1st Grade - Gateway 1

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 <, =, or > 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. 46+10. b. 46+20. c. 46+50.” (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. 6+8=___, b. 10+___=16, c. ___-4=7.” (1.NBT.2b, 1.OA.8)

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 2+5. ‘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. 4+2=2+4. b. 3+6=6+4. c. 5+3=1+7 d. 6+4=5+3. e. 6+3=9+2.” 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. 7+10, 7+2+8, 10+9, 4+9+6.”

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. 7+3=10, 10=7+3, 10=3+6.” 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. 6+4=10, B. 10-4=6, C. 2+2+2=6, D. 6=2+4.” 

• 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., 8+6=8+2+4=10+4=14]; decomposing a number leading to a ten [e.g., 13-4=13-3-1=10-1=9]; using the relationship between addition and subtraction [e.g., knowing that, one knows that 8+4=12, one knows 12-8=4]; and creating equivalent but easier or known sums [e.g., adding by 6+7 creating the known equivalent 6+6+1=12+1=13]). 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, 3+10, 10+5, 13-10, 15-10.”

• 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.”

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.

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.”

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, 40+1 (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.

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.”