1st Grade - Gateway 2
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Rigor & Mathematical Practices
Rigor & the Mathematical Practices| Score | |
|---|---|
Gateway 2 - Meets Expectations | 88% |
Criterion 2.1: Rigor and Balance | 6 / 8 |
Criterion 2.2: Math Practices | 10 / 10 |
The materials reviewed for ORIGO Stepping Stones 2.0 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).
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 ORIGO Stepping Stones 2.0 Grade 1 partially meet expectations for rigor. The materials give attention throughout the year to procedural skill and fluency and spend sufficient time working with engaging applications of mathematics. The materials partially develop conceptual understanding of key mathematical concepts and partially balance the three aspects of rigor.
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 ORIGO Stepping Stones 2.0 Grade 1 partially meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.
The materials include some problems and questions that develop conceptual understanding throughout the grade level. Students have few opportunities to independently demonstrate conceptual understanding throughout the grade.
Cluster 1.OA.A includes representing and solving problems involving addition and subtraction. Modules 4, 5, 6, 7, 8, and 9 explore a variety of real-world applications using a few mathematical representations.
Some opportunities exist for students to work with addition and subtraction that address conceptual understanding through the use of some visual representations and different strategies. Examples include:
Module 2, Lesson 2, Addition: Counting on, rather than counting all, Step 3 Teaching the lesson, students are shown how to count on starting at 5. “Invite one student to come to the front and use their fingers to show a number from five to ten, starting from the class’s left, Make sure they use both hands to show each number. For example, to show six, they show five fingers raised on their right hand and one finger raised on their left.”
Module 7, Lesson 2, Number: Writing three-digit numbers to 120 (without teens), Student Journal, Step Up, pages 246 and 247, students use base ten blocks to determine the number, then write the number on the number expanders, and write it on the expander without it expanded.
Module 8, Lesson 1, Addition: Exploring combinations of ten, Step 3 Teaching the lesson, “Allow time for pairs to explore the different combinations of ten, then paste groups of animals onto paper, and write the matching equation next to each group (MP2). Afterward, have them leave their work at their desk and move around to look at the combinations made by other pairs. Then lead a discussion about the different combinations. Ask students to share observations about making ten.”
Module 11, Lesson 5, Algebra: Counting in steps of two, Step 2 Starting the lesson, “Organize students into pairs. Open the Flare Number Board online tool. Ask the students to identify patterns on the hundred chart (MP7). Afterward, invite pairs to show and explain the patterns they identified. Reset the hundred chart and work with the students to shade the numbers you say when you start at 5 and count by fives. Repeat for the multiples of ten, using a different shade. Then have a student shade the multiples of two in a third shade to match the chart, as shown. Then discuss the points below: What do you notice about these numbers on our chart? (MP7) Why do you think the tens column has three colors on each number? (The numbers are in the twos, fives, and tens patterns.) When looking at these patterns, are these the only numbers we can say when we count by twos, fives, or tens? Why do you think that?” This lesson addresses conceptual understanding of addition by examining the patterns on a 100s chart.
However, the instructional materials do not regularly provide students opportunities to independently demonstrate conceptual understanding throughout the grade-level. Examples include:
Module 7, Lesson 7, Subtraction: Introducing the think-addition strategy (near-doubles facts), Step 3 Teaching the lesson, “Project slide 3, as shown, and discuss the points below: What do you see in this picture? How is it the same as the previous picture? (It is a think-addition card.) How is it different? (It has different numbers and one flap is down.) What equations could we create from this card? (8 +___ = 17, 17 - 8 = ___.) (MP2) What strategy could we use if we wanted to think addition? (MP5) Who can tell us how you use the strategy to find the missing number” This lesson addresses filling in the blanks instead of the conceptual understanding of using addition to solve subtraction problems.
Module 8, Lesson 5, Addition: Reinforcing the commutative property, Student Journal, page 294, Step Up, “Write an addition fact to match each picture. Then write the turnaround fact.” This worksheet gives students a domino and students are to write 2 addition facts based on the dots on the dominoes. These problems address the commutative property but not a conceptual understanding of the commutative property and when to best use it.
Module 10, Lesson 1, Subtraction: Writing related facts, Student Journal, page 358, Step Up, Question 1, “Write numbers to match each picture.” The worksheet has students count the animals in the pictures and fill in the blanks instead of building conceptual understanding of subtraction.
Indicator 2b
Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.
The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Materials attend to the First Grade expected fluencies, add and subtract within 20, demonstrating fluency for addition and subtraction within 10.
The instructional materials develop procedural skills and fluencies throughout the grade-level. Opportunities to formally practice procedural skills are found throughout practice problem sets that follow the units. Practice problem sets also include opportunities to use and practice emerging fluencies in the context of solving problems. Ongoing practice is also found in Assessment Interviews, Games, and Maintaining Concepts and Skills.
The materials attend to the Grade 1 expected fluencies: 1.OA.6 add and subtract within 20, demonstrating fluency for addition and subtraction within 10. In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluency. Examples include:
Module 5, Lesson 1, Addition: Introducing the double-plus-1 strategy, Maintaining concepts and skills, students practice adding within 10 and subtracting within 5.
Module 7, Lesson 7, Subtraction: Introducing the think-addition strategy (near-doubles facts) Student Journal, Question 2, “Figure out the number of dots that are covered. Then complete the facts.” Students are practicing subtraction fluency within 10.
Module 8, Lesson 1, Addition: Exploring combinations of ten, Maintaining concepts and skills, “This lesson provides projectable practice that is designed to foster fluency of basic facts. Project or read the facts to the students, allowing a few seconds between each fact that you show or read. Be sure to alternate this delivery from one lesson or module to the next. Roll over the image below to reveal the focus of the content.” Students are practicing fluency with 10.
Module 11, Lesson 3, Addition/subtraction: Reinforcing basic fact strategies, Student Journal, Question 2, “Write the answers on the race track.” Students are practicing subtraction and addition fluency.
Maintaining Concepts and Skills lessons incorporate practice of previously learned skills from the prior grade level. For example, Maintaining Concepts and Skills in Module 2, Lesson 1, Addition: Reviewing concepts, provides practice for adding within 10 and subtracting within 5.
Each module contains a summative assessment called Interviews. According to the program, “There are certain concepts and skills, such as the ability to route count fluently, that are best assessed by interviewing students.” For example, in Module 7’s Interview 1 has students subtracting within 10 and Interview 2 has students counting from 86 to 120.
“Fundamentals Games” contain a variety of computer/online games that students can play to develop grade level fluency skills. For example Add ‘em up, students demonstrate fluency of adding within 20 (1.OA.6).
Some lessons provide opportunities for students to practice the procedural fluency of the concept being taught in the “Step Up” section of the student journal.
Indicator 2c
Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.
The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.
Materials include multiple routine and non-routine applications of the mathematics throughout the grade level. Teachers routinely engage students in single and multi-step application problems during the Step In Discussion at the beginning of lessons. Examples include:
Module 1, Lesson 12, Data: Creating and Interpreting graphs, Student Journal, page 38, Step In Discussion, students represent and interpret data in routine problems. (1.MD.4) “A group of students voted for their favorite animal at the zoo. They each placed a counter beside their favorite animal to show their vote. What does the graph tell you? What is the most popular animal at the zoo? How many students voted for each animal? How many students voted in total? How many more students voted for the tiger than the giraffe?”
Module 4, Lesson 6, Subtraction: Solving Word Problems, Student Journal, page 134, Step In Discussion, students solve subtraction word problems in a real-world routine problem. (1.OA.1) “This puzzle has 10 pieces. Kuma takes out 2 pieces. How many pieces are left in the box? Write an equation to show your thinking. This puzzle costs 4 dollars to buy. Anya pays with a 5 dollar bill. How much money should she get back? Write an equation to show your thinking.”
Module 10, Lesson 9, Subtraction: Solving word problems (using comparisons), Student Journal, page 382, Step In Discussion, students solve non-routine real-world problems as they use number tracks as a strategy for subtraction. (1.OA.1) “Manuel compares the number of blocks in each box. How many more blocks does the bigger box hold? What equation could you write to figure out the difference? Hannah buys the bigger box of blocks. She takes out 5 blocks. How many blocks are left in the box? What equation could you write?” Two containers are provided and labeled 9 blocks and 12 blocks.
Materials consistently provide opportunities for students to independently engage with routine and non-routine applications of mathematics. These are found across the grade level within Thinking Tasks, Problem Solving Activities, and Investigations. Examples include:
Module 8, More Math, Investigation 2, students organize and write multiple addition equations using one digit numbers in a non-routine problem. (1.MD.4) “How many different ways can you make this addition equation true using only one-digit numbers? __ + __ = 12.”
Module 9, More Math, Thinking Tasks, Questions 1 and 2, students add two digit numbers and write an equation for a non-routine problem. (1.NBT.4 and 1.OA.8). The question includes an image of an apple with 45 cents on a price tag and asks, “Chloe has 25 cents. How much more does she need to buy the apple? You can draw pictures to help.” Question 2, “Write an addition equation to show what you did in Question 1.”
Module 11, More Math, Problem Solving Activity 4, students reason about addition or subtraction and choose a strategy to solve a routine word problem. (1.OA.1) “Reece is cleaning out his fish tank. He has 12 fish in total. Nine of the fish are swimming around the tank, and the rest are hiding behind plants. How many fish are hiding?”
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 ORIGO Stepping Stones 2.0 Grade 1 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency.
The curriculum addresses conceptual understanding, procedural skill and fluency, and application standards, when called for, and evidence of opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. There are multiple lessons where one aspect of rigor is emphasized. The materials have an overemphasis on fluency, procedures, and algorithms.
Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include:
Module 1, Lesson 4, Number: Representing quantities (11 to 20), Step 3, Teaching the lesson, students draw number cards and represent the number with cubes, counters, coins, or drawing a picture.
Module 9, Lesson 7, Addition: Introducing place-value methods, Student Journal, Step Up, students use conceptual understanding to solve addition problems. “1. Add the two groups. Then write the matching equation. Use blocks to help you. a. 50 + 20” Under 50 and 20 are base ten blocks representing the numbers.
Module 10, More Math, Problem Solving Activities, Activity 4, “Dad has baked 12 muffins for the soccer team. There are four muffins leftover. How many muffins has the soccer team eaten?” (1.OA.1)
Module 12, Lesson 1, Number: Working with place value (hundred chart), Step 3, Teaching the lesson, students use conceptual understanding to solve number puzzles and see patterns in a 100s chart. “I am thinking of a number that has a nine in the ones place and a four in the tens place. Which number is it?”
Examples of students having opportunities to engage in problems that use two or more aspects of rigor include:
Module 1, Lesson 9, Number: Reading ordinal number symbols, Step 3, Teaching the lesson, application and conceptual understanding are treated together. Students read the book Paint a Rainbow, students put each other in order, using the “numeral one and ordinal symbol 1st.”
Module 10, Lesson 6, Subtraction: Exploring the comparison model, application and conceptual understanding are treated together. Students read the book Bear and Badger, “They use cubes to model the subtraction story show on the spread” (pages 4 and 5) “introduce the language associated with comparison subtraction.”
Criterion 2.2: Math Practices
Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).
The materials reviewed for ORIGO Stepping Stones 2.0 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 ORIGO Stepping Stones 2.0 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 in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, alongside the learning targets or embedded within lesson notes.
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 modules. Examples include:
Module 1, Lesson 8, Number: Working with position, Student Journal, Step Up, page 27, students make sense and persevere in solving a word problem involving number position between 1 and 20. “Three friends collect baseball cards. Felipe has one more card than Samantha. Jamal has one fewer card than Felipe. How many cards could each person have?”
Module 3, Lesson 8, Number: Solving Puzzles, Lesson Notes, Step 3 Teaching the Lesson, students make sense of a number puzzle and persevere in solving it. The teacher is instructed to project a slide with the following word problem: “I am a two-digit number. My tens digit is greater than my ones digit. My number ends with a 7. What number could I be?” “Project slide 1, as shown. Read the clues and repeat each clue slowly. Then ask the problem-solving prompts below: What information do we know? How can it help us to solve the problem? What do we need to find out? What could you use to help solve the problem?
Module 7, Lesson 9, Subtraction: Reinforcing all strategies, Step 3 Teaching the lesson, students make sense of problems involving subtraction and persevere in solving them. In small groups, students are given word problem cards. The teacher asks “students to discuss a solution plan, then follow it to find the solution. Help them make sense of their problem by discussing the points below: How would you describe what is happening in your own words? What strategy do you think would be helpful?”
Module 9, Lesson 1, Addition: Extending the count-on strategy, Student Journal, page 321, students “make sense of count on addition problems and persevere in solving them”. Students use a number track from 84 to 94 to solve, “Valentina has 87 cents. Noah has 2 cents more than Valentina. Mary has 3 cents more than Noah. Ryan has 2 cents more than Mary. How much money does Ryan have? ___ cents” “If some students have difficulty, have them restate the problem in their own words to ensure understanding.”
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 modules. Examples include:
Module 2, Lesson 1, Addition: Reviewing concepts, Step 3 Teaching the Lesson, students reason quantitatively and abstractly as they decontextualize addition problems using connecting cubes. “Read the problem to the students. Ask, How could you use your cubes to show the addition in this problem? Read the problem again, and allow time for the students to model the problem using their connecting cubes. Then say, Turn to the student on your left and talk about how you used the cubes to show the problem. After, ask a few students to give the total and explain their thinking. Highlight examples where an addition equation is provided as part of the explanation. Repeat for the remaining two problems (slides 5 and 6). (MP2)”
Module 5, Lesson 3, Addition: Introducing the doubles-plus-two strategy, Step 3 Teaching the lesson, students reason abstractly and quantitatively as they write equations to match domino addition facts. “Project slide 1 and ask, What do you see on this card? (Dot arrangements, numbers.) How can you figure out the total? (Use a strategy, or count the dots.) What double will help you? (Double 4.) Invite individuals to describe their thinking. Project slide 2 to support the thinking that begins with double 4. As a student describes their thinking, project slide 3 to reinforce the thinking “4 plus 6 is double 4 add 2 more.” Ask, What addition fact helps us figure out the total? What addition fact can we write? What turnaround fact can we write? Have individuals write the facts 4 + 4 = 8, 4 + 6 = 10, and 6 + 4 = 10 on the board and relate each to the thinking above (MP2). Repeat the activity with 6 + 8 (slides 4 to 6).”
Module 8, Lesson 2, Addition: Using the associative property, Step 3 Teaching the lesson, students reason abstractly and quantitatively when they reason about the quantities in addition problems and how they are related, then represent them symbolically. Students make three different colored trains out of connecting cubes. The teacher asks, “How many cubes are in each train? How many cubes are there if the three trains are joined together? How do you know? What equation can we write to show the three numbers?”
Module 10, Lesson 1, Subtraction: Writing related facts, Step 4 Reflecting on the lesson, students contextualize and decontextualize as they write word problems and equations to match subtraction situations. Students view the big book, How Many Legs?, and “create various pictures using the animals. Encourage students to create stories to match the pictures and write the related subtraction facts (MP2).”
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 ORIGO Stepping Stones 2.0 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 meet the full intent of MP3 over the course of the year as it is explicitly identified for teachers in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, and alongside the learning targets or embedded within lesson notes.
Teacher guidance, questions, and sentence stems for MP3 are found in the Steps portion of lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments. In some lessons, teachers are provided questions and sentence stems to help students critique the reasoning of others and justify their thinking. Convince a friend, found in the Student Journal at the end of each module and Thinking Tasks in modules 3, 6, 9, and 12, provide additional opportunities for students to engage in MP3.
Students engage with MP3 in connection to grade level content, as they work with support of the teacher and independently throughout the units. Examples include:
Module 5, Student Journal, page 195, Convince a friend, students construct a viable argument as they compare place value for two digit numbers. “Nadia says 29 is greater than 32 because 9 is greater than both 3 and 2. Is she correct? Show your thinking.”
Module 7, Lesson 4, Number: Writing numbers and number names to 120, Step 4 Reflecting on the work, students construct viable arguments when they use base-ten blocks or pictures to justify their thinking about the value and representation of three-digit numbers. Given the numbers 117 and 107, the teacher asks, “How are these numbers the same? How are they different? Which number is greater? How do you know?” The teacher encourages “students to use base-ten blocks or draw pictures of base-ten blocks on the board to justify their thinking (MP3). Ask other students to respond using sentence stems such as: I agree/ disagree because ... , I don’t understand …, I figured it out by …”
Module 9, Lesson 11, Addition: Reinforcing place-value strategies (composing tens), Student Journal, page 351, Step Ahead, students construct viable arguments and critique the reasoning of others as they analyze an error in a two-digit addition problem. Students are given 27 + 14 = 311 with a picture of 3 base-ten ten rods and 11 unit cubes. “Jacinta added these two groups. Write the correct total. Then talk about the mistake that was made with the student beside you.”
Module 10, Student Journal, page 395, Convince a friend, students construct viable arguments and critique the reasoning of others as they reason about addition and subtraction. A picture includes a ten frame with 7 counters on the frame and 3 counters off the frame. “Chloe says she sees 7 + 3 = 10. Marvin says he sees 10 - 3 = 7. Who do you agree with? Show your thinking.”
Module 11, Lesson 1, Subtraction: Introducing the think-addition strategy (make-ten facts), Step 3 Teaching the lesson, students construct viable arguments and critique the reasoning of others as they reason about and solve subtraction equations. “Project the equation 15 - 9 = __ and the number track (slide 7). Instruct students to solve the problem using think-addition and make-ten strategies. . . Encourage students to listen attentively to others' answers and strategies. Prompt critique (MP3) with questions such as: Do you agree with the strategy that (Maka) used? Why or why not? Does anyone need (Maka) to explain something they heard in (his) answer? How is your strategy the same as (Maka’s) strategy? How is it different?”
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 ORIGO Stepping Stones 2.0 Grade 1 meet expectations for supporting 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.
Students have opportunities to engage with the Math Practices throughout the year. The MPs are often explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within lesson notes.
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, identify important quantities to make sense of relationships, and represent them mathematically. Students model with mathematics as they work with support of the teacher and independently throughout the modules. Examples include:
Module 2, Lesson 4, Addition: Reinforcing the count-on strategy, Student Journal, page 52, Step In, students model with mathematics as they reason about addition facts. “There are 6 pennies in the purse and some outside the purse. How could you figure out the total number of pennies? What addition fact could you write?”
Module 4, Lesson 3, Subtraction: Writing equations, Step 3 Teaching the lesson, students model with mathematics as they create and model subtraction stories. “Organize students into small groups and distribute the resources. Explain that each group is going to create and solve their own Cupcake Capers story, using one of the following: the Cupcake Capers online tool, concrete materials like connecting cubes, paper to draw pictures, or by acting out the story (MP4). Afterward, invite each group to present their subtraction story to the class, highlighting the tool or strategy they used to solve the problem, and how it was modeled (MP4).”
Module 7, Lesson 3, Number: Writing numbers and number names to 120 (without teens), Step 3 Teaching the lesson, students model mathematics as they “compare the different models they have used and recognize that they all represent the value in each place of a three-digit number.” “Distribute the expanders and markers to each group. Have them choose a number between 101 and 110, then represent their number with base-10 blocks, on the expander, and in words.” The teacher says, “You represented your number in three different ways. How are they the same? How are they different? Students should notice that each model represents the number of hundreds, tens, and ones in their number. (MP4)”
Module 8, More math, Problem solving activity 4, Word problems, students model with math as they represent addition and subtraction word problems.“ Directions state, “Project slide 1 and read the word problem with the students. Ask, what do we need to solve the problem? Is there information we do not need? How could you show your thinking? (For example, act it out, draw a diagram, or write an equation.” Question d, “Amber has 3 green beads, 4 blue beads, 4 red beads, and 5 white beads. She wants to put the beads into two groups so they each have an equal number of beads. How many of each color could Amber put into each group?”
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 modules to support their understanding of grade level math. Examples include:
Module 1, Lesson 1, Number: Representing quantities (up to ten), Step 2 Starting the lesson, students use appropriate tools in order to represent five. “Organize students into pairs to explore the different ways they can represent five. Allow them to choose from a variety of hands-on resources to support their thinking (MP5). Invite pairs of students to share and model their answers. Record the different representations around the numeral 5 on the board. Connect each representation to the numeral to form a number web.”
Module 7, Lesson 7, Subtraction: Introducing the think-addition strategy (near-doubles facts), Student Journal, page 262, “students choose between the think-addition strategies of doubles-plus-1 and doubles-plus-2 to solve subtraction problems, and choose math tools to support their thinking”. Question 1b, students are given a picture of a domino with 5 dots on one side with the number 5 above it and no dots on the other side with a fill-in-the-blank space above it. The total 12 is written below the domino as is ___ + 5 = 12. Step 3 Teaching the lesson, “Inform students that they can use math tools such as connecting cubes, counters, ten-frames, and number tracks to support their thinking (MP5).”
Module 10, Lesson 3, Subtraction: Writing related equations (multiples of ten), Step 3 Teaching the lesson, students select tools to solve a real world problem involving subtraction. On slide 6, students see pictures of snacks with price tags attached: apples 20¢, pear 10¢, banana 30¢, orange 40¢, and nuts 50¢, “I have 50 cents. If I buy the ____. How much money will I have left? Encourage students to select a tool they could use to solve the problem. If necessary suggest things such as a hundred chart, base-10 blocks, dimes, or their fingers. (MP5) Students may apply counting or place-value strategies and figure out the answer in their head.”
Module 11, More math, Problem solving activity 4, Word problems, students choose different strategies as tools to solve real world problems involving addition and subtraction. Slide 1, “Natalie has 15 balloons. Some of the balloons are yellow and some of the balloons are red. How many of each color might Natalie have?” The teacher asks, “How could you show your thinking? (For example, act it out, draw a diagram, or write equations.)”
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 ORIGO Stepping Stones 2.0 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. MP6 is explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes.
Students have many opportunities to attend to precision in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:
Module 4, Lesson 12, 2D Shapes: Composing shapes, Student Journal, page 153, Step Up, Question 2, students attend to the precision of mathematics by accurately tracing shapes to create new shapes. “2) Choose 3 different pattern blocks. a) Join them. Then trace around them. b) How many sides does your new shape have?”
Module 5, Lesson 10, Number: Introducing comparison symbols, Step 3 Teaching the lesson, students attend to the precision of mathematics by accurately using mathematical symbols when comparing two-digit numbers. “Write the numbers of cubes on the board with the great number first, then with the smaller number first. Allow space to write is less than or is greater than between each pair of numbers. Ask, What words can we write between the numbers to describe how they compare? Encourage students to suggest writing is greater than and is less than. Write the appropriate phrase between each pair of numbers. Say, We can write symbols instead of writing all those words. Does anybody know the symbols that we can write? Write the matching symbolic sentence below each word sentence, for example, 8 > 5 and 5 < 8. Ask, What is different about the two symbols? Bring out that the symbols point in opposite directions. (MP6)”
Module 8, Lesson 10, Data: Recording in a tally chart, Step 3 Teaching the lesson, students attend to precision when they “accurately record data and interpret a tally chart.” Pairs of students collect five to ten crayons. The teacher says, “I want you to count the total number of crayons you have and represent them using tally marks. If students are struggling, discuss the points below (MP6): How many crayons do you have? How many tally marks would you draw to show one crayon? Two crayons? What does a tally mark look like? How many tally marks are shown in each group? (5.)”
Students have frequent opportunities to attend to the specialized language of math in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:
Module 1, Lesson 5, Number: Writing teen number names, Step 4 Reflecting on the work, students attend to the specialized language of mathematics by defining a teen number. Discuss the students’ answers to Student Journal 1.5. Ask the students to share and justify the number names they colored for Step Ahead. Ask, Why did you not color the word twenty? Why did you not color the word eight? How did you decide what numbers to color? How would you tell someone what a teen number is? Organize students into pairs to discuss the questions. Then invite students to share their definitions with the class. (MP6) Compare the varying definitions. In context, many students will consider a teenager as somebody whose age ends in teen, while those who adopt a more mathematical standpoint may consider a teen number as a number that is represented with one ten and some more ones. Welcome each of the perspectives as they are each socially or mathematically correct.”
Module 2, Lesson 8, Addition: Introducing the doubles strategy, Step 3 Teaching the lesson, students engage in the specialized language of mathematics by accurately reading a doubles fact. “Open the Addtron online tool. Invite a student to drag pictures onto the work area to show a double. Have the class say the double using correct language and without counting. (MP6) For example, “Double five is ten,” or “Five add five is ten.” Then ask another student to use the writing tool to write the doubles fact in the white panel. Repeat for different doubles.”
Module 3, Module overview, Vocabulary development, students can attend to the specialized language of math as teachers are provided a list of vocabulary terms. “The bolded vocabulary below will be introduced and developed in this module. These words are also defined in the student glossary at the end of each Student Journal. A support page accompanies each module where students create their own definition for each of the newly introduced vocabulary terms. The unbolded vocabulary terms below were introduced and defined in previous lessons and grades. Addition, balance, cents, clock, coins, corners, count on, dime, double, equals, equation, fact, fewer, hour, length, less, longer than, longer, longest, measure, minute hand, more, number name, number, ones, order, penny, shape, shorter, shortest, sides, smallest, subtract, tens, total.” Students are provided with a Building Vocabulary support page. The page includes: Vocabulary term (the bolded terms), Write it in your own words, and Show what it means.
While there are examples of the intentional development of MP6, Attend to precision, throughout materials, there is also evidence of imprecise language or content connections that are not grade-specific. Example include:
Module 9, Lesson 3, Addition: Exploring patterns (hundred chart), Step 4 Reflecting on the work, the term “turnaround” is used for the commutative property and “add” is used in place of the word, “plus”. “Write 2 + 46 = ___ on the board and ask, How could you figure out the total? As students explain their strategy, encourage thinking that uses the turnaround. Ask, What is the turnaround for 2 add 46? What is the total?”
Module 11, Lesson 9, Money: Relating all coins, Step 3 Teaching the lesson, connects to grade 2 content. “MP6 - when students accurately describe the trade between coins”. The teacher asks, “How many nickels could you trade for one quarter? (5) Have each group count out 25 pennies to represent the value of one quarter. The 25 pennies are then split into groups or stacks of five to determine the equivalent number of nickels. The same reasoning is then applied to figure out the number of nickels that can be traded for one dime. (MP4 and MP6)” This connects to 2.MD.8, solving word problems involving money.
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 ORIGO Stepping Stones 2.0 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 throughout the year and they are often explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes.
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 throughout the modules to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently. Examples include:
Module 1, Lesson 6, Number: Representing teen numbers, Step 3 Teaching the lesson, students look for and make use of structure while representing teen numbers on ten-frames. “Distribute a ten-frame and 20 counters to each pair. Ask, How many counters do you need to fill the frame? How can you show a number that is greater than ten? Establish that 10 counters fill the frame and that loose counters can be placed beside the frame to show a number that is greater than ten. Say, Use the frame to show 14. What does it look like? How many counters are on the frame? How many counters are beside the frame? Reinforce the language of 10 and 4 more. Repeat for 17 and 12. (MP7)”
Module 2, Lesson 9, Addition: Reinforcing the doubles strategy, Student Journal, page 68, Step Up, Problem 1a, students look for and make use of structure when completing problems using the doubles strategy. “Use the same strategy to figure out these.” Students are given a picture of 2 identical bead strings with the bead segmented into 5 and 2 beads. “Double 5 is ___. Double 2 is ___. So Double 7 is ___.”
Module 9, Lesson 7, Addition: Introducing place-value methods, Student Journal, page 338, Step Up, Question 1a, students look for and make use of structure as they “use known facts and place value thinking to solve addition problems.” Students see a picture of the numeral 50 and 5 base-ten rods and the numeral 20 and 2 base-ten rods. “Add the two groups. Then write the matching equation. Use blocks to help you.” Reflecting on the work, “Discuss the students’ answers to Student Journal 9.7. Encourage students to explain their thinking. Ask, Is it easy to add tens? Why? Prompt several responses such as “Adding 50 and 20 is just like adding 5 and 2, because 50 is 5 tens and 20 is 2 tens.” (MP7)”
Module 10, Lesson 4, Subtraction: Writing related addition and subtraction facts, Step 2 Starting the lesson, students look for and make use of structure when they “use the structure of the same parts and total to write related addition and subtraction facts.” Students are given a picture of a domino with 6 dots on one side and one dot on the other side, the teacher asks, “What two addition facts can we write to show the total of these two numbers? (6 + 1 = 7 and 1 + 6 = 7.) What two subtraction facts can we write to match? (Yes. Either 7 - 1 = 6 and 7 - 6 = 1.) What do you notice about all four facts? (The same numbers are used in different positions.) (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 throughout the materials, with support of the teacher or during independent practice, to use repeated reasoning in order to make generalizations and build a deeper understanding of grade level math concepts. Examples include:
Module 4, Lesson 2, Subtraction: Reviewing concepts (take from), Step 2 Starting the lesson, students look for and express regularity in repeated reasoning by counting orally forward and backward. “Distribute one numeral card to each student. Say, Today we are going to play a game called I have, who has? I will start and when you hear a question that your card answers, you stand up and continue the game. Ready? I have (19), who has 18? Prompt the student with the card for 18 to stand up and repeat the question for their number. Afterward, have students exchange cards, and start the game with a different number, such as 9 and counting forward. Repeat as time allows (MP8)”
Module 6, Lesson 5, Subtraction: Reinforcing the think-addition strategy (count-on facts), Step 3 Teaching the lesson, students look for and express regularity in repeated reasoning by using the known count-on strategy to find the missing part in a subtraction situation. “Write the two equations that match the card on the board, discussing the think-addition strategy as 4 add what makes 5. Point out that the unknown number can be one of the parts and does not have to be the total. Invite the students to talk about which strategy they would use to solve the problem. Encourage students to share their thinking with the class. Repeat the discussion for slides 3 to 5. (MP8)”
Module 7, Lesson 10, Time: Introducing half-past the hour (analog), Step 3 Teaching the lesson, students look for and express regularity in repeated reasoning when they “make connections between half-past the hour shown on an analog clock and one-half represented with an area model (circle).” Students view the Flare Clocks online tool showing 4:00. The teacher asks, “Where would the minute hand point if it went halfway around the clock? What do you think that would tell us about the time? Prompt students to discuss and describe the position of the minute hand when it points at the 6, as halfway between one on-the-hour time and the next on-the-hour time.” The teacher asks, “When have you heard the words half and one-half before? Encourage and highlight responses that refer to one-half as one of two equal parts that make one whole. Students who make connections between concepts like this are demonstrating flexible thinking. (MP8)”
Module 12, Lesson 5, Subtraction: Exploring patterns, Student Journal, page 447, Step Up, Questions 2a-b, students look for and express regularity in repeated reasoning when they “extend subtraction patterns to find unknowns in equations.” Directions state, “Think about the numbers between 1 and 50. a. Write all the numbers that have 6 in the ones place. b. Write the numbers that are 2 less than the numbers you wrote.” Step 4 Reflecting on the work, the teacher asks, “What is the answer when you subtract 2 from 11? What do you think will be the answer when you subtract 2 from 21? What will be the answer if you subtract 2 from 61? What happens in the ones place? What happens in the tens place? (MP8)”