1st Grade - Gateway 2
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Rigor & Mathematical Practices
Gateway 2 - Partially Meets Expectations | 66% |
|---|---|
Criterion 2.1: Rigor | 6 / 8 |
Criterion 2.2: Math Practices | 6 / 10 |
The instructional materials reviewed for JUMP Mathematics Grade 1 partially meet expectations for Gateway 2.The instructional materials partially meet expectations for rigor by developing conceptual understanding of key mathematical concepts, giving attention throughout the year to procedural skill and fluency, and spending some time working with routine applications. The instructional materials do not always treat the three aspects of rigor together or separately, but they do place heavier emphasis on procedural skill and fluency. The instructional materials partially meet expectations for practice-content connections. Although the instructional materials meet expectations for identifying and using the MPs to enrich mathematics content, they partially attend to the full meaning of each practice standard. The instructional materials partially attend to the specialized language of mathematics.
Criterion 2.1: Rigor
Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
The instructional materials reviewed for JUMP Math Grade 1 partially meet expectations for rigor by developing conceptual understanding of key mathematical concepts, giving attention throughout the year to procedural skill and fluency, and spending some time working with routine applications. The instructional materials do not always treat the three aspects of rigor together or separately, but they do place heavier emphasis on procedural skill and fluency.
Indicator 2a
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
The instructional materials reviewed for JUMP Math Grade 1 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.
While conceptual understanding is not explicitly identified or labeled in the materials, the materials include problems and questions that develop conceptual understanding throughout the grade level. Students are given repeated opportunities in the program to develop an understanding of place value and to use that understanding, along with properties of operations to add and subtract. Examples include:
- Teacher Resource, Part 1 Unit 3, Lesson OA1-12, Extensions 5, “Miss B asks students who are wearing shoes with laces to stand in a line. She counts 3 people. She then asks students who are not wearing shoes with laces to stand in a line beside them, She counts 3 extra people in that line. How many people are not wearing shoes with laces? a) Pretend counters are people and then act out the story to answer the question. b) Draw stick people to answer the question. c) Did you get the same answer for parts a) and b)? d) In pairs, explain why your answer to parts a) and b) are the same.” (1.OA.6) Students are developing conceptual understanding while making connections as to why the answers to part a and b are the same.
- Teacher Resource, Part 2, Unit 1, Lesson NBT1-17, students use tens and ones blocks to compare two numbers. Students represent numbers up to 50 and compare numbers with the same number of tens, the same number of ones, and different numbers of tens and ones. (1.NBT.2,3)
- Teacher Resource, Part 2, Unit 2, Lesson NBT1-28, Activity 1, “Emphasize that students can find 50 + 20 by counting the number of tens. (5 + 2) 50 + 20 = 5 tens + 2 tens = 7 tens = 70.” (1.NBT.2,4) In this activity, students apply the concept of adding one digit numbers to adding tens blocks.
- Teacher Resource, Part 2, Unit 5, Lesson G1-1, Extension 2, “In groups of three or four, students use 10 feet of yarn or string to create shapes. As students work, ASK: How many vertices will your shape have? How many sides?” (1.G.1)
The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. The Extension questions, Activity Centers, Assessment and Practice Books, and Black Line Masters all provide opportunities for students to independently demonstrate conceptual understanding. Examples include:
- Assessment and Practice Book 1, Lesson NBT1-4, Problem 2, “15 is ___tens block and ___ ones blocks.” (1.NBT.2) This helps build the foundation for place value that is needed for larger numbers. Students count the number of tens blocks and ones blocks to answer how many tens blocks and ones blocks make up a number. It is noted in the Teacher Resource that students may place actual tens and ones blocks on the chart and count how many they use.
- Teacher Resource, Part 2, Unit 2, Lesson NBT1-35, Extensions 3, “Beth says ‘10 more than 37 is 47.’ She writes 37 + 10 = 47. Do they mean the same thing? Explain how you know.” Students show their place value understanding of tens and ones to add 10 more to a number. (1.NBT.4,5)
- Teacher Resource, Part 2, Unit 6, Lesson MD-20, Extension 3, “a) How did I sort these shapes? Group A: cylinder, cube, rectangle, square Group B: cone, triangle b) In pairs, explain your answers to part a). Do you agree with each other? Discuss why or why not.” (1.MD.4 and 1.G.1)
- Teacher Resource, Part 2, Unit 3, Lesson OA1-59, Extension 1, Students create subtraction word problems for the pictures on BLM Apple Trees (L-106). Students write a number sentence and solve the problem. (1.OA.1)
Indicator 2b
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
The instructional materials reviewed for JUMP Math Grade 1 meet expectations for attending to the standards that set an expectation of procedural skill and fluency.
The Teacher Resource states, “Mental math is a mathematical framework that includes number sense, computational fluency, and the application of number concepts through purposeful and varied practice, not just rote memorization. Essential mental math concepts, skills, exercises, and assessments that can be used throughout the year are presented in this section.” The Mental Math section contains addition and subtraction fluency strategies such as “adding 2 to an even number” or “add a one-digit number to 10 by replacing the zero in 10 by the one-digit number.” This section also includes exercises, checklists, and the directions for a modified “Go Fish” game.
It was also recommended in the Instructional Strategies section under “Use daily routines” to “Establish predictable routines that support deliberate practice of math fluency. For example, incorporate exercises from the Mental Math section into your daily schedule.”
While procedural skill and fluency are not explicitly identified or labeled, the instructional materials develop procedural skill and fluency throughout the grade level. Opportunities to develop, practice, and demonstrate fluency are provided extensively throughout the materials. Examples include:
- Teacher Resource, Part 1, Unit 3, Lesson OA1-22, “Teach students to complete addition sentences such as 7 + ___ = 10 by holding up seven fingers and using the fact that they have 10 fingers altogether, so the number of fingers not up goes in the blank.” (1.OA.5,6)
- Teacher Resource, Part 1, Unit 6, Lesson OA1-44, Problem 3, “7 + 8 = 7 + __ + __ = 10 + __.” (1.OA.3,6) Students add by breaking up a one-digit number to make 10 with a given addend. Students first represent this with blocks, then with numbers rather than objects, and finally mentally. Students use BLM Using 10 to Add to practice adding numbers across 10.
- Teacher Resource, Part 2, Unit 2, Lesson NBT1-33, Activity, “Each student rolls a pair of dice to create a two-digit number. Students record their number and write numbers that are 1 more, 1 less, 10 more, and 10 less.” (1.NBT.5)
- Teacher Resource, Part 2, Unit 3, Lesson OA1-70, Exercise 2, “Find the unknown number by writing a related addition sentence. a) 12 -???? = 8 b) 13 - ????= 7 c) 14 - ????= 9.” (1.OA.4-6) Students use their fluency within 10 to solve number sentences by making 10, finding unknowns using 10, and solving subtraction sentences by solving related addition sentences.
The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade level. Examples include:
- Assessment and Practice Book 1, Lesson OA1-38, Problem 10, “__ + __ = 14 so 14 - 7 = __.” (1.OA.4,6) Students use a related addition fact within 10 to subtract (Problems 1-6) and doubles up to 20 to subtract (Problems 9-16).
- Assessment and Practice Book 2, Lesson NBT1-41, Problems 15-19, students separate the tens and ones to add by writing the number of tens and ones in a place value chart. (1.NBT.4)
- Assessment and Practice Book 2, Lesson MD1-24, Problem 4, “How many more students like apples than bananas?” (1.MD.4; 1.OA.1,6) Problems 4-6, students use addition and subtraction within 20 to answer questions about a picture graph.
Indicator 2c
Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
The instructional materials reviewed for JUMP Math Grade 1 partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied; however, there are missed opportunities concerning the variety of problem types called for by the Standards.
The instructional materials provide students opportunities to engage in routine application of grade-level mathematics. The 1.OA.A cluster heading calls for students to “Represent and solve problems involving addition and subtraction.” Grade 1 standard 1.OA.1 calls for students to “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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem” (see Table 1, CCSSM page 88). All problem types are not represented equally, as there is a missed opportunity for students to work with both addends unknown or starts unknown problems.
Students are given multiple opportunities to practice representing addition and subtraction problems with drawings and objects in routine applications. Both addends unknown and starts unknown situations are underrepresented in the materials. Examples of other problem types include:
- Teacher Resource, Part 1, Unit 3, Lesson OA1-26, Extension 3, “There are monkeys swinging in 3 trees. There are 9 monkeys altogether swinging in the trees. One of the trees has 2 monkeys swinging in it. a) How many monkeys might be swinging in each of the other two trees? b) in pairs, explain how you did part a). Say what you used for the monkeys and the trees.” (1.OA.2,3,6)
- Teacher Resource, Part 1, Unit 6, Lesson OA1-51, “A pet store has 5 cats. The store has 4 dogs. How many animals are in the pet store?” (1.OA.1)
- Teacher Resource, Part 2, Unit 2, Lesson NBT1-38, “23 students are in the gym. 5 more children come in. How many students are in the gym now? Ask students to find the answer by counting on.” (1.NBT.4)
- Teacher Resource, Part 2, Unit 3, Lesson OA1-69, Exercises: “a) Mark buys 2 muffins. Emma buys 3 muffins. Ron buys 1 muffin. How many muffins do they buy altogether? b) 8 turtles are on a log. 3 crawl away. 3 more crawl away. How many turtles are on the log now? c) 9 horses are in a field. 2 horses join them. 3 horses run away. How many horses are in the field now?” (1.OA.1,2,4,8)
The instructional materials have some opportunities for students to engage in non-routine application throughout the grade level. Examples of non-routine applications include:
- Teacher Resource, Part 1, Unit 2, Lesson NBT1-8, Extension 2, “a) 8 people line up to play soccer. 3 fewer people line up to skip rope. How many people are lined up altogether? Use cubes to act out the story. b) In pairs, explain how you know your answer is correct? Do you agree with each other? Discuss why or why not.” (1.NBT.3)
- Teacher Resource, Part 1, Unit 6, Lesson OA1-46, Extension 2, “Solve the problem. Use any tool you think will help. Then write your answer using a number sentence and a word sentence. a) Sal lost 3 stickers. He had 15 stickers to start. Now how many stickers does he have? b) Sal got 3 stickers for his birthday. He had 15 stickers before his birthday. Now how many stickers does he have? c) In pairs, take turns explaining what tools you used in parts a) and b) and why you used it. d) In pairs, take turns explaining what the symbols in your number sentences mean.” (1.OA.6)
- Teacher Resource, Part 2, Unit 3, Lesson OA1-68, Extension 4, “Josh has some buttons. Cathy has 1 more button than Josh. Sandy has 3 more buttons than Cathy. Who has more buttons, Josh or Sandy? How many more? Use any tool you think will help.” (1.OA.1,4)
The Teacher Resource states, “The deepest work in a JUMP math lesson often happens in the extension questions, which appear at the end of most lesson plans.” It goes on to say, “All students should be given the opportunity to engage with the extension questions.” However, there are instances where the extension questions state that they are for students who know a particular skill. Examples include:
- Teacher Resource, Part 1, Unit 1, Lesson OA1-1 “Extensions 2 and 3 are for students who can write numbers.” Extension 2 states, “Write the numbers in the correct order. a) 2, 1, 3 b) 4, 6, 5 c) 9, 7, 6, 8 .”
- Teacher Resource, Part 1, Unit 2, Lesson NBT1-7, Extension 2 states, “NOTE: Extension 2 is for students who know how to count in the twenties. Circle the greater number. a) 21 or 25 b) 27 or 24 c) 29 or 20 d) 17 or 20.”
- Teacher Resource, Part 1, Unit 2, Lesson NBT1-9, Extension states, “NOTE: This extension is for students who know how to count in the twenties. a) Make a sentence using ‘is greater than’ and the following pairs of numbers: i) 25 and 27 ii)29 and 22 iii) 17 and 25 b) Make a sentence using ‘is less than’ and the following pairs of numbers: i) 24 and 28 ii) 25 and 21 iii) 12 and 23.”
Indicator 2d
Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
The instructional materials reviewed for JUMP Math Grade 1 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. The instructional materials address specific aspects of rigor, and the materials integrate aspects of rigor, however, not all aspects are addressed equally. Heavy emphasis is placed on conceptual understanding and procedural skill and fluency. While students are given opportunities to engage with application problems throughout the materials, these are often teacher directed.
All three aspects of rigor are present independently throughout the materials. Examples include:
- Conceptual Understanding: Teacher Resource, Part 2, Unit 1, Lesson NBT1-14, Exercises: “Ellen collects 10 leaves every day. a) How many leaves does she have after 3 days? b) How many leaves does she have after 8 days? c) How many leaves does she have after 10 days?” Students demonstrate conceptual understanding in this lesson.
- Procedural Skill and Fluency: Teacher Resource, Part 1, Unit 6, Lesson OA1-42, students add two one-digit numbers with sums greater than ten by first regrouping to make a 10. Students continue to practice this procedural skill and fluency in the accompanying Assessment and Practice Book pages.
- Application: Teacher Resource, Part 2, Unit 3, Lesson OA1-58, Extension 5, “A birthday cake is cut into 12 pieces. There are 10 people at the birthday party. After everyone who wants a piece has one, there are 5 pieces left. How many people at the party didn’t want a piece of cake? a) In pairs, talk about the problem. What do you know about the pieces of cake? What do you know about the people at the party? What do you need to find out? How are you going to model the problem? b) Answer the question by yourself. Model what each step means in the story.”
Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials; however, a heavy emphasis is placed on conceptual understanding and procedural skill and fluency. Examples of multiple aspects of rigor that are engaged simultaneously include:
- Teacher Resource, Part 1, Unit 4, Lesson OA1-33, “Draw a number line from 0 to 10 on the board. Ask students to come to the board to show how they would subtract 8 - 3, 6 - 2, 9 - 4, 5 - 3, 8 - 4, and 7 - 2.” Students demonstrate conceptual understanding and procedural skill and fluency when they use number lines to subtract. Students also practice this skill in the accompanying Assessment and Practice Book pages.
- Teacher Resource, Part 1, Unit 6, Lesson OA1-53, Extension 2, “a) Before my birthday party, I got 7 presents. At my birthday party, I got 8 more presents. Then my aunt and uncle came over and I got 1 more birthday present. How many presents do I have now? Write a number sentence to show your answer. b) In pairs explain how you found the answer. Do you agree with each other? Discuss why or why not.” This lesson incorporates application and procedural skill and fluency when students determine whether they need to add or subtract to solve word problems.
- Teacher Resource, Part 2, Unit 2, Lesson NBT1-29, Exercises “Draw and cross out tens to subtract. a) 30 - 20 b) 50 - 30 c) 60 - 40.” Students demonstrate conceptual understanding and procedural skill and fluency when they draw base ten blocks and cross out tens to subtract pairs of two-digit multiples of 10.
Criterion 2.2: Math Practices
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
The instructional materials reviewed for JUMP Math Grade 1 partially meet expectations for practice-content connections. Although the instructional materials meet expectations for identifying and using the MPs to enrich mathematics content, they partially attend to the full meaning of each practice standard. The instructional materials partially attend to the specialized language of mathematics.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
The instructional materials reviewed for JUMP Math Grade 1 meet expectations for identifying the Standards for Mathematical Practice (MPs) and using them to enrich mathematics content within and throughout the grade level.
All 8 MPs are clearly identified throughout the materials, with few or no exceptions. Examples include:
- The MPs are identified at the beginning of each unit in the “Mathematical Practices in this Unit”
- “Mathematical Practices in this Unit” includes suggestions as to how students might demonstrate an MP. For example, Teacher Resource, Part 2, Unit 5, “In G1-10 Extension 5, students create designs from pattern blocks. They look for and make use of structure when they notice that some blocks have the same side lengths that fit well together and can be used to make neat designs.” (MP7)
- “Mathematical Practices in this Unit” gives the MPs that can be assessed in the unit.
- The MPs are also identified in the materials in the lesson margins.
- In optional Problem Solving Lessons designed to develop specific problem-solving strategies, MPs are identified in specific components/ problems in the lesson.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The instructional materials reviewed for JUMP Math Grade 1 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of MPs 4 and 7.
Examples of the materials carefully attending to the meaning of some MPs include:
- MP1: Teacher Resource, Part 1, Unit 5, Lesson MD1-4, Extension 3, In part f, students complete BLM Taller and Shorter. Students make sense of the problems and persevere in solving them when they put three names in order from tallest to shortest based on clues that are given.
- MP2: Teacher Resource, Part 1, Unit 3, Lesson OA1-14,“Ask a student to put dots on a domino to show 3 + 6. Thyen ask how you could use the same domino to show 6 + 3. ASK: What could I do to this domino to make it show 6 + 3 instead of 3 + 6? Demonstrate turning it around. ASK: Does turning the domino around change the total number of dots on it? (no) How does turning the domino around change the addition sentence? (it becomes 6 + 3 = 9) What stays the same and what changes? (the numbers being added and the total stays the same, but the order of the numbers being added changes) How do those numbers change? (the order of the numbers is reversed or switched) Distribute dominoes and have students turn them around to write two addition sentences.” Students reason abstractly and quantitatively when they rotate dominoes to help them understand why you can change the order of the addends but the total stays the same.
- MP5: Teacher Resource, Part 2, Unit 4, Lesson MD1-13, Extension 3, “Lynn has 28 marbles. Greg has 22 marbles. How many marbles should Lynn give to Greg so that they have the same number of marbles? Use any tool you think will help. Explain what each step means in the story.” Students use tools strategically to help them solve a problem about marbles.
- MP6: Teacher Resource, Part 1, Unit 4, Lesson OA1-39, Extension 2, “Students attend to precision when they explain how a picture shows that 14 - 4 - 2 is the same as 14 - 6 and then express that mathematically by using the equal sign.”
- MP8: Teacher Resource, Part 2, Unit 2, Lesson NBT1-31, Extension 1, “Students look for and express regularity in repeated reasoning when they use tens and ones blocks to subtract 20 from a number in the twenties and then recognize that the answer is always the ones digit of the number in the twenties, because they are always removing both the tens blocks.”
Examples of the materials not carefully attending to the meaning of MPs 4 and 7 include:
- MP4: Teacher Resource, Part 2, Unit 2, Lesson NBT1-41, Extensions, problem 2, “Mindy is a farmer. She has cows and pigs. There are 37 cows on the farm. There are 8 pigs on the farm. She sells 3 animals. Now how many animals are on the farm? Use number sentences to show your work. Explain what each step means in the story.” Students do not model with mathematics since they are told what mathematical model to use.
- MP7: Teacher Resource, Part 2, Unit 3, Lesson OA1-64, Extensions, problem 3, “Draw a part-total picture to solve the problem. a) There are 60 fish in a pond. 20 are green and the rest are brown How many are brown?” This problem doesn’t require students to use structure to solve.
- MP7: Teacher Resource, Part 2, Unit 5, Lesson G1-6, Extensions, problem 2, “A shape is missing from the square. Which shape is it? Explain.” A rectangle is show with a missing piece and different triangles are given as possible answers. Students do not use structure to solve the problem as they match the missing piece.
Indicator 2g
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2g.i
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
The instructional materials reviewed for JUMP Math Grade 1 partially meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
There are few opportunities in the Teacher Resource or the Assessment & Practice for students to construct viable arguments or analyze the arguments or the work of others. MP3 is identified in the margins of the lesson. Examples of where the materials prompt students to construct viable arguments or analyze the arguments of others include, but are not limited to:
- Teacher Resource, Part 2, Unit 6, Lesson MD1-21, Extension 3, “If you know 10 - 7 = 3, how can you find 20 - 7 without subtracting? Explain. b) In pairs, explain your answer to part a). Do you agree with each other? Discuss why or why not.”
- Teacher Resource, Part 1, Unit 2, Lesson NBT1-4, Extension 2, students draw two groups of 5 dots and discuss, in groups, if you start at 5 and count on 5 more do you always get to 10. “Do you agree with each other? Why or why not? If students counted 5 numbers starting at 5 (5, 6, 7, 8, 9) instead of counting 5 numbers after 5 (6, 7, 8, 9, 10), their partners will have the opportunity to critique incorrect reasoning. NOTE: Encourage partners to ask questions and challenge each other’s thinking (MP.3)-see page A-43 for sample sentences and question stems.”
- Teacher Resource, Part 1, Unit 5, Lesson MD1-9, Extension 1, “Maria creates a path with 6 cubes by tracing along some sides of the figure. She thinks the path is 6 cubes long. Jake measures Maria’s path and thinks it is 8 cubes long. How long is the path? Who is correct? Explain.” A picture is included.
- Teacher Resource, Part 2, Unit 5, Lesson G1-3, Extension 3, “Alex solved the given problem. Do you agree with Alex’s thinking? Why or why not. a) Matt gives away 11 books. He has 8 books left. How many did he have to start with? Alex says: He has 8 books left and “left” means subtract, so I should subtract 11 - 8. He started with 3 books. b) Lily gives away 5 shirts. Then she gives away 3 more shirts. How many shirts did she give away altogether? Alex says: She gives away 3 shirts, and when you give things away, the number gets smaller, so I should subtract 5 - 3. She has 2 shirts.” Students evaluate the solutions given by Alex and determine if they agree or disagree and why.
Examples where the materials miss opportunities to prompt students to construct viable arguments or analyze the arguments of others include, but are not limited to:
- Teacher Resource, Part 1, Unit 6, Lesson OA1-53, Extension 2, “a) Before my birthday party, I got 7 presents. At my birthday party, I got 8 more presents. Then my aunt and uncle came over and I got 1 more birthday present. How many presents do I have now? Write a number sentence to show your answer. b) In pairs, explain how you found the answer. Do you agree with each other? Discuss why or why not.” Explaining how one finds an answer is not students creating a mathematical argument.
- Teacher Resource, Part 2, Unit 1, Lesson NBT1-22, Extension 2, Students determine which line is longer using clues and explain how they know. “a) Can you tell which line is longer using the clues? Explain. Clue A: The green line is longer than the red line. Clue B: The red line is shorter than the yellow line. b) In pairs, explain your answers to part a). Do you agree with each other? Discuss why or why not.” Explaining how students found an answer is not students creating a mathematical argument.
Indicator 2g.ii
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
The instructional materials reviewed for JUMP Math Grade 1 partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. While students are given opportunities to construct viable arguments and analyze the reasoning of others, the materials provide limited assistance to teachers in engaging students in both constructing viable arguments and analyzing the arguments of others.
Teacher Resource, Part 1 states, “When students work with a partner, many of them will benefit from some guidance, such as displaying question or sentence stems on the board to encourage partners to understand and challenge each other’s thinking, use of vocabulary, or choice of tools or strategies. For example:
- I did ___ the same way but got a different answer. Let’s compare our work.
- What does __ mean?
- Why is __ true?
- Why do you think that__?
- I don’t understand__. Can you explain it a different way?
- Why did you use__? (for example, a particular strategy or tool)
- How did you come up with__? (for example, an idea or strategy)
Once all students have answered the ASK question, have volunteers articulate their thinking to the whole class so other students can benefit from hearing their strategies.” While these generic question and sentence stems are provided, there is no further guidance or examples for how or when they should be used.
The majority of opportunities for students to engage in MP3 occur in the extension problems. These include sample answers and often refer teachers back to the prompts listed on page A-43, but give no further guidance on how to build students ability to construct an argument around their thinking or how to critique the reasoning of others. Teachers are often prompted, “In pairs, have students explain their thinking. Do they agree with each other? Discuss why or why not”, however, no guidance is given as to which questions to ask in regards to that specific problem, how to help the students defend their answer, or why an answer makes sense. Additionally, materials include some sample explanations relating to the correct answer being given, but do not always give guidance for teachers on how to effectively guide the conversation if an incorrect answer is being defended. Examples include:
- Teacher Resource, Part 1, Unit 6, Lesson OA1-42, Extension 2, “a) Draw circles to show 3 + 3. b) Draw circles like you did for part a), but show 4 + 3. c) Partner A: Draw circles to show 5 + 5. Change your picture just enough to show 6 + 5. Use a different color to show the change. Partner B: Draw circles to show 4 + 4. Change your picture just enough to show 5 + 4. Use a different color to show the change. Partners A and B: Talk about what you did the same way. d) How can you find 7 + 4 if you know 6 + 4 = 10? e) In pairs, explain your answers to part d). Do you agree with each other? Why or why not?” Sample answers are given. The text then states, “NOTE: In part e) encourage partners to ask questions to understand and challenge each other’s thinking (MP.3)-See page A-43 for sample sentence and question stems.” No suggestions are given for questions students could ask their partners, which questions from page A-43 are relevant to this problem, or how students could defend their thinking.
- Teacher Resource, Part 2, Unit 2, Lesson NBT1-40, Extension 3, “Peter says that 35 < 28 because when he made the numbers with tens and ones blocks, he needed more blocks to make 28 than to make 35. Do you agree with Peter? Why or why not?" There is no guidance given for the teacher in how to assist students in analyzing Peter’s reasoning, or how to guide the conversation when they have the misconception that Peter is correct. "Answer: No. Sample explanations:
- Any number in the 30s is greater than 28 because 28 is only in the 20s, so you say it first when counting.
- 35 has 3 tens and 28 has 2 tens and 8 ones, which is less than 3 tens. Eight ones is less than the extra ten that 35 has.
- It doesn’t matter how many blocks are used, but how many ones there are in the blocks. Three tens blocks means more ones than 2 tens blocks and 8 ones blocks.”
- Teacher Resource, Part 2, Unit 4, Lesson MD1-13, Extension 4, “Ivan, Karen, and Carl each solve the problem shown below: There are 8 balloons. There are 3 fewer stickers than balloons. How many stickers are there? Ivan says: 8 + 3 = 11, so there are 11 stickers. Karen says: 8 - 3 = 5, so there are 5 stickers. Carl says: 8 - 3 = 6, so there are 6 stickers. Who do you agree with? What mistakes did the other people make?” A sample answer is given, however, there is no additional guidance for teachers to help students construct an argument about who they think is correct or how to determine the mistakes that each person made.
- Teacher Resource, Part 2, Unit 6, Lesson MD1-21, Extension 3, “a) If you know 10 - 7 = 3, how can you find 20 - 7 without subtracting? Explain. b) In pairs, explain your answers to part a). Do you agree with each other? Discuss why or why not. Selected sample answer: a) 20 is 10 more than 10, so 20 - 7 is 10 more than 10 - 7. Since 10 - 7 = 3, then 20 - 7 = 13.” While a sample answer is provided, there is no guidance for the teacher to help students construct a viable argument or how to discuss their answers with a partner.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The instructional materials reviewed for JUMP Math Grade 1 partially meet expectations for explicitly attending to the specialized language of mathematics.
Accurate mathematics vocabulary is present in the materials; however, while vocabulary is identified throughout the materials, there is no explicit directions for instruction of the vocabulary in the teacher materials of the lesson. Examples include, but are not limited to:
- Vocabulary is identified in the “Terminology” section at the beginning of each unit.
- “Vocabulary” is identified at the beginning of each lesson.
- The vocabulary words and definitions are bold within the lesson.
- There is not a glossary.
- There is not a place for the students to practice the new vocabulary in the lessons.