers with ten ones and some more ones. They learn that 10 ones is equivalent to a unit called a ten. In the first activity students count a collection of 16 objects and represent their count. In the second activity, students compose teen numbers with a ten and some ones. This lays the groundwork for a later unit in which students compose and decompose 2-digit numbers into tens and ones.”
Unit 6, Length Measurements within 120 Units, Section A, Lesson 1, Preparation connects 1.MD.1 (Order three objects by length; compare the lengths of two objects indirectly by using a third object) to the work comparing lengths of objects from K.MD.2. Lesson Narrative states, “In kindergarten, students compared the length of two objects directly by lining up the endpoints. They described the objects using language such as longer and shorter. In this unit the words ‘longer than’ and ‘shorter than’ are encouraged, although students may use ‘taller than’ in certain contexts related to height.”
Indicator 1G
In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.
The materials reviewed for Open Up Resources K–5 Math Grade 1 foster coherence between grades and can be completed within a regular school year with little to no modification.
According to the Grade 1 Course Guide, About These Materials, “Each grade level contains 8 or 9 units. Units contain between 8 and 28 lesson plans. Each unit, depending on the grade level, has pre-unit practice problems in the first section, checkpoints or checklists after each section, and an end-of-unit assessment. In addition to lessons and assessments, units have aligned center activities to support the unit content and ongoing procedural fluency. The time estimates in these materials refer to instructional time. Each lesson plan is designed to fit within a class period that is at least 60 minutes long. Some units contain optional lessons, and some lessons contain optional activities that provide additional student practice for teachers to use at their discretion.”
According to the Grade 1 Course Guide, Scope and Sequence, Pacing Guide, “Number of days includes 2 days for assessments per unit. Upper bound of the range includes optional lessons.” For example:
155 days (lower range) to 162 days (upper range).
Per the Grade 1 Course Guide, A Typical Lesson, “A typical lesson has four phases: 1. a Warm-up 2. one or more instructional activities 3. the lesson synthesis 4. a Cool-down. In grade 1, some lessons do not have Cool-downs. During these lessons, checkpoints are used to formatively assess understanding of the lesson.” In Grade 1, each lesson is composed of the following:
5-10 minutes Warm-up
10-25 minutes (each) for one to three Instructional Activities
5-10 minutes Lesson Synthesis
0-5 minutes Cool-down
Overview of Gateway 2
Rigor & the Mathematical Practices
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).
Gateway 2
v1.5
Criterion 2.1: Rigor and Balance
Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and spend sufficient time working with engaging applications of mathematics. There is a balance of the three aspects of rigor within the grade.
Indicator 2A
Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
Materials develop conceptual understanding throughout the grade level. According to the Grade 1 Course Guide, Design Principles, conceptual understanding is a part of the design of the materials. Balancing Rigor states, “There are three aspects of rigor essential to mathematics: conceptual understanding, procedural fluency, and the ability to apply these concepts and skills to mathematical problems with and without real-world contexts. These aspects are developed together and are therefore interconnected in the materials in ways that support student understanding. Opportunities to connect new representations and language to prior learning support students in building conceptual understanding. Access to new mathematics and problems prompts students to apply their conceptual understanding and procedural fluency to novel situations.” Additionally, Purposeful Representations states, “Across lessons and units, students are systematically introduced to representations and encouraged to use representations that make sense to them. As their learning progresses, students are given opportunities to make connections between different representations and the concepts and procedures they represent.” Examples include:
Unit 1, Adding, Subtracting, and Working with Data, Section A, Lesson 2, Activity 2, Launch, students develop conceptual understanding as they write addition expressions for sums within ten. Launch states, “Groups of 2. Give each group a set of cards, two recording sheets, and access to 10-frames and two-color counters. ‘We are going to learn a game called Check It Off. Let’s play a round together. First we take out all of the cards greater than five. We will not use those cards in this game. Now I am going to pick two number cards and find the sum of the numbers. The sum is the total when adding two or more numbers.’ Choose two cards. ‘What is the sum of the numbers? How do you know?’ 30 seconds: quiet think time. 1 minute: partner discussion. Share responses. ‘Now I check off the sum. What addition expression represents the sum of the numbers?’ 30 seconds: quiet think time. Share responses. ‘I record the expression on my recording sheet next to the sum. Now it’s my partner’s turn.’” (1.OA.5, 1.OA.6)
Unit 3, Adding and Subtracting Within 20, Section B, Lesson 13, Activity 1, Launch and Student Work Time, students develop conceptual understanding as they solve Take From, Change Unknown story problems using a method of their choice. Launch states, “Groups of 2. Give students access to double 10-frames and connecting cubes or two-color counters. Display and read the numberless and questionless story problem. ‘What do you notice? What do you wonder?’ 30 seconds: quiet think time. 1 minute: partner discussion. Record responses. If needed, ‘What question could we ask?’ In Student Work Time, Student Facing states, “1. There are students standing in the classroom. Some of the students sit down on the rug. There are still some students standing. 2. There are 15 students standing in the classroom. Some of the students sit down on the rug. There are still 5 students standing. How many students sat down on the rug? Show your thinking using drawings, numbers, or words. Equation: ___.” (1.OA.1, 1.OA.5, 1.OA.6)
Unit 8, Putting It All Together, Lesson 9, Warm-up, Student Work Time, students develop conceptual understanding as they use true and false statements to compare two-digit numbers. Student Facing states, “Decide if each statement is true or false. Be prepared to explain your reasoning. , , .” (1.NBT.3)
According to the Grade 1 Course Guide, materials were designed to include opportunities for students to independently demonstrate conceptual understanding, when appropriate. Design Principles, Coherent Progress states, “Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals.” A Typical Lesson states, “The Cool-down task is to be given to students at the end of the lesson. Students are meant to work on the Cool-down for about 5 minutes independently and turn it in. The Cool-down serves as a brief formative assessment to determine whether students understood the lesson. Students’ responses to the Cool-down can be used to make adjustments to further instruction.” Examples include:
Unit 3, Adding and Subtracting Within 20, Section A, Lesson 2, Cool-down, students show a conceptual understanding of addition facts. Student Facing states, “How does knowing help you with ___? Show your thinking using drawings, numbers, or words.” (1.OA.3)
Unit 5, Adding Within 100, Section C, Lesson 12, Activity 2, Student Work Time and Activity Synthesis, students demonstrate conceptual understanding as they use what they know about the base-ten structure of numbers to create different expressions. Students are provided counting cubes. In Student Work Time, Student Facing states, “37, 22, 18, 56, 41. Choose 2 numbers from above and write an addition expression to make each statement true. a. This sum has the smallest possible value. Expression: ____ b. This sum has the largest possible value. Expression: ____ c.You do not need to make a new ten to find the value of this sum. Expression: ____ d. If you make a new ten to find the value of this sum, you will still have some more ones. Expression: ____ e. If you make a new ten to find the value of this sum, you will have no more ones. Expression: ____ Be ready to explain your thinking in a way that others will understand. f. If you have time: Choose 2 numbers from above and write an addition expression where the value is closest to 95. How do you know the value is closest to 95?” Activity Synthesis states, “Are there other numbers you could use? How do you know?” (1.NBT.C)
Unit 8, Putting It All Together, Section C, Lesson 8, Activity 1, Launch, students demonstrate conceptual understanding as they represent numbers within 100 using drawings, words, numbers, expressions, and equations. Launch states, “Give each student a piece of blank paper and access to connecting cubes in towers of 10 and singles. ‘We are going to create a class book. First you will plan out your page. Pick your favorite number between 20 and 100. You will represent your number in as many different ways as you can. You need to include at least three expressions. Let’s make a page together.’ Display the number 84. ‘What are some ways that I can represent this number?” (I can draw 8 tens and 4 ones, 7 tens and 14 ones, , ) 30 seconds: quiet think time. 1 minute: partner discussion. Record responses. If needed, ask: ‘How can we represent 84 using only 6 tens? What other addition expressions could we write?’” (1.NBT.B)
Indicator 2B
Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
According to the Grade 1 Course Guide, Design Principles, Balancing Rigor, “Warm-ups, practice problems, centers, and other built-in routines help students develop procedural fluency, which develops over time.” Examples include:
Unit 1, Adding, Subtracting, and Working with Data, Section A, Lesson 2, Activity 1, Student Work Time, students develop procedural fluency as they match expressions to dot images and find the total. Student Work Time states, “‘In this activity, draw a line to connect each dot image to its matching expression. Then, find the total. On the second page, complete the missing expressions or the missing dot images.’ 5 minutes: independent work time, ‘Share your work with your partner.’ 3 minutes: partner discussion” Student Facing states, “1. Match each pair of dots to an expression. Then, find the total. 2. Draw the missing dots to match the expression. Then, find the total. 3. Write the missing expression to match the dots. Then, find the total.” Expressions include: , , , , . (1.OA.6)
Unit 3, Adding and Subtracting Within 20, Section A, Lesson 5, Warm-up, Student Work Time, students develop procedural fluency as they select numbers that make an equation true. Student Facing states, “Find the number that makes each equation true. ___, ___, ___, ___.” (1.OA.6, 1.OA.8)
Unit 6, Length Measurements Within 120 Units, Section A, Lesson 2, Warm-up, Student Work Time, students develop procedural fluency as they add numbers within 100. Student Facing states, “Find the value of each expression mentally. , , , .” (1.NBT.4)
According to the Grade 1 Course Guide, materials were designed to include opportunities for students to independently demonstrate procedural skill and fluency, when appropriate. Design Principles, Coherent Progress states, “Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals.” A Typical Lesson states, “The Cool-down task is to be given to students at the end of the lesson. Students are meant to work on the Cool-down for about 5 minutes independently and turn it in. The Cool-down serves as a brief formative assessment to determine whether students understood the lesson. Students’ responses to the Cool-down can be used to make adjustments to further instruction.” Examples include:
Unit 3, Adding and Subtracting Within 20, Section A, Lesson 2, Activity 3, Student Work Time, students demonstrate fluency by finding the value of sums within 10. In Student Work Time, Student Facing states, “Find the value of each sum. a. ___ b. ___ c. ___ d. ___ e. ___ f. ___ g. ___ h. ___.” Student Work Time states, “Read the task statement. 5 minutes: independent work time. 3 minutes: partner discussion.” (1.OA.5, 1.OA.6, 1.OA.8)
Unit 4, Numbers to 99, Section A, Lesson 4, Activity 2, Student Work Time, students demonstrate procedural skill and fluency as they practice adding and subtracting multiples of 10 from multiples of 10. In Student Work Time, Student Facing states, “e. ___ f. ___ g. ___ h. ___.” Student Work Time states, “5 minutes: independent work time. 5 minutes: partner work time.” (1.NBT.2c, 1.NBT.4, 1.NBT.6)
Unit 8, Putting It All Together, Section A, Lesson 2, Cool-down, students demonstrate procedural fluency by using the subtraction and addition relationship to add or subtract within 10. Student Facing states, “Mai is still working on ___. Write an addition equation she can use to help figure out the difference. Addition equation: ___.” (1.OA.6)
Indicator 2C
Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics.
According to the Grade 1 Course Guide, Design Principles, Balancing Rigor, “Access to new mathematics and problems prompts students to apply their conceptual understanding and procedural fluency to novel situations.” Multiple routine and non-routine applications of the mathematics are included throughout the grade level, and these single- and multi-step application problems are included within Activities or Cool-downs.
Students have the opportunity to engage with applications of math both with teacher support and independently. According to the Grade 1 Course Guide, materials were designed to include opportunities for students to independently demonstrate application of grade-level mathematics, when appropriate. Design Principles, Coherent Progress states, “Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals.” A Typical Lesson states, “The Cool-down task is to be given to students at the end of the lesson. Students are meant to work on the Cool-down for about 5 minutes independently and turn it in. The Cool-down serves as a brief formative assessment to determine whether students understood the lesson. Students’ responses to the Cool-down can be used to make adjustments to further instruction.”
Examples of routine applications of the math include:
Unit 2, Addition and Subtraction Story Problems, Section A, Lesson 2, Activity 2, Student Work Time, students solve and write equations for Result Unknown word problems. Student Work Time states, “‘Now you will solve the problems and write equations to match. You can solve the problems in any way that makes sense to you.’ Read problems aloud. 5 minutes: partner work time. ‘Find another group and discuss each problem. Share the equation you wrote and how it matches the story.’ 5 minutes: small-group discussion.” Student Facing states, “a. There was a stack of 6 books on the table. Someone put 4 more books in the stack. How many books are in the stack now? Show your thinking using drawings, numbers, or words. Equation: ___ b. 9 books were on a cart. The librarian took 2 of the books and put them on the shelf. How many books are still on the cart? Show your thinking using drawings, numbers, or words. Equation: ___ c. 2 kids were working on an art project. 7 kids join them. How many kids are working on the art project now? Show your thinking using drawings, numbers, or words. Equation:___ d. The librarian had 8 bookmarks. He gave 5 bookmarks to kids at the library. How many bookmarks does he have now? Show your thinking using drawings, numbers, or words. Equation: ___.” (1.OA.1)
Unit 3, Adding and Subtracting within 20, Section C, Lesson 20, Cool-down, students solve real-world word problems with three addends. Student Facing states, ”Jada visited the primate exhibit. She saw 8 monkeys, 4 gorillas, and 7 orangutans. How many primates did she see? Show your thinking using drawings, numbers, or words. Equation: ___.” (1.OA.2, 1.OA.6)
Unit 4, Numbers to 99, Section A, Lesson 4, Activity 1, Launch and Student Work Time, students solve story problems involving adding and subtracting multiples of 10. Launch states, “Groups of 2. Give students access to connecting cubes in towers of 10 and singles and double 10-frames.” Student Work Time states, “Read the task statement. 7 minutes: independent work time. 3 minutes: partner discussion. Monitor for students who show: towers of 10, base-ten drawings, ___ tens and ___ tens, expressions or equations.” In Student Work Time, Student Facing states, “a. Jada is counting collections of cubes. In Bag A there are 30 cubes. In Bag B there are 2 towers of 10. How many cubes are in the two bags all together? Show your thinking using drawings, numbers, or words. b. Tyler is counting a collection of cubes. In Bag C there are 7 towers of 10. He takes 40 cubes out of the bag. How many cubes does he have left in the bag? Show your thinking using drawings, numbers, or words.” (1.NBT.2c, 1.NBT.4, 1.NBT.6)
Examples of non-routine applications of the math include:
Unit 3, Adding and Subtracting Within 20, Section D, Lesson 28, Activity 1, Launch and Student Work Time, students generate, articulate, and solve their own addition and subtraction problems. Launch states, “Give students access to double 10-frames and connecting cubes or two-color counters. Display and read the questionless story problem. ‘What is this story missing? What kind of questions could you ask? (How many pencils did they have altogether? How many more pencils does Noah have than Elena?)’ 30 seconds: quiet think time. 1 minute: partner discussion. Share and record responses. ‘We have been solving different kinds of story problems. Today, you and your partner will write and solve addition and subtraction story problems using objects we have in our classroom.’” Student Work Time states, “‘Partner A will pick a number less than 20. Partner B will use objects in the room to write a story problem and ask a question for which the number Partner A picked is the answer. Together, solve the story problem and write an equation. Switch roles for problem 2.’ 10 minutes: partner work time.” In Student Work Time, Student Facing states, “Noah had 8 pencils. Elena had 5 pencils. Han had 4 pencils..a Addition story problem: Solve the story problem. Show your thinking using drawings, numbers, or words. Equation: ___ b. Subtraction story problem: Solve the story problem, Show your thinking using drawings, numbers, or words. Equation: ___.” (1.OA.1, 1.OA.2, 1.OA.3, 1.OA.6)
Unit 5, Adding Within 100, Section B, Lesson 8, Activity 3, Student Work Time, students solve story problems involving addition with two-digit and one-digit numbers. Student Work Time states, “Read the task statement. 3 minutes: independent work time. 3 minutes: partner discussion.” Student Facing states, “a. Priya watched a football game. The home team scored 35 points in the first half. In the second half they scored 6 more points. How many points did they score all together? Show your thinking using drawings, numbers, or words. b. At the football game, 9 fans cheered for the visiting team. There were 45 fans who cheered for the home team. How many fans were at the game all together? Show your thinking using drawings, numbers, or words.” (1.NBT.4)
Unit 6, Length Measurements Within 120 Units, Section B, Lesson 7, Cool-down, students solve a problem by reasoning about measurements with different units. Student Facing states, “Priya says that the length of the shoe is 5 paper clips. Is her measurement accurate? Why or why not?” An image of a high-top sneaker is shown with 5 paper clips. (1.MD.2)
Indicator 2D
The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.
All three aspects of rigor are present independently throughout the grade. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, or application include:
Unit 2, Addition and Subtraction Story Problems, Section C, Lesson 14, Activity 1, Launch and Student Work Time, students analyze and solve addition and subtraction application problems. Launch states, “Groups of 2, Give students access to connecting cubes or two-color counters. Display the image in the student book. ‘Tell a story about this picture.’ 1 minute: quiet think time. 2 minutes: partner discussion. Share responses.” In Student Work Time, Student Facing states, “There are 8 glue sticks and 3 scissors at the art station. How many fewer scissors are there than glue sticks? Mai created a picture. (An Image of eight red dots and three yellow dots is provided.) She is not sure which equation she should use to find the difference. , , Help her decide. Show your thinking using drawings, numbers, or words.” (1.OA.1, 1.OA.5, 1.OA.7)
Unit 3, Adding and Subtracting Within 20, Section A, Lesson 4, Activity 2, Student Work Time and Activity Synthesis, students develop conceptual understanding as they justify that they have found all the ways to make 10. An image of 10 counters in a ten frame is displayed. Students have access to counters and a 10-frame. In Student Work Time, Student Facing states, “a. Show all the ways to make 10. b. How do you know that you have found all the ways? Be ready to explain your thinking in a way that others will understand.” Activity Synthesis states, “‘How do you know that you found all of the ways?’ (I started by filling my 10-frame with red counters and then flipped over the first red counter to make it yellow. That was . I kept flipping over a one red counter at a time to make it yellow and kept writing expressions.)” (1.OA.3, 1.OA.6)
Unit 7, Geometry and Time, Section C, Lesson 15, Activity 2, Launch and Student Work Time, students develop procedural fluency as they write times after reading one or both hands on a clock. Launch states, ”Groups of 2, Give students their Half Past Clock Cards. ‘Write the times on the new clock cards that show half past.’ 2 minutes: independent work time.” Student Work Time states, “What time is shown on each clock? Work on the questions by yourself and then compare your work with your partner’s.” In Student Work Time, Student Facing states, “1. For each clock, write the time. a. Clock shows 2:00. b. Clock shows 4:30. c. Clock shows 6:30. d. Clock shows 12:00. e. Clock shows 8:00.” (1.MD.3)
Multiple aspects of rigor are engaged simultaneously throughout the materials in order to develop students’ mathematical understanding of a single unit of study or topic. Examples include:
Unit 1, Adding, Subtracting, and Working with Data, Section B, Lesson 8, Activity 2, Launch and Student Work Time, students develop conceptual understanding alongside procedural fluency as they sort shapes into categories and explain their strategies for sorting. Launch states, “Give students access to colored pencils or crayons and copies of the three-column table.” In Student Work Time, Student Facing states, “a. Show how you sorted the shape cards. Be sure that someone else who looks at your paper can see how many shapes are in each category. b. Complete the sentences: 1. The first category has ___ shapes. 2. The second category has ___ shapes. 3. The third category has ___ shapes. 4. There are ___ shapes all together.” (1.MD.4)
Unit 3, Adding and Subtracting Within 20, Section A, Lesson 6, Activity 1, Student Work Time, students develop conceptual understanding alongside application as they use addition to solve routine problems. In Student Work Time, Student Facing states, “Han is playing Shake and Spill. He has some counters in his cup. Then he puts 3 more counters in his cup. Now he has 10 counters in his cup. How many counters did he start with? Show your thinking using drawings, numbers, or words. Equation: ___.” (1.OA.1, 1.OA.5, 1.OA.6)
Unit 6, Length Measurements Within 120 Units, Section A, Lesson 1, Activity 2, Launch, Student Work Time, and Activity Synthesis, students develop all three aspects of rigor, conceptual understanding, procedural skill and fluency, and application as they order objects by length. Launch states, “Groups of 4, Give each group 10–12 objects.” In Student Work Time, Student Facing states, “a. Pick 3 objects. With your partner, put the objects in order from shortest to longest. Trace or draw your objects. b. Pick 3 new objects. With your partner, put them in order from longest to shortest. Write the names of the objects in order from longest to shortest.” Activity Synthesis states, “Invite previously identified students to demonstrate how they ordered three objects from shortest to longest. Display the three objects with the endpoints lined up so all students can see. ‘What statements can you make to compare the length of their objects?’ (The ___ is longer than the ___ and ___.)” (1.MD.1)
Criterion 2.2: Math Practices
Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).
Indicator 2E
Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Narratives and Lesson Activities’ Narratives).
MP1 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with support of the teacher and independently throughout the units. Examples include:
Unit 2, Addition and Subtraction Story Problems, Section A, Lesson 4, Cool-down, students make sense of story problems and write equations. Student Facing, “Mai has 3 books. She gets some more books from the library. Now she has 7. How many more books did she get? Show your thinking using drawings, numbers, or words. Equation:___.” Preparation, Lesson Narrative states, “This lesson provides an opportunity to assess student progress on making sense of different types of story problems, the methods they use to solve, and the equations they write to match the problems.”
Unit 3, Adding and Subtracting Within 20,Section C, Lesson 15, Activity 1, Launch, Student Work Time, and Activity Narrative, students solve a story problem with three addends in which two of the addends make 10. Launch states, “Groups of 2. Give students access to double 10-frames and connecting cubes or two-color counters. ‘What kind of birds do you see where you live? Where do you see the birds?’ (I see pigeons on wires. I see a big bird in the park. I see red birds at the bird feeder. I hear loud birds in the morning.). 30 seconds: quiet think time. 1 minute: partner discussion. Share and record responses. Write the authentic language students use to describe the birds they see and where they see them. ‘Louis Fuertes was a bird artist. When he was a child, he loved to paint the birds he saw.’ Consider reading the book The Sky Painter by Margarita Engle. ‘We are going to solve some problems about birds.’'' Student Work Time states, “3 minutes: independent work time. 2 minutes: partner discussion. As students work, consider asking: ‘How are you finding the total number of birds? How did you decide the order to add the numbers? Is there another way you can add the numbers?’ Monitor for students who use the methods described in the narrative.” In Student Work Time, Student Facing states, “7 blue birds fly in the sky. 8 brown birds sit in a tree. 3 baby birds sit in a nest. How many birds are there altogether? Show your thinking using objects, drawings, numbers, or words.” An image of a blue bird is shown. Activity Narrative states, “Students are given access to double 10-frames and connecting cubes or two-color counters. Students read the prompt carefully to identify quantities before they start to work on the problem. They have an opportunity to think strategically about which numbers of birds to combine first since 3 and 7 make 10. They also may choose to use appropriate tools such as counters and a double 10-frame strategically to help them solve the problem (MP1, MP5).”
Unit 6, Length Measurements Within 120 Units, Section C, Lesson 17, Activity 2, students make sense of addition and subtraction word problems. Launch states, “Take turns reading a problem you came up with in the previous activity. Your partner group will act out the story with connecting cubes, then solve the problems. Then switch roles.” In Student Work Time, Student Facing states, “1. Group A: Read your problems to your partner group. 2. Group B: a. Act out and solve the problems. Show your thinking using drawings, numbers, or words. b. Write an equation to represent each story problem. c. What do you notice about the story problems and the equations you wrote?” Activity Narrative states, “The purpose of this activity is for students to solve addition and subtraction word problems by acting out the stories. Acting out gives students opportunities to make sense of a context (MP1).”
MP2 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with support of the teacher and independently throughout the units. Examples include:
Unit 2, Addition and Subtraction Story Problems, Section B, Lesson 6, Activity 2, Launch, Student Work Time, and Activity Narrative, students consider two different equations that represent the same story problem. Launch states, “Groups of 2. Give students access to 10-frames and connecting cubes or two-color counters. ‘We just solved a problem about pet fish. What else do you know about pets?’ 30 seconds: quiet think time. 1 minute: partner discussion. If needed ask, ‘What kinds of pets are there?’ Student Work Time states, “Read the task statement. 3 minutes: independent work time. 2 minutes: partner discussion. Monitor for a student who uses objects or drawings to show that each equation matches the story.” In Student Work Time, Student Facing states, “Tyler and Clare want to know how many pets they have together. Tyler has 2 turtles. Clare has 4 dogs. Tyler wrote the equation . Clare wrote the equation . Do both equations match the story? Why or why not? Show your thinking using drawings, numbers, or words.” Activity Narrative states, “Students contextualize the problem and see that each number represents a specific object’s quantity, no matter which order it is presented, and connect these quantities to written symbols (MP2).”
Unit 5, Adding Within 100, Section C, Lesson 14, Activity 1, Launch, Student Work Time, and Activity Narrative, students solve two-digit addition word problems. Launch states, “Give students access to connecting cubes in towers of 10 and singles. The table shows the number of cans four students collected for their class’ food drive. ‘What do you notice? What do you wonder?’ (They collected a lot of cans. Tyler collected the most. Han collected the least. I wonder how many they collected all together.)” Student Work Time states, “Read the task statement. 6 minutes: independent work time. ‘Check in with your partner. Be prepared to show or explain your thinking.’ 5 minutes: partner discussion.” In Student Work Time, Student Facing states, “a. Partner A: Write an equation to represent your thinking. How many cans did Lin and Priya collect altogether? How many cans did Han and Tyler collect altogether? How many cans did all four students collect altogether? b. Partner B: Write an equation to represent your thinking. How many cans did Tyler and Priya collect altogether? How many cans did Lin and Han collect altogether? How many cans did all four students collect altogether?” Activity Narrative states, “The purpose of this activity is for students to apply their understanding of place value and properties of operations to solve two-digit addition real world problems (MP2). Students may use any method and representation that helps them make sense of the problems in context.”
Unit 8, Putting It All Together, Section B, Lesson 5, Activity 1, Launch, Student Work Time, and Activity Narrative, students solve addition and subtraction story problems. Launch states, “Groups of 2. Give each group access to connecting cubes in towers of 10 and singles. Display the image in the student book. ‘What do you notice in this picture? What do you wonder? (There are bright colors. This looks like stars in the sky. Why is there red in the sky? Where is this?). This is a picture of something called the Helix Nebula. It is one of many interesting things that can be seen in our sky. People who are interested in learning more about stars, planets, or anything else that is found in the sky, can visit a planetarium to learn all about these things. We are going to solve some problems about a field trip to the planetarium.’” Student Work Time states, “8 minutes: independent work time. 4 minutes: partner discussion. Monitor for students who solve the problem about bright and dim stars with addition and for students who solve the same problem with subtraction.” In Student Work Time, Student Facing states, “Solve each problem. Show your thinking using drawings, numbers, or words. a. There are 7 first graders and some second graders at the planetarium. There are 18 students at the planetarium. How many second graders are at the planetarium? b. When the show started, 18 stars lit up in the sky. 13 stars were bright. Some of the stars were dim. How many stars were dim? c. Together, Diego and Tyler saw 15 shooting stars during the show. Diego saw 6 shooting stars. Tyler saw the rest. How many shooting stars did Tyler see? d. In the gift shop, Elena bought 12 star stickers. She also bought some planet stickers. Elena bought 20 stickers. How many planet stickers did she buy?” Activity Narrative states, “The purpose of this activity is for students to make sense of and solve Put Together/Take Apart, Addend Unknown story problems (MP2). In the synthesis, students discuss different methods used to solve these problems, including using addition and subtraction.”
Indicator 2F
Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Activity Narratives and Lesson Activities’ Activity Narratives).
According to the Grade 1 Course Guide, Design Principles, Learning Mathematics By Doing Mathematics, “Students learn mathematics by doing mathematics, rather than by watching someone else do mathematics or being told what needs to be done. Doing mathematics can be defined as learning mathematical concepts and procedures while engaging in the mathematical practices - making sense of problems, reasoning abstractly and quantitatively, making arguments and critiquing the reasoning of others, modeling with mathematics, making appropriate use of tools, attending to precision in their use of language, looking for and making use of structure, and expressing regularity in repeated reasoning. By engaging in the mathematical practices with their peers, students have the opportunity to see themselves as mathematical thinkers with worthwhile ideas and perspectives.”
Students construct viable arguments, in connection to grade-level content, as they work with support of the teacher and independently throughout the units. Examples include:
Unit 3, Adding and Subtracting Within 20, Section A, Lesson 6, Activity 2, Student Work Time and Activity Narrative, students construct arguments as they solve addition and subtraction stories. In Student Work Time, Student Facing states, “a. Noah is playing Shake and Spill with 10 counters. 4 of the counters fall out of the cup. How many counters are still in the cup? Show your thinking using drawings, numbers, or words. Equation: ____.” Activity Narrative states, “During the synthesis, students focus on sharing equations and comparing the start and change unknown problems, as well as how the commutative property can help them solve story problems with an unknown start. As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).”
Unit 5, Adding Within 100, Section A, Lesson 1, Activity 1, Launch and Student Work Time, students construct viable arguments as they apply their place value understanding to add an amount of tens or ones to a two-digit number. Launch states, “Groups of 2. Give each group a set of number cards and a paperclip. Give students access to connecting cubes in towers of 10 and singles. ‘Remove the 0, 6, 7, 8, 9 and 10 from the number cards. We are going to play a game where you must figure out the number your partner added. Let’s play a round together. All of you are partner A and I am partner B.’ Invite a student to spin. ‘You spun (43). I will draw a number card and decide whether to add that many ones or that many tens. I will say the sum aloud. The sum is (93). What number did I add? Talk with your partner. Be ready to explain how you know.’ (You added 50. In order to get from 43 to 93 you add 5 tens. 53, 63, 73, 83, 93.) 1 minute: partner discussion. Share responses.” Student Work time states, “‘Now you will play with your partner. For each round, decide whether you will add tens or ones and see if your partner can guess what you added.’ 15 minutes: partner work time. As students work, consider asking: ‘How did you choose to add tens or ones? How did you determine the number your partner added?’” In Student Work Time, Student Facing states, “Partner A: Spin to get a starting number. Partner B: Pick a number card without showing your partner. Choose whether to add that many ones or tens to your starting number. Make sure you don't go over 100. Tell your partner the sum. Partner A: Tell your partner what number you think they added and explain your thinking. Switch roles and repeat.” Activity Narrative states, “Throughout the activity, students explain how they add and how they determined the unknown addend with an emphasis on place value vocabulary (MP3).”
Unit 8, Putting It All Together, Section C, Lesson 8, Cool-down, students construct arguments as they interpret representations of numbers up to 100. Student Responses states, “Represent numbers to show the base-ten structure. Represent the same number with different amounts of tens and ones.” Preparation, Lesson Narrative states, “Students represent a two-digit number in as many ways as they can. They are encouraged to think about representations of their number that have different amounts of tens. Then, they do a gallery walk to compare representations their classmates made.”
Students critique the reasoning of others, in connection to grade-level content, as they work with support of the teacher and independently throughout the units. Examples include:
Unit 1, Adding, Subtracting, and Working with Data, Section B, Lesson 7, Activity 1, Launch, Student Work Time, and Activity Narrative, students begin to critique the reasoning of others as they sort math tools and understand how a partner sorted the tools. Launch states, “Groups of 2, Give each group a bag of math tools and access to the blackline masters.” Student Work Time states, “‘Sort your math tools. Use the tables if they are helpful.’ 4 minutes: partner work time. ‘Explain to another group how you sorted your tools. Make sure to tell them the groups you used and how many objects are in each group.’ 3 minutes: small group discussion. MLR2 Collect and Display. Circulate, listen for, and collect the language students use to describe how they sorted. Listen for categories, the number of shapes in each category, and math tool names. Record students’ words and phrases on a poster titled ‘Words to describe how we sorted’ and update throughout the lesson.” Activity Narrative states, “Students identify attributes of the objects and sort them into two or more groups. Students may choose to use one of the blackline masters to organize as they sort. When students share how they sorted with their partner, they use their own mathematical vocabulary and listen to and understand their partner's thinking (MP3, MP6).”
Unit 3, Adding and Subtracting Within 20, Section C, Lesson 19, Activity 1, Launch, Student Work Time, and Activity Narrative, students create an argument and critique the reasoning of others as they analyze methods for adding within 20 and use those methods flexibly to find sums. Launch states, “Groups of 2, Give students access to double 10-frames and connecting cubes or two-color counters.” Student Work Time states, “Read the task statement. ‘Use double 10-frames and counters to determine how each method works. Show your thinking in a way that others will understand.’ 10 minutes: partner work time. 3 minutes: partner discussion. Monitor for students who can explain each method using 10-frames.” In Student Work Time, Student Facing states, “Lin, Han, and Kiran are finding the value of . (An image of a double ten frame, eight red counters, and seven yellow counters are shown.) Lin thinks about . Han thinks about . Kiran thinks about . Explain how each student’s method works. Show your thinking using drawings, numbers, or words.” Activity Narrative states, “Throughout this activity, students must justify and explain the work of the given characters. Students share their thinking and have opportunities to listen to and critique the reasoning of their peers (MP3).”
Unit 4, Numbers to 99, Section B, Lesson 6, Activity 2, Launch, Student Work Time, and Activity Narrative, students construct an argument and critique reasoning when they analyze a collection of connecting cubes arranged in towers of 10. Launch states, “Groups of 2. Give students access to connecting cubes in towers of 10 and singles. ‘Noah counted a collection of connecting cubes. He says there are 50 cubes. Do you agree or disagree? Explain how you know. You will have a chance to think about it on your own and talk to your partner about Noah’s thinking before you write your response.’” Student Work Time states, “1 minute: quiet think time. ‘Share your thinking with your partner.’ 2 minutes: partner discussion. ‘Explain why you agree or disagree with Noah. Write the word “agree” or “disagree” in the first blank. Then write why you agree or disagree.’ 3 minutes: independent work time.” In Student Work Time, Student Facing states, “Noah organized his collection of connecting cubes. He counts and says there are 50 cubes. Do you agree or disagree? Explain how you know. I ___ with Noah because.” Activity Narrative states, “When students explain that they disagree with Noah because a ten must include 10 ones, they show their understanding of a ten and the foundations of the base-ten system (MP3).”
Indicator 2G
Materials support the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Instructional Routines and Lesson Activities’ Instructional Routines).
MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities to solve real-world problems, model situations with appropriate representations, and describe what they do with the model and how it relates to the problem. Students model with mathematics as they work with support of the teacher and independently throughout the units. Examples include:
Unit 2, Addition and Subtraction Story Problems, Lesson 1, Cool-down, Section A Checkpoint, students represent and solve Add To and Take From, Result Unknown story problems using a strategy that makes sense to them. They also write an expression to represent the action in a story problem. Teachers observe in order to capture evidence of student thinking using the checkpoint checklist. Student Response states, “Retell the story. Represent a story problem with objects or drawings. Explain how a representation matches the story.” Preparation, Lesson Narrative states, “When students connect expressions back to the story problem and explain the connection, they model with mathematics (MP4).”
Unit 4, Numbers to 99,Section D, Lesson 23, Activity 1, Student Work Time, Launch, and Instructional Routine, students apply their place value understanding to estimate quantities of objects and accurately count familiar objects. Student Facing states, “Experiment 1: How many objects are in 2 handfuls? a. Record an estimate that is: too low, about right, too high. b. Now find the exact number ___. Experiment 2: How many objects are in 2 handfuls? a. Record an estimate that is: too low, about right, too high. b. Now find the exact number ___. Experiment 3: How many objects are in 2 handfuls? a. Record an estimate that is: too low, about right, too high. b. Now find the exact number ___.” Launch states, “Groups of 2, Display for all to see approximately 15–25 beans or other small objects. ‘How many objects do you think are in this pile?’ 1 minute: partner discussion. Share responses. ‘How could we find out exactly?’ (Count them.).” Student Work Time states, “‘How many objects are in 2 handfuls? Let's do an experiment.’ Give each group a bag of objects. ‘Take turns and grab a handful. Estimate how many objects you both grabbed altogether. Then find out how many you have exactly. You will do this experiment three times.’ 5 minutes: partner work time. Monitor for students who: count by ones group the objects into groups of 10 and then count the tens and ones.” Preparation, Lesson Narrative states, “When students recognize the mathematical features of familiar real world objects and solve problems, they model with mathematics (MP4).”
Unit 8, Putting It All Together, Section B, Lesson 6, Activity 2, Student Work Time and Instructional Routine, students use given information to ask and answer different questions. In Student Work Time, Student Facing states, “Write and answer 2 questions using the information. Use the picture for the first one if it is helpful. a. Diego went on 7 rides. Priya went on 11 rides. b. Jada went on 3 rides. Kiran went on 6 rides. Noah went on 9 rides.” Instructional Routine states, “When students recognize the mathematical features of things in the real world and ask questions that arise from a presented situation, they model with mathematics (MP4).”
MP5 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities to identify and use a variety of tools or strategies, working with the support of the teacher and independently, throughout the units to support their understanding of grade-level math. Examples include:
Unit 4, Numbers to 99, Section A, Lesson 1, Activity 2, Launch, Student Work Time, and Instructional Routine, students organize and count a collection of 40 objects. Launch states, “Groups of 2. Give each group a bag of objects. Give students access to double 10-frames, cups, paper plates, or other tools to help organize a count. ‘Now you will work with your partner to count more collections. Each partner will show on paper how many there are and show how you counted.’” Student Work Time states, “5 minutes: partner work time. ‘Switch bags with another group. Work with your partner to count the collection. Each partner will show on paper how many there are and show how you counted them.’ 5 minutes: partner work time. As students work, consider asking: ‘How can you use what we learned in the last Student Work Time to help you organize your count? Tell me about what you have written here. How many does it show? Does your representation match how you counted?’ Monitor for students who organize objects into groups of ten using cups, paper plates, or other tools, groups using double 10-frames.” Instructional Routine states, “The purpose of this activity is for students to practice counting and representing collections with multiples of 10 objects. Students count one bag with their partner. When students have finished counting and recording, they trade bags with a different group and count a new collection. During the launch, teachers may choose to provide time for students to reflect on how they worked together in the previous activity. During the synthesis, students discuss using a tool that organizes the objects in groups of ten, and how that is helpful when counting a collection.”
Unit 5, Adding Within 100, Lesson 6, Activity 2, Launch, Student Work Time and Lesson Narrative, students add one-digit and two-digit numbers and deepen their understanding of place value. Student Facing, “Elena and Andre found the value of . a. Elena started with . What does Elena need to do next? Show your thinking using drawings, numbers, or words. b. Andre started with . What does Andre need to do next? Show your thinking with drawings, numbers, or words. c. Find the value of . Show your thinking using drawings, numbers, or words. Launch, “Give students access to connecting cubes in towers of 10 and singles. Display . “Elena and Andre found the value of . Elena showed her first step by writing . What do you notice about her first step?” (She only added 6. Maybe she wanted to make the next ten. She wanted to make a ten with .) 30 seconds: quiet think time. 1 minute: partner discussion. “What does she need to do to finish her work?” (She needs to add 9 in all. She added 6, now she needs to add 3 more to 40.) 2 minutes: independent work time. 1 minute: partner discussion. Record student thinking as equations . “Where do you see 9 in this equation?” . Student Work Time, “Display and read Andre’s first step. “Now decide what Andre needs to do next. Then find the value of using any method that makes sense to you. Show your thinking with drawings, numbers or words.” 4 minutes: independent work time. 3 minutes: partner work time. Monitor for students who represent composing a ten in different ways, including with connecting cubes and with different equations.” Lesson Narrative, “Completing the start of a calculation as students do here requires critically analyzing, understanding, and expressing different strategies (MP3). Students then have an opportunity to add using one of these methods and the representations that make sense to them. Monitor for students who show composing a new unit of ten using connecting cubes or base-ten diagrams. Students use appropriate tools strategically as they choose which tools help them add (MP5).”
Unit 6, Length Measurements within 120, Section B, Lesson 8, Activity 1, Launch, Student Work Time, students measure a length that is over 100 length units long and count the number of units using grouping methods. Launch states, “Groups of 3–4. Give each group 120 base-ten cubes, string, and scissors. ‘Today we are going to measure the height of one of your group members. Choose whose height you will measure and cut a piece of string that is the same length as their height.’ 2 minutes: small-group work.” Student Work Time states, “‘Measure the length of the string using small cubes. Represent the measurement using drawings, numbers, or words.’ 15 minutes: partner work time. Monitor for groups who: have measurements between 100–110 cubes, created groups of ten to organize the cubes.” In Student Work Time, Student Facing states, “Represent your measurement using drawings, numbers, or words.” In Preparation, Lesson Narrative states, “The purpose of this lesson is for students to count a quantity between 100 and 110. In the first Student Work Time, students measure how tall they are using base-ten cubes and represent their work in a way that makes sense to them (MP5).”
Indicator 2H
Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Narratives and Lesson Activities’ Narratives).
Students have many opportunities to attend to precision and the specialized language of math, in connection to grade-level content, as they work with support of the teacher and independently throughout the units. Examples include:
Unit 1, Adding, Subtracting and Working with Data, Section B, Lesson 7, Warm-up, Launch, and Activity Synthesis, students describe attributes of mathematical objects. Activity Narrative states, “The activity provides an opportunity for students to describe mathematical objects in different ways, including non-mathematical characteristics such as color as well as mathematical characteristics such as the number of corners and the category or properties of the shapes. (MP6). If possible, display the objects themselves rather than the image or provide students with a set of the objects. Some students may not know the names of the shapes. Prompt them to use the language that makes sense to them.” Launch states, “Groups of 2. Display the image. ‘What do you notice? What do you wonder?’ 1 minute: quiet think time.” Activity Synthesis states, “How are the shapes alike? How are they different?”
Unit 4, Numbers to 99, Section B, Lesson 10, Cool-down, students attend to precision as they write numbers using their knowledge of base-ten representations. Student Facing states, “Write the number that matches each representation. a. , b. an image of 63 base ten blocks, c. 7 ones + 9 tens.” Activity Narrative (for Activity 1) states, “Students must attend to the units in each representation and the meaning of the digits in a two-digit number, rather than always writing the number they see on the left in a representation in the tens place and the number they see on the right in a representation in the ones place (MP6).”
Unit 4, Numbers to 99, Section C, Lesson 14, Activity 1, Student Work Time, Launch, and Activity Synthesis, students use precise mathematical language as they determine which number is greater and represent their number in any way they choose. In Student Work Time, Student Facing states, “Each partner spins a spinner. Each partner shows the number any way they choose. Compare with your partner. Which number is more?” Launch states, “Groups of 2, Give each group two paper clips and access to connecting cubes in towers of 10 and singles. Display 35 and 52. ‘Which number is more? Show your thinking using math tools. Be ready to explain your thinking to your partner.’ 2 minutes: independent work time. 2 minutes: partner discussion. ‘Which is more and how do you know?’ (53 is more because it has more tens than 35.).” Student Work Time states, “Read the task statement. ‘Each partner can choose to use Spinner A or B for each turn.’ 10 minutes: partner work time.” Activity Narrative states, “Listen for the way students use place value understanding to compare the numbers and the language they use to explain how they know one number is more than the other (MP3, MP6). In the synthesis, students are introduced to the terms greater than and less than.” Activity Synthesis states, “‘Are there any other words or phrases that are important to include on our display?’ As students share responses, update the display by adding (or replacing) language, diagrams, or annotations. Remind students to borrow language from the display as needed. Display 93 and 26. ‘Which is more? How do you know? (93 is more because 9 tens is more than 2 tens.) We can say, ‘93 is greater than 26.’ We can also say, ‘26 is less than 93.’” Display 62 and 64. ‘Which number is more? How do you know? (64 is more. They both have 6 tens but 64 has 4 ones and that is more than the 2 ones in 62.) We can say that 64 is greater than 62. We can also say 62 is less than 64.’”
Unit 5, Adding Within 100, Section A, Lesson 3, Cool-down, students use precision as they explain how to add expressions. Student Facing states, “Find the value of . Show your thinking using drawings, numbers, or words. Write equations to show how you found the value.” Preparation, Lesson Narrative states, “In this lesson, students add two-digit numbers using methods of their choice and write equations to match their thinking. Students interpret and compare different methods for finding the value of the same sums. Students also practice explaining their own methods and listening to the methods of their peers. Students have opportunities to revise how they explain their own and others' methods and consider how representations of their own thinking (for example, drawings or equations) can help them explain or interpret their work (MP3, MP6).”
Unit 6, Length Measurements Within 120 Units, Section A, Lesson 3, Activity 2, Student Work Time and Launch, students attend to precision when they compare the length of two objects using a third object. In Student Work Time, Student Facing states, “a. Will the teacher’s desk fit through the door? Show your thinking using drawings, numbers, or words. b. Will a student desk fit through the door? Show your thinking using drawings, numbers, or words. c. Which is longer, the bookshelf or the rug? Show your thinking using drawings, numbers, or words. d. Which is longer, the file cabinet or the bookshelf? Show your thinking using drawings, numbers, or words. e. Which is shorter, the bookshelf or the teacher’s desk? Show your thinking using drawings, numbers, or words. f. Will the teacher’s desk fit next to the bookshelf? Show your thinking using drawings, numbers, or words.” Launch states, “Groups of 2. Give students access to measuring materials. ‘Have you ever seen someone move a large piece of furniture, like a couch, from one room to another? Is it easy to move big pieces of furniture? Why or why not?’ 30 seconds: quiet think time. Share responses. ‘I have been thinking about getting a new desk. If I do, I will have to move this desk out of the room. I am not sure if this desk will fit through the door. How can we check to see if it will fit?’ (We could measure with a string.). 30 seconds: quiet think time. 1 minute: partner discussion. Share responses. ‘You are all going to check to see if my desk will fit through the door. You are also going to compare the length of some other objects in the room.” Student Work Time states, “15 minutes: partner work time. Monitor for a group that measures the width of the teacher's desk and one that measures the length.” Activity Narrative states, “When students decide if the teacher's desk will fit through the door or compare other large pieces of furniture, they will need to be precise about which lengths they are measuring as objects like the teacher's desk, a rug, and a bookcase, have a length, width, and in some cases a height (MP6).”
Unit 7, Geometry and Time, Section A, Lesson 3, Launch, and Activity Synthesis, students use specialized language as they compare attributes of shapes. Activity Narrative states, “This Warm-up prompts students to compare four shapes. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of two- and three-dimensional shapes.” Launch states, “Groups of 2. Display the image ‘Pick one that doesn’t belong. Be ready to share why it doesn’t belong.’ 1 minute: quiet work time” Activity Synthesis states, “Let’s find at least one reason why each one doesn’t belong. What solid shapes do the images for A, B, and C show? (cube, cone, and cylinder) Does D show a solid shape? Why or why not? (Maybe it is supposed to be a sphere. It looks like it is just a circle.) A circle is not one of our solid shapes. We call it a flat shape.”
Indicator 2I
Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources K–5 Math Grade 1 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Narratives and Lesson Activities’ Narratives).
MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently throughout the units. Examples include:
Unit 2, Addition and Subtraction Story Problems, Section D, Lesson 18, Activity 1, Student Work Time and Activity Synthesis, students look for and make use of structure as they interpret equations with a symbol for the unknown and connect them to story problems. Student Work Time states, “‘You have two sets of cards. One set of cards has the story problems we used in the last lesson. The other set of cards has equations with unknown values. Work with your partner to match the story problems to the equations. One story has more than one equation. Be sure you can explain how you know they match.’ 10 minutes: partner work time.” Activity Synthesis states, “‘Which equation matches Card C? How do you know?’ (__. 9 represents how many students were sliding. 6 represents how many students leave so that is . The box represents how many are left, which is the answer to the problem.) Repeat for problems F and H. Display equation cards 6 and 8. ‘What do you notice about these equations? (They both have a total of 9 and one part is 4. The other part is the unknown. They both match problem G.). How does each of these equations match the story problem?’ (There are 9 students jumping Double Dutch and 4 students jumping on their own. I need to find the difference, so I can subtract to find the answer or I can say that ___. 9 equals 4 plus some more students.).” Activity Narrative states, “The purpose of this activity is for students to match story problems to equations with a symbol for the unknown (MP2). Each equation is written to match the way the numbers are presented in the story problem. Problem G has more than one equation, which prompts students to discuss the relationship between addition and subtraction (MP7). During the synthesis, students discuss how an equation with a symbol for the unknown matches a Take From, Result Unknown story problem.”
Unit 5, Adding Within 100, Section A, Lesson 1, Warm-up, Student Work Time and Activity Synthesis, students look for and make use of structure as they subitize or use grouping strategies to describe the images they see. In Student Work Time, Student Facing states, “How many do you see? How do you see them?” Activity Synthesis states, “How did we describe the second image using tens and ones? How many tens do you see? How many ones? (Some people said they saw it as 3 tens and 5 ones.) How could we describe the last image using tens and ones? (3 tens and 9 ones) How could we write equations to go with the last image? ( or ).”Preparation, Lesson Narrative states, “When students look for ways to see and describe numbers as groups of tens and ones and connect this to two-digit numbers, they look for and make use of the base-ten structure (MP7).”
Unit 7, Geometry and Time, Lesson 14, Cool-down, students look for and make use of structure as they learn about the position of the hands on an analog clock at half past the hour. Student Facing states, “Circle the clock that shows 2:30.” Activity 2 Narrative states, “The purpose of this activity is for students to connect their understanding of half of a circle to the minute hand moving halfway around the face of a clock (MP7).”
MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities to use repeated reasoning in order to make generalizations and build a deeper understanding of grade-level math concepts as they work with support of the teacher and independently throughout the units. Examples include:
Unit 3, Adding and Subtracting Within 20, Section C, Lesson 17, Cool-down, students use repeated reasoning to add within 20. Students see that they can decompose one addend in order to make a ten. Student Facing states, “8 birds are sitting in a tree. 6 birds are sitting on the grass. How many birds are there all together? Show your thinking using drawings, numbers, or words. Equation: ___.” Lesson Narrative states, “When students identify and use equivalent expressions, they look for and make use of structure (MP7) and here they repeatedly make a 10 to find the value of expressions (MP8).”
Unit 4, Numbers to 99, Lesson 7, Section A, Activity 1, Student Work Time and Activity Synthesis, students use repeated reasoning to extend their understanding of teen numbers as a ten and some ones to an understanding of all two-digit numbers as some tens and some ones. In Student Work Time, Student Facing states, “Partner 1 draws 2 number cards and uses them to make a two-digit number. Each partner says the number. Partner 2 builds the number using cubes. Partner 1 checks to see if they agree. Each partner makes a drawing of the number and records how many tens and ones. Switch roles and repeat.” Student Work Time states, “10 minutes: partner work time. As students work, consider asking: ‘How do you say this two-digit number? What is your plan for building the number? How many tens does this number have? How many ones does this number have?’” Activity Synthesis states, “Display the number 24 and a base-ten drawing of 4 tens and 2 ones. ‘Tyler made a drawing of 24. Do you agree with how he showed 24? Why or why not? (No, because he drew 4 tens and 2 ones instead of 2 tens and 4 ones. He made the number 42 instead of 24.). Tyler’s drawing shows 42, not 24. They both have the digits 2 and 4, but they are in different places, which makes them different numbers.’” Activity Narrative states, “Students choose two number cards and create a two-digit number. As they build the two-digit numbers with towers of 10 and singles, students see that each two-digit number is composed of a number of tens and a number of ones (MP8).”
Unit 6, Length Measurements Within 120 Units, Section A, Lesson 4, Warm-up, Student Work Time and Activity Synthesis, students use repeated reasoning to make ten to find sums within 50. In Student Work Time, Student Facing states, “Find the value of each expression mentally. , , , .” Activity Narrative states, “When students notice how they can make a ten when finding the value of each expression or when they use one sum to find the value of the next sum, they look for and make use of structure and express regularity in repeated reasoning (MP7, MP8).” Activity Synthesis states, “Did anyone have the same method but would explain it differently? Did anyone approach the problem in a different way?”
Overview of Gateway 3
Usability
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports; partially meet expectations for Criterion 2, Assessment; and meet expectations for Criterion 3, Student Supports.
Gateway 3
v1.5
Criterion 3.1: Teacher Supports
The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.
Indicator 3A
Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for providing teachers guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
Within the Course Guide, several sections (Design Principles, A Typical Lesson, How to Use the Materials, and Key Structures in This Course) provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include but are not limited to:
Resources, Course Guide, Design Principles, Learning Mathematics by Doing Mathematics, “A problem-based instructional framework supports teachers in structuring lessons so students are the ones doing the problem solving to learn the mathematics. The activities and routines are designed to give teachers opportunities to see what students already know and what they can notice and figure out before having concepts and procedures explained to them. The teacher has many roles in this framework: listener, facilitator, questioner, synthesizer, and more.”
Resources, Course Guide, A Typical Lesson, “A typical lesson has four phases: 1. a warm-up; 2. one or more instructional activities; 3. the lesson synthesis; 4. a cool-down.” “A warm-up either: helps students get ready for the day’s lesson, or gives students an opportunity to strengthen their number sense or procedural fluency.” An instructional activity can serve one or many purposes: provide experience with new content or an opportunity to apply mathematics; introduce a new concept and associated language or a new representation; identify and resolve common mistakes; etc. The lesson synthesis “assists the teacher with ways to help students incorporate new insights gained during the activities into their big-picture understanding.” Cool-downs serve “as a brief formative assessment to determine whether students understood the lesson.”
Resources, Course Guide, How to Use the Materials, “The story of each grade is told in eight or nine units. Each unit has a narrative that describes the mathematical work that will unfold in that unit. Each lesson in the unit also has a narrative. Lesson narratives explain: the mathematical content of the lesson and its place in the learning sequence; the meaning of any new terms introduced in the lesson; how the mathematical practices come into play, as appropriate. Activities within lessons also have narratives, which explain: the mathematical purpose of the activity and its place in the learning sequence, what students are doing during the activity, what the teacher needs to look for while students are working on an activity to orchestrate an effective synthesis, connections to the mathematical practices, when appropriate.”
Resources, Course Guide, Scope and Sequence lists each of the eight units, a Pacing Guide to plan instruction, and Dependency Diagrams. These Dependency Diagrams show the interconnectedness between lessons and units within Grade 1 and across all grades.
Resources, Course Guide, Course Glossary provides a visual glossary for teachers that includes both definitions and illustrations. Some images use examples and nonexamples, and all have citations referencing what unit and lesson the definition is from.
Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Several components focus specifically on the content of the lesson. Examples include:
Unit 3, Adding and Subtracting Within 20, Overview, describes how subtraction correlates with addition. “Subtraction work occurs throughout the unit and becomes the focus in the last section. Students consider taking away and counting on as methods for subtracting. They understand subtraction as an unknown-addend problem and use their knowledge of addition to find the difference of two numbers.”
Unit 4, Numbers to 99, Section C, Lesson 14, Activity 1, Launch, provides prompts for the teacher to start the lesson. “Groups of 2: Give each group two paper clips and access to connecting cubes in towers of 10 and singles. Display 35 and 52. “Which number is more? Show your thinking using math tools. Be ready to explain your thinking to your partner.” 2 minutes: independent work time 2 minutes: partner discussion “Which is more and how do you know?” (53 is more because it has more tens than 35.)”
Unit 8, Putting It All Together, Lesson 6, Activity 1, "The purpose of this activity is for students to practice solving Compare, Difference Unknown story problems (MP2). In the synthesis, students revisit a representation of a Compare problem that was introduced in a previous unit. This representation lays the foundation for working with tape diagrams in grade 2.The teacher may want to incorporate movement into this activity by writing each problem on a piece of chart paper and placing each one in a different location around the classroom. Students can solve the problem at one location, discuss the problem with their partner, then move on to a new problem at a new location."
Indicator 3B
Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject.
Unit Overviews and sections within lessons include adult-level explanations and examples of the more complex grade-level concepts. Within the Course Guide, How to Use the Materials states, “Activities within lessons also have narratives, which explain: the mathematical purpose of the activity and its place in the learning sequence, what students are doing during the activity, what the teacher needs to look for while students are working on an activity to orchestrate an effective synthesis, connections to the mathematical practices, when appropriate.” Examples include:
Unit 1, Adding, Subtracting, and Working With Data, Section B, Lesson 7, Activity 1, “The purpose of this activity is for students to sort math tools, name the groups they used to sort, and tell the number of objects in each group. Students identify attributes of the objects and sort them into two or more groups. Students may choose to use one of the blackline masters to organize as they sort. When students share how they sorted with their partner, they use their own mathematical vocabulary and listen to and understand their partner’s thinking (MP3, MP6). Students may describe the objects’ attributes by referring to shape names, number of sides, color, or other attributes. Encourage students to tell how many tools are in each category. During the synthesis, students are introduced to the term category. They discuss different categories that were used to sort the math tools.”
Unit 5, Adding Within 100, Section B, Lesson 6, Activity 2, “The purpose of this activity is for students to add one-digit and two-digit numbers with composing a ten and deepen their understanding of place value. In this activity, students make sense of two different addition methods where an addend is decomposed to make a ten. Students then determine the next step needed to find the value of the original sum. Invite students to use different representations to make sense of these methods including connecting cubes and base-ten drawings. Completing the start of a calculation as students do here requires critically analyzing, understanding, and expressing different strategies (MP3).”
Unit 6, Length Measurements Within 120 Units, Section A, Lesson 1, Lesson Narrative, “In kindergarten, students compared the length of two objects directly by lining up the endpoints. They described the objects using language such as longer and shorter. In this unit the words “longer than” and “shorter than” are encouraged, although students may use “taller than” in certain contexts related to height. In this lesson, students compare the length of objects and consider how they know which is longer or shorter. Then, they order three objects by length.”
Also within the Course Guide, About These Materials, Further Reading states, “The curriculum team at Open Up Resources has curated some articles that contain adult-level explanations and examples of where concepts lead beyond the indicated grade level. These are recommendations that can be used as resources for study to renew and fortify the knowledge of elementary mathematics teachers and other educators.” Examples include:
Resources, Course Guide, About These Materials, Further Reading, K-2, “Units, a Unifying Idea in Measurement, Fractions, and Base Ten. In this blog post, Zimba illustrates how units ‘make the uncountable countable’ and discusses how the foundation built in K-2 measurement and geometry around structuring space allows for the development of fractional units and beyond to irrational units.”
Resources, Course Guide, About These Materials, Further Reading, Entire Series, “The Number Line: Unifying the Evolving Definition of Number in K-12 Mathematics. In this article, the authors (Lahme, McLeman, Nakamaye, and Umland) focus their attention on the selection of definitions, notation, and graphical conventions surrounding the development of the real numbers from kindergarten to grade 12, and address the work that students might do in later years.”
Indicator 3C
Materials include standards correlation information that explains the role of the standards in the context of the overall series.
The materials reviewed for Open Up Resources K-5 Mathematics Grade 1 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.
Correlation information can be found within different sections of the Course Guide and within the Standards section of each lesson. Examples include:
Resources, Course Guide, About These Materials, CCSS Progressions Documents, “The Progressions for the Common Core State Standards describe the progression of a topic across grade levels, note key connections among standards, and discuss challenging mathematical concepts. This table provides a mapping of the particular progressions documents that align with each unit in the K–5 materials for further reading.”
Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress in the Mathematical Practices, The Standards for Mathematical Practices Chart, “The unit-level Mathematical Practice chart is meant to highlight a handful of lessons in each unit that showcase certain Mathematical Practices. Some units, due to their size or the nature of their content, may have fewer predicted chances for students to engage in a particular Mathematical Practice. A dash in the chart indicates that there may not be enough opportunities to reliably look for this Mathematical Practice in the unit. One primary place Mathematical Practice 4 is tagged is the optional modeling lesson at the end of each unit. Aside from these lessons, optional activities and lessons are not included in this chart.”
Resources, Course Guide, Scope and Sequence, Dependency Diagrams, All Grades Unit Dependency Diagram identifies connections between the units in grades K-5. Additionally, a “Section Dependency Diagram” identifies specific connections within the grade level.
Resources, Course Guide, Lesson and Standards, provides two tables: a Standards by Lesson table, and a Lessons by Standard table. Teachers can utilize these tables to identify standard/lesson alignment.
Unit 1, Adding, Subtracting, and Working With Data, Section B, Lesson 8, Standards, “Building On: K.CC.B.4, Addressing: 1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Building Towards: 1.MD.C.4.”
Explanations of the role of specific grade-level mathematics can be found within different sections of the Resources, Course Guide, Unit Overviews, Section Overviews, and Lesson Narratives. Examples include:
Resources, Course Guide, Scope and Sequence, each Unit provides Unit Learning Goals, for example, “Students add and subtract within 10, and represent and interpret categorical data.” Additionally, each Unit Section provides Section Learning Goals, “organize and represent data.”
Unit 2, Addition and Subtraction Story Problems, Overview, “In kindergarten, students solved a limited number of types of story problems within 10 (Add To/Take From, Result Unknown, and Put Together/Take Apart, Total Unknown, and Both Addends Unknown). They represented their thinking using objects, fingers, mental images, and drawings. Students saw equations and may have used them to represent their thinking, but were not required to do so. Here, students encounter most of the problem types introduced in grade 1: Add to/Take From, Change Unknown, Put Together/Take Apart, Unknowns in All Positions, and Compare, Difference Unknown. The numbers are kept within 10 so students can focus on interpreting each problem and the relationship between counting and addition and subtraction. This also allows students to continue developing fluency with addition and subtraction within 10.”
Unit 4, Numbers to 99, Section D, Section D Overview, "In this section, students deepen their understanding of the base-ten structure by representing two-digit numbers with different amounts of tens and ones. They also extend their comparison work by comparing numbers expressed in different ways."
Unit 6, Length Measurements Within 120 Units, Section C, Lesson 14, Lesson Narrative, "In previous lessons, students solved Take From, Start Unknown, Compare, Bigger Unknown, and Compare, Smaller Unknown problems. They showed their thinking using drawings, numbers, or words. Throughout the year, students solved all types of story problems with unknowns in all positions. In this lesson, students learn that they can use equations to make sense of story problems in different ways."
Indicator 3D
Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The materials reviewed for Open Up Resources K-5 Math Grade 1 provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The materials include a Family Letter, found under Resources, that provides an introduction to the math curriculum, available in English and Spanish. Each unit has corresponding Family Support Materials, in English and Spanish, that provide a variety of supports for families. These supports are found on the main website: https://access.openupresources.org/curricula/our-k5-math/index.html, and are accessible through the Family and Student Roles. Examples include:
Resources, Family Letter, provides information about: “What is a problem-based curriculum?; What supports are in the materials to help my student succeed?; and What can my student do to be successful in this course?”
Family Role, Unit 1, Adding, Subtracting, and Working With Data, Family Materials, “After bringing in groceries, ask your student to sort items into categories, describe the categories, and make a representation using drawings, tally marks, or numbers. Questions that may be helpful as they work: How did you decide to sort? What questions can you answer based on your data display?” Parents can use suggestions to support student progress.
Student Resource, Unit 2, Addition and Subtraction Story Problems, Section A, Practice Problems, Section Summary, “We solved story problems and represented them with objects, drawings, words, and equations.” This section includes example story problems with associated drawings to help the student remember strategies introduced in the lessons.
Family Role, Unit 7, Geometry and Time, Family Materials, “Play “I spy” with your child to help your student identify shapes in the real-world. Say: I spy a solid shape that rolls. What could my shape be? I spy a cylinder (cube, cone, sphere). What object is a cylinder?”
Indicator 3E
Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.
The materials explain and provide examples of instructional approaches of the program and include and reference research-based strategies. Both the instructional approaches and the research-based strategies are included in the Course Guide under the Resources tab for each unit. Design Principles describe that, “It is our intent to create a problem-based curriculum that fosters the development of mathematics learning communities in classrooms, gives students access to mathematics through a coherent progression, and provides teachers the opportunity to deepen their knowledge of mathematics, student thinking, and their own teaching practice.” Examples include:
Resources, Course Guide, Design Principles, “In order to design curriculum and professional learning materials that support student and teacher learning, we need to be explicit about the principles that guide our understanding of mathematics teaching and learning. This document outlines how the components of the curriculum are designed to support teaching and learning aligning with this belief.” Principles that guide mathematics teaching and learning include: All Students are Capable Learners of Mathematics, Learning Mathematics by Doing Mathematics, Coherent Progression, Balancing Rigor, Community Building, Instructional Routines, Using the 5 Practices for Orchestrating Productive Discussions, Task Complexity, Purposeful Representations, Teacher Learning Through Curriculum Materials, and Model with Mathematics K-5.
Resources, Course Guide, Design Principles, Community Building, “Students learn math by doing math both individually and collectively. Community is central to learning and identity development (Vygotsky, 1978) within this collective learning. To support students in developing a productive disposition about mathematics and to help them engage in the mathematical practices, it is important for teachers to start off the school year establishing norms and building a mathematical community. In a mathematical community, all students have the opportunity to express their mathematical ideas and discuss them with others, which encourages collective learning. ‘In culturally responsive pedagogy, the classroom is a critical container for empowering marginalized students. It serves as a space that reflects the values of trust, partnership, and academic mindset that are at its core’ (Hammond, 2015).”
Resources, Course Guide, Design Principles, Instructional Routines, “Instructional routines provide opportunities for all students to engage and contribute to mathematical conversations. Instructional routines are invitational, promote discourse, and are predictable in nature. They are ‘enacted in classrooms to structure the relationship between the teacher and the students around content in ways that consistently maintain high expectations of student learning while adapting to the contingencies of particular instructional interactions.’ (Kazemi, Franke, & Lampert, 2009)”
Resources, Course Guide, Key Structures in This Course, Student Journal Prompts, Paragraph 3, “Writing can be a useful catalyst in learning mathematics because it not only supplies students with an opportunity to describe their feelings, thinking, and ideas clearly, but it also serves as a means of communicating with other people (Baxter, Woodward, Olson & Robyns, 2002; Liedke & Sales, 2001; NCTM, 2000).”
Indicator 3F
Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for including a comprehensive list of supplies needed to support the instructional activities.
In the Course Guide, Materials, there is a list of materials needed for each unit and each lesson. Lessons that do not have materials are indicated by none; lessons that need materials have a list of all the materials needed. Examples include:
Resources, Course Guide, Key Structures in This Course, Representations in the Curriculum, provides images and explanations of representations for the grade level. “5-frame and 10-frame (K-2): 5- and 10-frames provide students with a way of seeing the numbers 5 and 10 as units and also combinations that make these units. Because we use a base-ten number system, it is critical for students to have a robust mental representation of the numbers 5 and 10. Students learn that when the frame is full of ten individual counters, we have what we call a ten, and when we cannot fill another full ten, the ‘extra’ counters are ones, supporting a foundational understanding of the base-ten number system. The use of multiple 10-frames supports students in extending the base-ten number system to larger numbers.”
Resources, Course Guide, Materials, includes a comprehensive list of materials needed for each unit and lesson. The list includes both materials to gather and hyperlinks to documents to copy. “Unit 1, Lesson 13 - Gather: Connecting cubes, Materials from a previous activity; Copy: Favorite Special Class Data.”
Unit 8, Putting it All Together, Section B, Lesson 5, Materials Needed, “Activities: Connecting cubes in towers of 10 and singles (Activity 1).”
Indicator 3G
This is not an assessed indicator in Mathematics.
Indicator 3H
This is not an assessed indicator in Mathematics.
Criterion 3.2: Assessment
The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.
The materials reviewed for Open Up Resources K-5 Math Grade 1 partially meet expectations for Assessment. The materials identify the content standards and mathematical practices assessed in formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance, but do not provide suggestions for following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.
Indicator 3I
Assessment information is included in the materials to indicate which standards are assessed.
The materials reviewed for Open Up Resources Math Grade 1 meet expectations for having assessment information in the materials to indicate which standards are assessed.
The materials consistently and accurately identify grade-level content standards for formal assessments for the Section Checkpoints and End-of-Unit Assessments within each assessment answer key. Examples from formal assessments include:
Resources, Course Guide, Summative Assessments, End-of-Unit Assessments, “All summative assessment problems include a complete solution and standard alignment. Multiple choice and multiple response problems often include a reason for each potential error a student might make.”
Unit 2, Addition and Subtraction Story Problems, Section A, Lesson 2, Cool-down, “Assessing 1.OA.A.1, Mai put 5 books on the shelf. Then Noah put 4 books on the shelf. How many books are on the shelf now? Show your thinking using drawings, numbers or words."
Unit 4, Numbers to 99, Assessments, Section D Checkpoint, “For this Checkpoint Assessment, the content assessed is listed below for reference. Represent two-digit numbers in different ways, using different amounts of tens and ones (for example ). Represent a number with tens and ones in more than one way. Recognize when the same number is represented with different amounts of tens and ones. Compare two-digit numbers represented in different ways.” (1.NBT.3)
Unit 7, Geometry and Time, Assessments, End-Of-Unit Assessment, Problem 4, “1.G.A.3: Students identify whether or not the same amount of a square is shaded. They are given two images of the same size square with half of one square shaded and a quarter of the other square shaded. Students should note that the size of the pieces is smaller when the (same) whole is divided into more pieces.”
Guidance for assessing progress of the Mathematical Practices can be found within the Resources, Course Guide, How to Use These Materials, Noticing and Assessing Student Progress in Mathematical Practices, How to Use the Mathematical Practices Chart, “Because using the mathematical practices is part of a process for engaging with mathematical content, we suggest assessing the Mathematical Practices formatively. For example, if you notice that most students do not use appropriate tools strategically (MP5), plan in future lessons to select and highlight work from students who have chosen different tools.” In addition, “...a list of learning targets for each Mathematical Practice is provided to support teachers and students in recognizing when engagement with a particular Mathematical Practice is happening…the ‘I can’ statements are examples of types of actions students could do if they are engaging with a particular Mathematical Practice.” Examples include:
Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade 1, MP3 is found in Unit 6, Lessons 1 and 5.
Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade 1, MP6 is found in Unit 6, Lessons 1-3, 6, and 7.
Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practice Student Facing Learning Targets, “MP2: I can Reason Abstractly and Quantitatively. I can think about and show numbers in many ways. I can identify the things that can be counted in a problem. I can think about what the numbers in a problem mean and how to use them to solve the problem. I can make connections between real-world situations and objects, diagrams, numbers, expressions, or equations.”
Indicator 3J
Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The materials reviewed for Open Up Resources K-5 Math Grade 1 partially meet the expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The assessment system provides multiple opportunities to determine students' learning. Each summative, End-of-Unit or End-of-Course Assessment, provides an explanation about the assessment item, potential student misconceptions, answer key, and standard alignment. According to the Resources, Course Guide, Summative Assessments, “All summative assessment problems include a complete solution and standard alignment. Multiple choice and multiple response problems often include a reason for each potential error a student might make.” Suggestions to teachers for following up with students are general, as teachers are encouraged to return to previously taught lessons. While teachers can refer back to specific lessons, it is incumbent on the teacher to determine which additional practice meets the needs of individual students. Examples include:
Unit 1, Adding, Subtracting, and Working with Data, Assessments, End-of-Unit Assessment, Problem 4, “1.MD.C.4: Students use an image of pattern blocks to complete a table to represent how the blocks could be sorted. The shapes are organized in groups and laid out in lines on the page to facilitate counting. Students also find the total number of pattern blocks. They can do this by counting the shapes or they can use the information from the table they created. Students could choose categories other than triangle, rhombus, and square but these are the most likely choices. For example, they could choose shapes with three sides, shapes with four sides, and shapes with more than four sides and then they would have one category with no shapes.”
Unit 6, Length Measurements Within 120 Units, Assessments, End-of-Unit Assessment, Problem 4, “1.NBT.A.1. Students identify the number of objects in a collection between 100 and 120, grouped as 10 tens and some ones. If students miscount the towers of ten they may write 98 or 118, for example, and this does not necessarily show a conceptual misunderstanding.”
Unit 7, Geometry and Time, Assessments, End-of-Unit Assessment, Problem 5, “1.MD.B.3: Students read time from clocks. Students may select the distractor A because it has the digit 5. The distractor D has the hour and minute hands reversed so students may select this inadvertently or may not understand that the minute hand is longer than the hour hand on clocks.” The solution to the problem is provided. Additional Support, “If a student struggles to read time from clocks, provide additional instruction either in a small group or individually using OUR Math Grade 1 Unit 7 Lesson 15 and/or Lesson 16.”
Formative assessments include Section Checkpoints, Lesson Cool-downs, and Practice Problems. While these assessments provide multiple opportunities to determine students’ learning and sufficient guidance to teachers for interpreting student performance, there are minimal suggestions to teachers for following-up with students. Examples of formative assessments include:
Unit 2, Addition and Subtraction Story Problems, Assessments, Section B Checkpoint, Teaching Instructions, “For this Checkpoint Assessment, the content assessed is listed below for reference.” There is a Sample Observation Checklist created for teachers to reference when scoring the problem. The checklist includes a section for student names, and then checkboxes for “retell the story, represent the story with objects or drawings, explain how their representation matches the story, answer the question correctly, represent the story with equations.”
Unit 3, Adding and Subtracting Within 20, Section C Checkpoint, Additional Support, "If a student struggles to add within 20, including 3 addends, provide additional instruction either in a small group or individually using OUR Math Grade 1 Unit 3 Lesson 16. (1.OA.C.6)"
Indicator 3K
Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
The materials reviewed for Open Up Resources K-5 Math Kindergarten meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
Formative assessments include instructional activities, Practice Problems and Section Checkpoints in each section of each unit. Summative assessments include End-of-Unit Assessments and End-of-Course Assessments. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types including multiple choice, multiple response, short answer, restricted constructed response, and extended response. Examples include:
Unit 2, Addition and Subtraction Story Problems, Assessments, End-of-Unit Assessment, Problem 2, 1.OA.1, 1.OA.6, “After recess, Tyler collected 6 footballs. Then he collected some baseballs. Altogether, Tyler collected 10 balls. How many baseballs did Tyler collect? Show your thinking with drawings, numbers, or words. Write an equation to match the story problem.”
Unit 3, Adding and Subtracting Within 20, Assessments, Section C Checkpoint, Practice Problems, Problem 1, 1.OA.2, “There are 5 bananas, 6 oranges, and 4 apples in a bowl. How many pieces of fruit are in the bowl? Show your thinking using objects, drawings, numbers, or words. Equation: _____.”
Unit 6, Length Measurements Within 120 Units, Assessments, End-of-Unit Assessment, Problem 1, 1.MD.1, three images of rectangles of varying orientations and lengths are provided. “a. Write a sentence comparing the length of Rectangle A and the length of Rectangle B”; and ” b. Write a sentence comparing the length of Rectangle A and the length of Rectangle C.”
Unit 8, Putting It All Together, Section B, Lesson 4, Cool-down, supports the full intent of MP4 (Model with mathematics) as students solve an unknown addend problem. “Clare counted 8 sharks swimming in a tank. Then some more sharks swam by. Clare counted 13 sharks all together. How many more sharks swam by? Show your thinking using drawings, numbers, or words.”
Indicator 3L
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
The materials reviewed for Open Up Resources K-5 Math Grade 1 provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
The general accommodations are provided in the Course Guide in the section Universal Design for Learning and Access for Students with Disabilities. These assessment accommodations are offered at the program level and not specific to each assessment. Examples include:
Course Guide, How to Assess Progress, Summative Assessment Opportunity, “In K-2, the assessment may be read aloud to students, as needed.”
Course Guide, Universal Design for Learning and Access for Students with Disabilities, Action and Expression, Develop Expression and Communication, “Offer flexibility and choice with the ways students demonstrate and communicate their understanding; Invite students to explain their thinking verbally or nonverbally with manipulatives, drawings, diagrams.”
Course Guide, Universal Design for Learning and Access for Students with Disabilities, Accessibility for Students with Visual Impairments, “It is important to understand that students with visual impairments are likely to need help accessing images in lesson activities and assessments, and prepare appropriate accommodations. Be aware that mathematical diagrams are provided in scalable vector graphics (SVG format), because this format can be magnified without loss of resolution. Accessibility experts who reviewed this curriculum recommended that students who would benefit should have access to a Braille version of the curriculum materials, because a verbal description of many of the complex mathematical diagrams would be inadequate for supporting their learning. All diagrams are provided in SVG file type so that they can be rendered in Braille format.”
Criterion 3.3: Student Supports
The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Indicator 3M
Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics as suggestions are outlined within each lesson. According to the Resources, Course Guide, Universal Design for Learning and Access for Students with Disabilities, “Supplemental instructional strategies that can be used to increase access, reduce barriers and maximize learning are included in each lesson, listed in the activity narratives under ‘Access for Students with Disabilities.’ Each support is aligned to the Universal Design for Learning Guidelines (udlguidelines.cast.org), and based on one of the three principles of UDL, to provide alternative means of engagement, representation, or action and expression. These supports provide teachers with additional ways to adjust the learning environment so that students can access activities, engage in content, and communicate their understanding.” Examples of supports for special populations include:
Unit 4, Numbers to 99, Section D, Lesson 19, Activity 2, Access for Students with Disabilities, “Action and Expression: Executive Functions. Invite students to plan a method with their partners, including the tools they will use, for decomposing 37 in multiple ways. Provides accessibility for: Organization, Attention”
Unit 7, Geometry and Time, Section A, Lesson 5, Access for Students with Disabilities, “Representation: Comprehension. Synthesis: Provide more examples and non-examples to reinforce the defining attributes of triangles. Provides accessibility for: Conceptual Processing, Visual-Spatial Processing”
Unit 8, Putting It All Together, Section B, Lesson 4, Activity 1, Access for Students with Disabilities, “Representation: Perception. Provide appropriate reading accommodations and supports to ensure student access to word problems and other text-based content. Provides accessibility for: Language, Visual-Spatial Processing, Attention.”
Indicator 3N
Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
While there are no instances where advanced students do more assignments than classmates, materials do provide multiple opportunities for students to investigate grade-level content at a higher level of complexity. These are found where problems are labeled as “Exploration” at the end of practice problem sets within sections, where appropriate. According to the Resources, Course Guide, How To Use The Materials, Exploration Problems, “Each practice problem set also includes exploration questions that provide an opportunity for differentiation for students ready for more of a challenge. There are two types of exploration questions. One type is a hands-on activity directly related to the material of the unit that students can do either in class if they have free time, or at home. The second type of exploration is more open-ended and challenging. These problems go deeper into grade-level mathematics. They are not routine or procedural, and they are not just “the same thing again but with harder numbers. Exploration questions are intended to be used on an opt-in basis by students if they finish a main class activity early or want to do more mathematics on their own. It is not expected that an entire class engages in exploration problems, and it is not expected that any student works on all of them. Exploration problems may also be good fodder for a Problem of the Week or similar structure.” Examples include:
Unit 1, Adding Subtracting, and Working With Data, Section A, Practice Problems, Problem 10 (Exploration), “Materials needed: Number cards 2–10; Two dot cubes. Directions: a. Choose a number card. Show 2 numbers on the dot cubes that add to make your number. b. Can you show another way?”
Unit 3, Adding and Subtracting Within 20, Section D, Practice Problems, Problem 6 (Exploration), “Mai was playing Number Card Subtraction. She started with a teen number. Then she drew a card and subtracted. Mai’s answer was the same as the number she subtracted. What could Mai’s teen number and card have been?”
Unit 6, Length Measurements within 120 Units, Section B, Practice Problems, Problem 6 (Exploration), “Priya and Noah want to measure their classroom in steps. Priya takes 28 steps to cross the room and Noah takes 26 steps. a. How could Priya and Noah get different measurements?; b. Measure the length of your classroom in steps.”
Indicator 3O
Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
The materials reviewed for Open Up Resources K-5 Math Grade 1 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
Students engage with problem-solving in a variety of ways. According to the Resources, Course Guide, Design Principles, Coherent Progression, “Each lesson starts with a warm-up to activate prior knowledge and set up the work of the day. This is followed by instructional activities in which students are introduced to new concepts, procedures, contexts, or representations, or make connections between them. The lesson ends with a synthesis to consolidate understanding and make the learning goals of the lesson explicit, followed by a cool-down to apply what was learned.” Examples of varied approaches include:
Unit 1, Adding, Subtracting, and Working WIth Data, Section B, Lesson 9, Activity 3, Student Work Time, “‘With your partner, find a group that represented the data in a different way from how you represented it. One person from each group switch papers with someone from the other group. With your partner, talk about what you notice is the same about each representation and what you notice is different.’3 minutes: partner discussion; ‘Share your thinking with the other group. What do you agree about?’ (We agree that each representation shows the same number of votes in each category and the same total number of votes.); 3 minutes: small group discussion.”
Unit 3, Adding and Subtracting Within 20, Section D, Lesson 25 Activity 1, Cognitive Support, “The purpose of this activity is for students to find differences using methods they choose. As students work, they may feel more comfortable with one method than another. The numbers were chosen to encourage different methods (counting on and taking away) so students can consider the numbers in a specific expression as they find the difference. During the activity synthesis, students share which method they used for a specific problem and why they chose it (MP3).”
Unit 5, Adding Within 100, Section A, Lesson 3, Cool-down, "Find the value of . Show your thinking using drawings, numbers or words. Write equations to show how you found the value."
Unit 7, Geometry and Time, Section B, Lesson 11, Activity 1, Activity Synthesis, “Invite previously identified students to share. ‘ _____ noticed that for both same-sized shapes, a half of the shape was bigger than a fourth of the shape. Do you think that will always be true? Why?’” Possible responses include, “Yes. When you cut a circle into halves, it is two pieces. Then if you cut it into fourths, you get four smaller pieces. Fourths are smaller than halves of the same-size shape.”
Indicator 3P
Materials provide opportunities for teachers to use a variety of grouping strategies.
The materials reviewed for Open Up Resources K-5 Math Grade 1 provide opportunities for teachers to use a variety of grouping strategies.
Suggested grouping strategies are consistently present within the activity launch and include guidance for whole group, small group, pairs, or individuals. Examples include:
Unit 2, Addition and Subtraction Story Problems, Section C, Lesson 11, Activity 2, Launch, “Groups of 2. Give each group four towers of ten connecting cubes. Display one red tower of eight connecting cubes, one yellow tower of three connecting cubes, and the handful of yellow connecting cubes. ‘I have two towers and I need to make them the same number of cubes. But I only have these yellow cubes. How can I make them the same?’ 1 minute: quiet think time. 1 minute: partner discussion. Share and record responses.” Student Work Time, “‘Lin is working to make the number of cubes in each of her towers the same. Each problem will tell you what cubes she has to work with. Record your thinking for each tower.’ 8 minutes: independent work time. ‘Share your thoughts with your partner.’ 4 minutes: partner discussion. Monitor for a student who solved the problem with 7 yellow cubes and 3 red cubes by adding 4 red cubes or drawing 4 more red cubes.”
Unit 4, Numbers to 99, Section D, Lesson 19, Activity 1, Launch “Groups of 3–4. Give each group one bag of connecting cubes.” Student Work Time “Read the task statement, 10 minutes: partner work time. As students work, consider asking: ‘How did you organize your count? How will you show how you organized and counted?’ Monitor for students who represent the count as 5 tens and 15 ones in different ways.”
Unit 7, Geometry and Time, Section A, Lesson 5, Activity 2, Student Work Time, “ ‘Use the dot paper in your book to draw three triangles and three shapes that are not triangles. You may use the shape cards to help you.’ 6 minutes: independent work time. Monitor for some triangles and ‘not triangles’ to share during the lesson synthesis.”
Indicator 3Q
Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
Guidance is consistently provided to teachers to support students who read, write, and/or speak in a language other than English, providing scaffolds for them to meet or exceed grade-level standards. According to the Resources, Course Guide, Mathematical Language Development and Access for English Learners, “In an effort to advance the mathematics and language learning of all students, the materials purposefully engage students in sense-making and using language to negotiate meaning with their peers. To support students who are learning English in their development of language, this curriculum includes instruction devoted to fostering language development alongside mathematics learning, fostering language-rich environments where there is space for all students to participate.” Examples include:
Unit 1, Adding, Subtracting, and Working With Data, Section C, Lesson 11, Activity 1, “Access for English Learners - Reading, Representing: MLR6 Three Reads. To launch this activity, display the task statement. ‘We are going to read this statement 3 times.’ After the 1st Read, ask: ‘What is this situation about?’ Listen for and clarify any questions about the context. After the 2nd Read: ‘What are all the things we can count?’ (number of votes for each pet, number of classmates who took the survey). After the 3rd Read: ‘How can we know if a statement is true or false?’”
Unit 2, Addition and Subtraction Story Problems, Section A, Lesson 3, Activity 1, "Access for English Learners - Representing, Conversing: MLR7 Compare and Connect. Synthesis: After all methods have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, ‘How were the different methods the same?’ and ‘How were they different?’”
Unit 4, Numbers to 99, Lesson 1, Activity 1, Access for English Learners, "Conversing, Reading: MLR2 Collect and Display. Circulate, listen for, and collect the language students use as they work with their partners. On a visible display, record words and phrases such as: count, represent, representation, my representation shows … Invite students to borrow language from the display as needed, and update it throughout the lesson."
Indicator 3R
Materials provide a balance of images or information about people, representing various demographic and physical characteristics.
The materials reviewed for Open Up Resources K-5 Math Grade 1 provide a balance of images or information about people, representing various demographic and physical characteristics.
Materials represent a variety of genders, races, and ethnicities. All are indicated with no biases and represent different populations. Names refer to a variety of backgrounds such as: Priya, Han, Mai, Diego. Settings include rural, urban, and multicultural environments. Examples include:
Unit 2, Addition and Subtraction Story Problems, Section B, Lesson 6, Activity 3, students see two pictures with two people. One person is male, and the other is female; both appear to be different races/ethnicities.
Unit 5, Adding Within 100, Section C, Lesson 11, Activity 1, "The purpose of this activity is for students to interpret equations that represent different methods for addition. When students connect the quantities in the story problem to addition equations, they reason abstractly and quantitatively (MP2). Base-ten drawings are provided for Jada and Kiran’s way so that students can use the drawings and the equations to make sense of the different methods. Students compare methods that add tens and tens and ones and ones to methods that add on by place. Students may also relate the methods used by Kiran and Tyler to the make 10 methods they use when adding within 20."
Unit 7 Geometry and Time, Downloads, Section C, Lesson 16, Activity 2, “Diego says this clock shows 6:00. Priya says the clock shows 12:30. Who do you agree with? Why?”
Indicator 3S
Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.
The materials reviewed for Open Up Resources K-5 Math Grade 1 partially provide guidance to encourage teachers to draw upon student home language to facilitate learning.
The materials include a Spanish version of the Family Letter. The Family Role section also includes a Spanish Glossary and Family Materials to provide guidance for each unit.
The Course Guide, Mathematical Language Development and Access for English Learners outlines the program’s approach towards language development, “In an effort to advance the mathematics and language learning of all students, the materials purposefully engage students in sense-making and using language to negotiate meaning with their peers. To support students who are learning English in their development of language, this curriculum includes instruction devoted to fostering language development alongside mathematics learning, fostering language-rich environments where there is space for all students to participate.” While language routines are regularly embedded within lessons and support mathematical development, they do not include specific suggestions for drawing on students’ home language.
Indicator 3T
Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
The materials reviewed for Open Up Resources K-5 Math Grade 1 provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
According to Resources, Course Guide, Design Principles, Authentic Use of Contexts and Suggested Launch Adaptations, “The use of authentic contexts and adaptations provide students opportunities to bring their own experiences to the lesson activities and see themselves in the materials and mathematics. When academic knowledge and skills are taught within the lived experiences and students’ frames of reference, ‘They are more personally meaningful, have higher interest appeal, and are learned more easily and thoroughly’ (Gay, 2010). By design, lessons include contexts that provide opportunities for students to see themselves in the activities or learn more about others’ cultures and experiences. In places where there are opportunities to adapt a context to be more relevant for students, we have provided suggested prompts to elicit these ideas.” Examples include:
Unit 2, Addition and Subtraction Story Problems, Section A, Lesson 1, Warm-up, Instructional Routine, “The purpose of this warm-up is to elicit the idea that math is found everywhere in our world. Students look for mathematical situations in a picture of a library, which will be helpful when students solve story problems about the library in later activities. While students may notice and wonder many things about this image, noticing numbers or quantities in the image are the important discussion points.” It includes an image of a library.
Unit 6, Length Measurements WIthin 120 Units, Section C, Lesson 13, Activity 1, Launch, “Groups of 2. Give students access to connecting cubes in towers of 10 and singles. ‘There are many different arts and crafts that people enjoy doing. Making friendship bracelets, like the ones in the stories we solved, is one craft that lots of students like. What arts and crafts do you like? What arts and crafts do you know that other people enjoy?’ (painting, knitting, scrapbooking). 30 seconds: quiet think time. Share responses. ‘We are going to continue to solve problems about crafts that people enjoy.’”
Unit 7, Geometry and Time, Section B, Lesson 11, Activity 2, “Priya and Han are sharing roti. Priya says, I want half of the roti because halves are bigger than fourths. Han says, I want a fourth of the roti because fourths are bigger than halves because 4 is bigger than 2. Who do you agree with? Show your thinking using drawings, numbers or words. Use the circle if it helps you.”
Indicator 3U
Materials provide supports for different reading levels to ensure accessibility for students.
The materials reviewed for Open Up Resources K-5 Math Grade 1 provide supports for different reading levels to ensure accessibility for students.
In Resources, Course Guide, Universal Design for Learning and Access for Students with Disabilities, Representation, “Teachers can reduce barriers and leverage students’ individual strengths by inviting students to engage with the same content in different ways. Supports provide students with multiple means of representation, include suggestions that offer alternatives for the ways information is presented or displayed, develop student understanding and use of mathematical language symbols, and describe organizational methods and approaches designed to help students internalize learning.” The supports develop sense-making and accessibility for students. Examples include:
Course Guide, Mathematical Language Development and Access for English Learners, Math Language Routine, MLR6: Three Reads, “‘Use this routine to ensure that students know what they are being asked to do, create opportunities for students to reflect on the ways mathematical questions are presented, and equip students with tools used to actively make sense of mathematical situations and information’ (Kelemanik, Lucenta, & Creighton, 2016). This routine supports reading comprehension, sense-making, and meta-awareness of mathematical language. How It Happens: In this routine, students are supported in reading and interpreting a mathematical text, situation, diagram, or graph three times, each with a particular focus. Optional: At times, the intended question or main prompt may be intentionally withheld until the third read so that students can concentrate on making sense of what is happening before rushing to find a solution or method. 1. Read #1: “What is this situation about?” After a shared reading, students describe the situation or context. This is the time to identify and resolve any challenges with any non-mathematical vocabulary. (1 minute); 2. Read #2: “What can be counted or measured?” After the second read, students list all quantities, focusing on naming what is countable or measurable in the situation. Examples: “number of people in a room” rather than “people,” “number of blocks remaining” instead of “blocks.” Record the quantities as a reference to use when solving the problem after the third read. (3–5 minutes); 3. Read #3: “What are different ways or strategies we can use to solve this problem?” Students discuss possible strategies. It may be helpful for students to create diagrams to represent the relationships among quantities identified in the second read, or to represent the situation with a picture (Asturias, 2014). (1–2 minutes).”
Unit 3, Adding and Subtracting Within 20, Section B, Lesson 11, “The purpose of this activity is to elicit and discuss methods for adding a one-digit number to a teen number, within 20. Students are presented with a simple story problem type (Add To, Result Unknown) so discussion can focus on the methods students used to find the sum. Students represent and solve the problem in a way that makes sense to them (MP1). Some students may build the teen number, add counters and count all, while other students may count on from the teen number. Some students may see that the sum will still have 1 ten and just combine the ones.”
Unit 5, Adding Within 100, Section A, Lesson 3, Lesson Narrative “In this lesson, students add two-digit numbers using methods of their choice and write equations to match their thinking. Students interpret and compare different methods for finding the value of the same sums. Students also practice explaining their own methods and listening to the methods of their peers. Students have opportunities to revise how they explain their own and others’ methods and consider how representations of their own thinking (for example, drawings or equations) can help them explain or interpret their work (MP3, MP6).”
Indicator 3V
Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
The materials reviewed for Open Up Resources K-5 Math Grade 1 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Suggestions and/or links to manipulatives are consistently included within materials to support the understanding of grade-level math concepts. Examples include:
Unit 1, Adding, Subtracting, and Working With Data, Section A, Lesson 4, Activity 1, students use number cards, a game board, two-color counters, and access to 10-frames to subtract one or two from a number within 10. Launch, “Groups of 2. ‘We are going to learn a new way to play, Five in a Row. Last time we played, we added one or two to the number on our card. This time, you will take turns flipping over a card and choosing whether to subtract one or two from the number. Then put a counter on the number on the game board, The first person to get five counters in a row wins. Remember, your counters can be in a row across, up and down, or diagonally.’” Student Work Time, “10 minutes: partner work time. As students work, consider asking: ‘How did your subtract? How did you decide whether to subtract 1 or 2?’”
Unit 4, Numbers to 99, Section A, Lesson 4, Activity 1, “The purpose of this activity is for students to solve two story problems involving adding or subtracting multiples of 10. Students are presented with a familiar context from a previous lesson in which students counted cubes in different bags. The quantities of cubes are described using representations that students are familiar with, and students add or subtract in a way that makes sense to them. The familiar context and representations are used to help students make sense of adding and subtracting tens. In the synthesis, students compare and connect the different representations used for each problem (MP2).”
Unit 6, Length Measurements Within 120 Units, Section B, Lesson 3, Activity 1, “Students choose from a variety of objects: connecting cubes towers, pieces of string, and unsharpened pencils. As students compare the length of the paths, students may use a single tool, such as a piece of string to compare the two paths. They may mark or cut the string. Some students may choose the tower of connecting cubes and determine that breaking off or counting the cubes is a way to determine whether one length is shorter or longer than the other. Others may select and try different tools until they find one that has a length that is in between the length of the two paths.”
Criterion 3.4: Intentional Design
The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.
The materials reviewed for Open Up Resources K-5 Math Grade 1 do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards; do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other; have a visual design that supports students in engaging thoughtfully with the subject that is neither distracting nor chaotic; and partially provide teacher guidance for the use of embedded technology to support and enhance student learning.
Indicator 3W
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.
The materials reviewed for Open Up Resources K-5 Math Grade 1 do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable. According to the Course Guide, About These Materials, “Teachers can access the teacher materials either in print or in browser as a digital PDF. When possible, lesson materials should be projected so all students can see them.” While this format is provided, the materials are not interactive.
Indicator 3X
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
The materials reviewed for Open Up Resources K-5 Math Grade 1 do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
According to the Course Guide, Key Structures in this Course, Developing a Math Community, “Classroom environments that foster a sense of community that allows students to express their mathematical ideas—together with norms that expect students to communicate their mathematical thinking to their peers and teacher, both orally and in writing, using the language of mathematics—positively affect participation and engagement among all students (Principles to Action, NCTM).” While the materials embed opportunities for mathematical community building through student task structures, discourse opportunities and journal/reflection prompts do not reference digital technology.
Indicator 3Y
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
The materials reviewed for Open Up Resources K-5 Math Grade 1 have a visual design (whether print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
There is a consistent design within units and lessons that supports student understanding of the mathematics. According to the Course Guide, Design Principles, “Each unit, lesson, and activity has the same overarching design structure: the learning begins with an invitation to the mathematics, is followed by a deep study of concepts and procedures, and concludes with an opportunity to consolidate understanding of mathematical ideas.” Examples from materials include:
Each lesson follows a common format with the following components: Warm-up, one to three Activities, Lesson Synthesis, and Cool-down (when included in lessons). The consistent structure includes a layout that is user-friendly as each lesson component is included in order from top to bottom on the page.
Student materials, in printed consumable format, include appropriate font size, amount and placement of direction, and space on the page for students to show their mathematical thinking.
Teacher digital format is easy to navigate and engaging. There is ample space in the printable Student Task Statements, Assessment PDFs, and workbooks for students to capture calculations and write answers.
Indicator 3Z
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
The materials reviewed for Open Up Resources K-5 Math Grade 1 partially provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable. Lessons include links to Community Created Resources that provide teachers with Google Slides for each lesson. No additional guidance is provided within the slide decks. For example, Unit 1, Adding, Subtracting, and Working With Data, Section B, Lesson 8, Preparation, Downloads, “Community Created Resources: Google Slides.”