K-2nd Grade - Gateway 2

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for supporting the intentional development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.

Conceptual understanding is developed throughout the course using a three-part lesson structure. Each lesson has a Mind’s On Activity, an Action Task, and a Consolidate Activity. During teacher guidance in the Action task, the "And the Point Is" notes clarify the specific conceptual goal behind each activity. Students have individual opportunities to demonstrate conceptual understanding through performance tasks, wonder tasks, and your turn problems. Conceptual understanding is assessed through math routines such as Math Congress and Gallery Walks, Exit Tickets, and Self/Peer Assessment. Examples include:

• Kindergarten, Topic 7: Representing Addition and Subtraction, Lesson 3, Action Task, students develop conceptual understanding in using addition to describe a larger group made up of two smaller groups. Question 1 states, “Say: Use the part-part-whole model to show how many of each ball and how many in all. 1. How many basketballs are in the bin? How many soccer balls? How would you show this using addition?” Teacher Guidance, Action, Using the Action Part of the Lesson states, “Use one of these ideas for the main part of the lesson: Present the activity digitally. Set up a similar situation using bins of two types of balls (or other items) in the classroom and ask similar questions. Create a similar activity that builds on observations you make of students as they are engaged in play or talk in the classroom. You might provide students with actual balls, two colors of counters, ten-frames, and number paths to model the problem. Students might also use other strategies, such as counting using fingers.” Teacher Guidance, Probing and Extending states, “You could ask questions such as these of a small group to probe, challenge, and extend students’ thinking: If there were 9 balls, how many tennis balls and how many baseballs might there be? Would there be the same number of balls if you combined 2 baseballs and 7 tennis balls as 7 tennis balls and 2 baseballs? If there are 2 more tennis balls than baseballs in a bin, how many balls might there be?” (K.OA.1) 

• Grade 1, Topic 10: Subtracting within 20, Exit Ticket, students demonstrate conceptual understanding as they use a diagram to identify related addition and subtraction equations within 20 and explain the relationship between the two. The materials state, “Write one addition and one subtraction equation you see using the diagram.”Students are given a whole of 15 and one known part of 9, with the other part left blank to determine. (1.OA.6)

• Grade 2, Topic 3: Working with Equal Groups, Lesson 1, Minds On Activity, Questions 1-3 students develop conceptual understanding of even and odd numbers by using concrete representations to explore equal groups of objects. Question 1 states, “Choose a number of counters from 10 to 20.” Question 2 states, “Try to decompose your counters into groups of 2. Did it work?” Question 3 states, “Repeat the activity with 2 other numbers.” Teacher Experience, After the Minds On Activity states, “With students, use the first two rows of a hundred chart to mark the numbers that worked. [They will all fall into the 2, 4, 6, 8, or 10 column.] Tell students that these numbers are called even because they can be grouped into 2s. Point out the numbers that cannot be grouped into 2s. [They will all fall into the 1, 3, 5, 7, or 9 column.] Tell students that these numbers are called odd. Odd is the opposite of even.” Lesson 2, Minds On Activity and Action Task, students develop conceptual understanding of repeated addition as a representation of arrays. Questions 1 and 2 state, “What addition equation tells how many helmets there are?” and “What addition equation tells how many footballs there are?” Action Task, Question 1 states, “The number of stickers in Package A is 3 + 3 + 3 + 3 or 4 + 4 + 4. Why do both make sense?” (2.OA.C)

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for providing intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.

The materials include multiple pathways for fluency development, such as Number Talks and Data Talks, which target fluency and flexibility in thinking about numbers and operations while allowing students to use their own problem-solving strategies. Students engage in practice through Your Turn activities that provide procedural practice opportunities. Fluency is embedded within the three-part lesson structure, Minds On, Action Task, and Consolidate, and is assessed within the program’s assessment system, which includes specific skill and concept questions that help teachers monitor and support students’ procedural fluency development. Examples include:

• Kindergarten, Topic 8: Adding and Subtracting, Lesson 8, Action Task, students develop procedural skill and fluency as they add and subtract within 5. Question 1 states, “Say: Use the numbers in the box to complete the story. Then write an equation to show the addition. 1. I saw 1 snail. _____ joined it and now there are ____ snails.” The numbers in the box are 1, 2, 3, and 4. Question 2 states, “Say: Use the numbers in the box to complete the story. Then write an equation to show the subtraction. 2. I saw 5 crabs. _____ left and now there are _____ crabs.” The numbers in the box are 5, 1, 2, 3. Teacher Guidance, Probing and Extending states, “You could ask questions such as these of a small group to probe, challenge, and extend students’ thinking: Is there more than one way to fill in the blanks? Could you put the numbers in any of the blanks and it will still make sense? Could you say that there are 3 crabs and 4 leave?” (K.OA.5)

• Grade 1, Topic 7: Adding within 20, Lesson 3, Additional Practice, students demonstrate procedural skill and fluency when using a make-10 strategy in addition situations. The directions state, “Write the number pair that adds to 10. Question 5. How does knowing that 3 + 7 is 10 help you figure out 3 + 9? Question 6. What make-10 fact or facts would help you figure out 8 + 7? Explain.” (1.OA.6)

• Grade 2, Topic 8: Adding and Subtracting Numbers Less Than 100, Lesson 1, Additional Practice, students demonstrate procedural skill and fluency with addition and subtraction of two-digit numbers as they select strategies and calculate sums or differences. The directions state, “Choose a strategy to add or subtract. Calculate the sum or difference. Question 1. 44 + 38 Question 2. 65 - 17 Question 3. 18 + 61 Question 4.71-32. Topic Your Turn, Question 1, “Write a subtraction expression that has the same answer as 47-29 but is easier to calculate.” Question 6, “How could you figure out 70-54 by adding?” (2.NBT.5)

The materials for Experience Math Kindergarten through Grade 2 meet expectations for supporting the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.

Multiple routine and non-routine applications of mathematics are included throughout the grade level, with single- and multi-step application problems embedded within the three-part lesson structure, Minds On, Action Task, and Consolidate. Students engage in Wonder Tasks, Making Connections Tasks, and Brain Benders. Wonder Tasks are three-act, problem-based activities in which students formulate questions about situations and communicate their thinking. Making Connections Tasks integrate concepts from multiple domains and provide opportunities for students to apply mathematical skills and concepts while solving complex, multi-part problems. Brain Benders present problem-solving opportunities in real-world contexts. Examples include:

Examples include:

• Kindergarten, Topic 9: Simple 2-D Shapes, Lesson 1, Action Task: students apply their understanding of 2-dimensional shapes to locate examples of the shapes throughout the classroom and school. Action Task states, “Say: Which of the shapes on your checklist did you find? Where did you find them? Show your shapes. Teacher Guidance, Using the Action Part of the Lesson states, “Use one of these ideas for the main part of the lesson: Present the activity digitally. Explain to the students that they are going on a shape hunt. Provide students with Checkpoint 1 from the Resource Master Shape Finding Checklists. Go over the shape names with students, pointing out the pictures and attributes of each shape. You might provide digital tools so that students can take photos of where they find the shapes, or you might ask them to draw shapes they find.” Teacher Guidance, Probing and Extending states, “You could ask questions such as these of a small group to probe, challenge, and extend students’ thinking: Where did you find circles? Did any of the places where you found circles surprise you? Did you have any tiles? What shapes were the tiles? Did you find any rectangles on the wall? Did you find any shapes when you looked at flowers?” (K.G.1)

• Grade 1, Topic 4: Meanings of Addition and Subtraction, End of Topic Resources, Performance Task, students apply their understanding as they independently engage in a non-routine word problem involving addition and subtraction. Question 1 states, “There are some animals in a field. If 4 animals leave, there will be 9 animals. How many animals are there? Did you add or subtract to figure this out? Explain.” (1.OA.1)

• Grade 2, Topic 7: Time and Money, Lesson 3, Your Turn, Additional Practice, students apply their understanding of money as they represent the same amount in different ways to solve problems. Question 3 states, “How could you represent 87¢ using 6 coins?” (2.MD.8)

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade as reflected by the standards.

Multiple aspects of rigor are engaged simultaneously across the materials to develop students' mathematical understanding of individual lessons. Each topic within the curriculum supports a variety of instructional approaches that incorporate conceptual understanding, procedural fluency, and application in a balanced way. 

For example:

• Kindergarten, Topic 7: Representing Addition and Subtraction, Explorations, Exploration 7-D, students demonstrate conceptual understanding and application as they focus on takeaway or separating subtraction situations. Action Task states, “[Play the Action Task Video] Say: 1. How many grapes will Alice have left after she eats 3 of them? How do you know? 2. Use subtraction to tell what happened. [Play the Action Task Video again.] 3. How many are left after she eats another 1? How do you know? 4. Use subtraction to tell what happened.” (K.OA.1, K.OA.2)

• Grade 1, Topic 2: Representing Numbers, Lesson 6, Action Task: students demonstrate conceptual understanding and application as they compose numbers from limited options, and they decompose numbers in various ways. Question 1 states, “Make some towers of 5 counters. Make some towers of 8 counters.” Question 2 states, “Put a few towers into a group. How many counters are in the group?” Question 3 states, “Repeat the task 2 more times. Make different numbers.” Question 4 states, “What numbers can you compose using 5s and 8s?” (1.NBT.B) 

• Grade 2, Topic 6: Subtracting from 2-Digit Numbers, Lesson 3, Action Task, students engage in all three aspects of rigor, conceptual understanding, procedural fluency, and application as they use base-ten blocks to subtract, and apply subtraction to an authentic recycling context where students choose numbers of recycling boxes and determine how many still need to be emptied. Question 1 states, “Choose a number of recycling boxes between 40 and 50. How many boxes might be empty? Choose between 10 and 30. Figure out how many boxes still need to be emptied. Explain: How do you know your answer makes sense?” Teacher Guidance, Conversation Starters states, “Could 26 boxes be empty? Could 34? Would an answer close to 50 make sense or not? How could you model your number of boxes with base-ten blocks?” (2.NBT.5)

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students across the K-2 grade band engage with MP1 throughout the year. MP1 is found in the three-part lesson structure as students make sense of problems during Minds On discussions, persevere through open-ended Action Tasks, and reflect on strategies in the Consolidate portion of lessons. Essential Understandings connect new learning to big ideas, helping students analyze problem information and plan solution pathways, while Parallel Tasks provide differentiated entry points that allow all learners to engage in productive struggle. Students regularly interpret conditions in real-world problems, compare quantities, and choose tools to solve problems, while teacher supports such as prompts, embedded coaching videos, and “Probing and Extending” questions guide students in evaluating their solutions and asking “Does this make sense?” 

Across the grades, students engage in open-ended tasks that support key components of MP1, including sense-making, strategy development, and perseverance. These tasks prompt them to make sense of mathematical situations, develop and revise strategies, and persist through challenges. They are encouraged to analyze problems by engaging with the information and questions presented, using strategies that make sense to them, monitoring and evaluating their progress, determining whether their answers are reasonable, reflecting on and revising their approaches, and increasingly devising strategies independently. 

An example in Kindergarten includes:

• Topic 4: Comparing Quantities, Lesson 3, Student Experience Book, students interpret the context (bananas, apples, oranges), represent the quantities using counters or number paths, and determine possible solutions that are more than or fewer than a given set. They explain their thinking by answering “How many could he have?” and “How do you know?” Students evaluate whether their answers make sense by comparing groups and justifying their reasoning. Student Experience Book, Action Task states, “1. Kyle has fewer bananas than these. How many bananas could he have? How do you know? 2. Kyle has more apples than these. How many apples could he have? How do you know? 3. Kyle has fewer oranges than these. How many oranges could he have? How do you know?” Teacher Experience Guide, Action states, “Provide counters for students to use to represent the bananas, apples, and oranges, and provide access to number paths for students to use if they wish.” Teacher Experience Guide, Probing and Extending states, “You could ask questions such as these of a small group to probe, challenge, and extend students’ thinking: Count Kyle’s bananas. Kelley has a greater number of grapes than the number of Kyle’s bananas. How many grapes does Kelley have? Jordan has an equal number of mangoes as Kyle has bananas. How many mangoes does Jordan have? Count Kyle’s apples. Sasha has fewer strawberries than the number of Kyle’s apples. How many strawberries does Sasha have? Count Kyle’s oranges. Raven has a greater number of blueberries than the number of Kyle’s oranges. How many blueberries does Raven have? Kenji has a greater number of raspberries than Kyle has apples, but he does not have as many raspberries as Kyle has bananas. How many raspberries does Kenji have?” Teacher Experience Guide, Teacher Guidance, Providing Feedback states, “You can gain insight into what students are thinking by asking questions based on what they do or say. For example, if a student shows 8 as more than 3, you might respond by asking, How is 8 more than 3?”

An example in Grade 1 includes:

• Topic 6: Describing and Sorting Shapes, Lesson 2, Student Experience book, students consider the conditions given in the problem to determine a correct solution for sorting the shapes, helping them make sense of the problem. Student Experience Book, Action Task, “1. Sort the shapes so that the half-circle and the triangle are not together. 2. Sort the shapes again. This time the half-circle and triangle should be together. 3. Sort the shapes again. One group should have 2 shapes. The other group should have 4 shapes. 4. Make up a sorting rule that has something to do with measuring. Sort the shapes using your rule.” Teacher Experience Guide, Action states, “Students must consider what the conditions presented in each problem really mean so that they can create appropriate sortings.” Teacher Experience Guide, And the Point is… states, “This Action Task helps students realize that any set of shapes can be sorted in several ways. Some of those ways involve non-defining attributes (things like color or size), and some involve defining attributes (things that are true about every instance of that shape).”

An example in Grade 2 includes:

• Topic 7: Time and Money, Lesson 3, Student Experience Book, students make sense and persevere when considering combinations of coins and bills to make given amounts of money. Students complete a table for three given item prices. They persevere to find representations using exactly five pieces of money, more than five pieces, and fewer than five pieces to represent the price. Students also work with the following prices: 25 cents, 42 cents, 62 cents, 40, 45, and $221. Teacher Experience Guide, Action states, “Students must be organized and persevere in considering the options for coin or bill combinations to see how five pieces of money are possible.” Student Experience Book, Action Task, “1. Choose a price. Show the price in 3 ways in the top row of the table. Use 5 pieces of money (coins or bills). Use more than 5 pieces, if possible. Use fewer than 5 pieces, if possible. 2. Complete Question 1 for 2 other prices in the table above.” Teacher Experience Book, And the Point is… states, “This Action Task: allows students to show each price with five pieces of money (i.e., coins or bills), if possible, which adds a problem-solving element to the task. Let students show the same amount using both more and fewer pieces of money, which helps to reinforce the understanding that every amount greater than 4\cent can be shown in more than one way.”

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for supporting the intentional development of MP2: Reason abstractly and quantitatively, in connection with grade-level content standards, as expected by the mathematical practice standards.

Students across the K-2 grade band engage with MP2 throughout the year. MP2 is found in the three-part lesson structure as students move between concrete, pictorial, and abstract representations during Minds On discussions, reason about quantities and relationships in open-ended Action Tasks, and justify strategies in the Consolidate portion of lessons. Essential Understandings connect new learning to big ideas, supporting students in decontextualizing and contextualizing problems, while Parallel Tasks provide differentiated entry points that allow all learners to represent quantities flexibly. Students regularly create and interpret representations, consider units, and explain the meaning of quantities, while teacher supports such as prompts, embedded coaching videos, and “Probing and Extending” questions guide students in deepening their reasoning and making connections between mathematical ideas 

Across the grades, students participate in tasks that support key components of MP2, including reasoning with quantities, representing situations symbolically, and interpreting the meaning of numbers and symbols in context. These tasks encourage students to consider the units involved in a problem, analyze the relationships between quantities, and connect real-world scenarios to mathematical representations. Teachers are guided to support this development by modeling the use of mathematical notation, asking clarifying and probing questions, and facilitating conversations that help students make connections between multiple representations. 

An example in Kindergarten includes:

• Topic 11: Comparing Measurements Directly, Lesson 1, Student Experience Book, students compare the heights and lengths of block towers, as well as the distances to different locations in the classroom. Student Experience Book, Action Task states, “1. Which tower is taller? Is it also higher? If the towers were laid down, which would make a longer line? Select two locations in your classroom from which to compare the distances. Adjust directions as needed.] Say: 2. Is it farther from the door to the window or from the door to the board? How do you know?” Teacher Experience Guide, Planning states, “Students reason to relate longer, taller, and farther.” Teacher Experience Guide, Action states, “For the tower activity, have students either look at the provided photo or build two towers of blocks: one that is tall and placed on the floor and another that is shorter, but placed on a higher surface than the taller one. For the activity involving distances in the classroom, you may choose to measure distances to different destinations in your classroom. Have masking tape available to make paths to the destinations. If necessary, show how to cut pieces of string the lengths of the paths so that the lengths of the paths can be compared.” Teacher Experience Guide, Probing and Extending states, “For the tower activity, you could ask questions such as these of a small group to probe, challenge, and extend students’ thinking: Is it easy to tell which tower is taller? What could you do to decide? For the activity involving distances in the classroom, you could ask questions such as these: Why was it useful to show the paths with masking tape to decide which was longer? How could you be sure which is longer?” Teacher Experience Guide, Teacher Guidance, Providing Feedback states, “You can gain insight into what students are thinking by asking questions based on what they do or say. For example, if a student compares two path lengths without ensuring the strings are straight, you might curl up the strings in different ways so that one time, one seems longer and the other time, the other seems longer. Then you might ask, Can one string be longer sometimes but not other times?”

An example in Grade 1 includes:

• Topic 4: Meanings of Addition and Subtraction, Lesson 3, Student Experience Book, students use subtraction within 20 and reason about a real-life situation to determine a solution. They also create additional word problems using subtraction to find the solution. Student Experience Book, Action Task states, “1. Solve this problem. There are 12 classes in Andrea’s school. 3 classes have gone away to see a play. How many classes are still in school? Show how you know. 2. Make up 2 problems you can solve the same way. Start each problem with a number less than 20. Do not make up problems about a school.” Teacher Experience Guide states, “Students relate the situation involving classes that are gone as well as their own two situations to symbolic subtractions.” Teacher Experience Guide, In This Task states, “Students solve a problem related to a takeaway situation and create their own subtraction problems.” Teacher Experience Guide, And the Point Is… states, “This Action Task is designed so students can use the subtraction problem they solved in Question 1 as a model for creating their own problems in Question 2. By creating their own problems, students show that they understand when subtraction can be used.” Teacher Experience Guide, Using the Action Task states, “When students use a number path to solve a subtraction problem, make sure they see the value of removing counters from the right so that the last counter is actually on the number that represents the amount remaining. Similarly, when students use ten-frames to solve a subtraction problem, make sure they see the value of removing counters from the right and the bottom to make it easier to quickly recognize the amount remaining.” Teacher Experience Guide, Connecting Ideas and Experiences states, “Ask students to find how many years until they reach 10 years old. Ask students to think of an item that they have in their room that they have between 5 and 10 of. Have them imagine a situation where they would take away some of those items where subtraction is involved.” Teacher Experience Guide, Conversation Starters include, “Could it be 5 classes left? Why or why not? Could it be 10 classes left? Why or why not? If your problems are not about a school, could it be about people at a different place? Could it be about animals?”

An example in Grade 2 includes:

• Topic 6: Subtracting from Two-Digit Numbers, Lesson 3, Student Experience Book, students create subtraction problems and then reason about their problem and solution and what it represents. Student Experience Book, Action Task states, “1. Choose a number of recycling boxes between 40 and 50. How many boxes might be empty? Choose between 10 and 30. Figure out how many boxes still need to be emptied. How do you know your answer makes sense. 2. Try this again using different numbers.” Teacher Experience Guide states, “Students make sense of the quantities chosen in the problem, create a mathematically coherent representation, and use what they know about operations to solve the problem. Teacher Experience Guide, Conversation Starters as students work: Could 26 boxes be empty? 34? Would an answer close to 50 make sense or not?”

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, in connection with grade-level content standards, as expected by the mathematical practice standards.

Students across the K-2 grade band engage with MP3 throughout the year. MP3 is found in the three-part lesson structure, students share and justify their reasoning during Minds On discussions, construct arguments and solve open-ended problems in Action Tasks, and critique the reasoning of others in the Consolidate portion of lessons. Open questions provide multiple entry points and create opportunities for students to explain their thinking and respond to peers, supporting the development of mathematical communication skills. Structured routines such as Math Congress and Gallery Walks provide spaces for students to examine, compare, and critique mathematical strategies. Students regularly explain why their reasoning is mathematically valid and analyze the reasoning of others, while teacher supports such as prompts, embedded coaching videos, and “Probing and Extending” questions guide students in deepening their arguments and making connections between mathematical ideas.

Across the grades, students participate in tasks that support key components of MP3. These include constructing mathematical arguments, analyzing errors in sample student work, and explaining or justifying their thinking orally or in writing using concrete models, drawings, numbers, or actions. Students are encouraged to listen to or read the arguments of others, evaluate their reasoning, and ask clarifying questions to strengthen or improve the argument. They also have opportunities to make and test conjectures as they solve problems. Teachers are guided to support this development by providing opportunities for students to engage in mathematical discourse, set clear expectations for explanation and justification, and compare different strategies or solutions. Teachers are prompted to ask clarifying and probing questions, support students in presenting their solutions as arguments, and facilitate discussions that help students reflect on and refine their reasoning.

An example in Kindergarten includes:

• Topic 5: Sorting, Lesson 3, Student Experience Book, students learn that objects can be described by belonging to a specific category, such as triangles, or by being identified as not belonging to that category, such as all shapes except triangles. Student Experience Book, Action Task states, “Say: 1. Why do you think the things that are in the circle are there? 2. Why are the other things not in the circle? 3. Are there more things in the circle or out? How many more?” Teacher Experience Guide, Planning states, “Students figure out why things are in or not in the circle.” Teacher Experience Guide, Action states, “If students need help to get started, you might want to provide categories such as toys you use in the sand and toys you do not use in the sand, and ask students if they agree that each item has been sorted correctly into these categories. Students can then be encouraged to discuss any other categories to show why the items are in and out of the circle.” Teacher Experience Guide, Connecting Ideas and Experiences states, “To encourage students to share their own unique perspectives, you might ask students if they’ve ever visited a beach. Discuss what students remember hearing and seeing at the beach. Students may share the activities they remember doing at the beach.” Teacher Experience Guide, Probing and Extending states, “You could ask questions such as these of a small group to probe, challenge, and extend students’ thinking: What do you think the circle is meant to help you see? What is the difference between the things in the circle and the things outside of it? What makes the things outside the circle alike? Do you think it is okay that all those things are together even though they are so different?” Teacher Experience Guide, Teacher Guidance, Providing Feedback states, “You can gain insight into what students are thinking by asking questions based on what they do or say. For example, if a student says that there needs to be more circles since balls should not go with a water bottle, you might respond by asking, Do balls and water bottles have anything in common that would let them go together?”

An example in Grade 1 includes:

• Topic 3: Comparing Numbers within 100, Lesson 1, Student Experience Book, students explain their reasoning as to which of the two sets of items is larger. Student Experience Book, Action Task states, “1. Pick up more than 10 items in one hand. Pick up more than 10 items in your other hand. Count how many are in each hand. Write your 2 numbers. Which is more? How do you know? Use the symbols > and < to describe your comparison. 2. Repeat Question 1 with other numbers of items. 3. Suppose you know that 12 < 15. Suppose you know that 15 < 23. How does that help you compare 12 and 23?” Teacher Experience Guide, Action states, “Students explain which number is greater and why. They also reason to decide how many comparisons they actually need to make.” Teacher Experience Guide, Success Criteria states, “Share or co-construct the Success Criteria during the Action Task.” Teacher Experience Guide, Conversation Starters states, “Do you always need to count to decide which is greater? If you know which is greater, do you know which is less? Why? What strategies can you use to compare amounts?” Teacher Experience Guide, Using the Action Task states, “Students work as a team to complete this task. Pairs can share materials, make comparisons together, and complete one worksheet.” Teacher Experience Guide, Using the Action Task also states, “As you circulate, encourage students to try a variety of strategies, including counting, matching, estimating, and using benchmarks. Encourage students to try the counting tools, though you may want to point out that using them is optional — other strategies (for example, counting and thinking through a series of comparisons) are just as good. Students will discuss their strategies in the Consolidate section. Note that students may get stuck after doing their two comparisons. For example, if they have figured out that 14 < 18 and that 18 < 29, they may still need to compare 14 and 29.”

An example in Grade 2 includes:

• Topic 14: Adding and Subtracting Greater Numbers, Lesson 2, Student Experience Book, students create an addition problem using two three-digit numbers. Student Experience Book, Action Task states, “1. Choose 2 three-digit numbers. Each number should have different amounts of hundreds, tens and ones. The sum of your numbers should be very close to 600. Explain why your addition strategy worked. 2. Repeat Question 1 with other pairs of three-digit numbers.” Teacher Experience Guide, Action states, “Students explain why their strategies make sense.” Teacher Experience Guide, And the Point Is states, “Students should see how changing one addend impacts the other, further strengthening their understanding of addition and why certain strategies work.” Teacher Experience Guide, Math Practices and Processes states, “Students explain why their strategies make sense.” Teacher Experience Guide, Success Criteria states, “Share or co-construct Success Criteria 1 to 2 during the Action Task.” Teacher Experience Guide, Using the Action Task states, “Discuss how ‘close to 600’ can include amounts less than or greater than 600. Include examples.” Teacher Experience Guide, After the Action Task states, “If it is not mentioned, discuss how students can handle situations where there are more than 10 ones or more than 10 tens when the numbers are added.” Teacher Experience Guide, Conversation Starters states, “What does it mean to be close to 600? Is there only one correct answer? How do you know? How have you added three-digit numbers before?”

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for supporting the intentional development of MP4: Model with mathematics, in connection with grade-level content standards, as expected by the mathematical practice standards.

Students across the K-2 grade band engage with MP4 throughout the year. MP4 is found in the three-part lesson structure as students identify real-world problems and create mathematical models during Minds On discussions, apply and test models in Action Tasks, and refine their models in the Consolidate portion of lessons. Wonder Tasks, Making Connections Tasks, and Brain Benders provide authentic contexts where students select and use mathematical tools and representations to solve problems. Students regularly build and interpret models with physical and virtual manipulatives, while teacher supports such as embedded coaching videos, “And the Point Is” sections, and “Probing and Extending” questions guide students in making connections between models and mathematical ideas.

Across the grades, students participate in tasks that support the intentional development of MP4, including putting problems or situations in their own words and identifying important information, using the math they know to solve problems and everyday situations, modeling the situation with appropriate representations and strategies, describing how their model relates to the problem situation, and checking whether their answer makes sense, revising the model when necessary.

An example in Kindergarten includes:

• Topic 10: Representing Numbers from 10 to 20, Exploration 10-C: Making Dominoes, Student Experience Book, students represent numbers by arranging counters on folded paper to create dominoes, showing a total of 10 or a teen number. They record their representations with markers and compare how different arrangements can represent the same quantity. Student Experience Book, Action Task states, “Provide counters, large paper rectangles folded in half, and markers.] Say: 1. Arrange counters on your paper to make a domino that shows the number 10. Then use a marker to show 10 on a domino.” Teacher Experience Guide, Planning states, “Students make dominoes to represent quantities.” Teacher Experience Guide, Action, Using the Action Part of the Exploration states, “Use one of these ideas for the main part of the exploration: Present the activity digitally. Create a similar activity for students to do independently. Include examples of teen number arrangements and provide materials for students to make their own.” Teacher Experience Guide, Probing and Extending states, “You could ask questions such as these of a small group to probe, challenge, and extend students’ thinking: Did anyone put their dots in a group of 10? Why or why not? Could both sides of your domino have more than 10 dots? If the top of one domino for a certain teen number has more dots than another for the same number, what do you know about the bottoms?” Teacher Experience Guide, Providing Feedback states, “You can gain insight into what students are thinking by asking questions based on what they do or say. For example, if a student thinks you have to have the same number of dots on both sides of a domino, you could respond by saying, You could have the same number of dots on both sides, but you really don’t have to.”

An example in Grade 1 includes:

• Topic 9: Equality and Equations, Lesson 1, Student Experience Book, students place linking cubes on a pan balance and determine whether the amounts on each side are equal. Student Experience Book, Action Task states, “1. Choose 2 colors. Put a few cubes of each color on one side of the pan balance. Then put some cubes of the other 2 colors on the other side of the pan balance. 2. Use addition to describe each side of the pan balance. 3. Are the sides balanced? If they are balanced, write the equation they show using the symbol =. If they are not balanced, write what they show using the symbol ≠. 4. Repeat Questions 1 to 3. Use different numbers of cubes. If they are not balanced, tell why the two sides are not equal.” Teacher Experience Guide, Action states, “Students use equations to model what is seen on the pan balance.” Teacher Experience Guide, Using the Action Task states, “Test the pan balances before this task to make sure they balance accurately. Provide each group with at least 40 linking cubes: 10 each of 4 colors. Show students what the pan balance looks like when it is balanced: the two pans are level and the marker points straight down. Tell students that they can put the cubes on the pan balance one at a time or in trains (a number of cubes linked together). Make sure students know that if the sides balance, the equation is true. For example, if they balance 5 + 4 with 6 + 3, they could say 5 + 4 = 6 + 3 is true. However, if the sides do not balance, that could use the symbol ≠ or say the equation is false.” Teacher Experience Guide, Conversation Starters states, “Is it possible to have 1 + 4 on one side of the balance? How? Could there be a total of 6 cubes on one side and 8 cubes on the other side? Suppose there was a balanced pan balance with 1 red cube on one side and 2 yellow cubes on the other. What do you know about the other colors?”

An example in Grade 2 includes:

• Topic 11: Solving Addition and Subtraction Problems, Lesson 1, Student Experience Book, students interpret and solve word problems with the unknowns in different positions. They determine what they know and what they need to find out to solve them. Student Experience Book, Action Task states, “Forest School has students in Kindergarten through Grade 5. Solve Questions 1 to 3 to show how many students are in each grade. Explain your thinking. 1. Grade 3 has 16 more students than Grade 2. How many students are in Grade 2? 2. Kindergarten has 19 fewer students than Grade 1. How many students are in Grade 1? 3. Grade 4 has 21 more students than Grade 5. How many students are in Grade 4? 4. Next year, some new students are joining Grade 5. Grade 5 will then have 92 students. How many new students will be joining Grade 5?” Teacher Experience Guide, Action states, “As students show their work, they demonstrate how they are applying mathematics they know to real-life problems.”Teacher Experience Guide, And the Point Is states, “This Action Task is designed to have students carefully analyze what information is given in word problems, and how this can be used to figure out what is missing.” Teacher Experience Guide, In This Task states, “Students interpret and solve word problems with the unknowns in different positions.” Teacher Experience Guide, Using the Action Task states, “Students solve Questions 1 to 3 to complete the chart. Question 4 provides a different situation for students to consider.” Teacher Experience Guide, Conversation Starters include, “What information are you already given that you need to solve the problem? How did you know what you needed to figure out? How did you decide whether to add or subtract? Did you have a choice? Could the number of students in Grade 4 be less than 68? How do you know?”

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for supporting the intentional development of MP5: Use appropriate tools strategically, in connection with grade-level content standards, as expected by the mathematical practice standards.

Students across the K-2 grade band engage with MP5 throughout the year. MP5 is found in the three-part lesson structure as students access a range of physical and digital mathematical tools and learn to select and use them strategically based on context. Classroom manipulative kits from hand2mind are aligned with Brainingcamp virtual manipulatives, allowing students to move between concrete and digital representations. During Action Tasks, students choose tools such as base ten blocks, fraction tiles, or geometric instruments to support problem solving and reflect on their effectiveness. Embedded teacher supports, including Dr. Marian Small’s coaching videos, the Teacher Assistance Panel, “And the Point Is” sections, and “Probing and Extending” questions, guide teachers in helping students evaluate when tools are helpful and how they connect to mathematical ideas.

Across the grades, students participate in tasks that support key components of MP5. These include selecting and using appropriate tools and strategies to explore mathematical ideas, solve problems, and communicate their thinking. Students are encouraged to consider the advantages and limitations of various tools such as manipulatives, drawings, measuring devices, and digital technologies, and to choose tools that best support their understanding and reasoning. They have opportunities to use tools flexibly for investigation, calculation, representation, and sense-making. Teachers are guided to support this development by making a variety of tools available, modeling their effective use, and encouraging students to make strategic decisions about when and how to use tools. Teacher materials prompt opportunities for student choice in tool selection, promote discussion around tool effectiveness, and support the comparison of multiple tools or representations. Teachers are also encouraged to highlight how different tools can yield different insights and to help students reflect on their tool choices as part of the problem-solving process.

An example in Kindergarten includes:

• Topic 9: Simple 2-D Shapes, Lesson 4, Student Experience Book, students use tools to create shapes in multiple ways. Student Experience Book, Action Task states, “What shapes can you make? Can you make them using different tools?” Teacher Experience Guide, Planning states, “Students use appropriate tools to create shapes.” Teacher Experience Guide, Using the Action Task states, “Present the activity digitally. Set up stations with the various tools, including straws of different lengths, chenille stems, yarn with glue or tape and paper, geoboards with elastics, and a geoboard app or other digital tools for making shapes.” Teacher Experience Guide, Probing and Extending states, “What shapes can you make with a loop of yarn? What shapes can you make with straws? What shapes could you not make with straws? What shapes can you make with a geoboard? What shapes could you not make with a geoboard?”

An example in Grade 1 includes:

• Topic 2: Representing Numbers, Lesson 2, Student Experience Book, students choose a multiple of 10 and represent it in different ways. Student Experience Book, Action Task states, “Pick up some stacks of 10 linking cubes. Then fill in the blanks.” Teacher Experience Guide, Action states, “Students represent multiples of 10 using linking cubes and fingers.” Teacher Experience Guide, And the Point Is… states, “This Action Task is designed to reinforce the idea that 10, 20, 30, 40, 50, 60, 70, 80, and 90 are all groups of 10 and that they follow a pattern similar to counting to 10 by 1s.” Teacher Experience Guide, Using the Action Task states, “Provide each pair with 9 stacks of 10 linking cubes. As an alternative, if students are familiar with counting rods, you could use trains of orange counting rods. You could provide a printed copy of this task for students to record their answers.” Teacher Experience Guide, Conversation Starters states, “Is it easier for you to see how many tens are shown with linking cubes or with the tally marks? How many tens is 70?”

An example in Grade 2 includes:

• Topic 5: Comparing Numbers within 1,000, Lesson 3, Student Experience Book, students select digits to create three-digit numbers that meet given criteria. Student Experience Book, Action Task states, “Choose digits to complete the school numbers above. Use different numbers to make each statement below true. Show how you know your digits work. Use symbols to compare your numbers.” Teacher Experience Guide, Action states, “Students use base-ten blocks and number lines to help them compare numbers.” Teacher Experience Guide, And the Point Is… states, “This Action Task is designed to reinforce for students which digits really matter when comparing two numbers and allow students to choose which materials make the most sense for them to use and in which situation.” Teacher Experience Guide, Using the Action Task states, “You might provide copies of the reproducible page School Cards. Students can cut out the cards, pencil in their choices for the digits, and move the cards around to check their work.” Teacher Experience Guide, Conversation Starters states, “Are there any schools you already know have more students than other schools? What do you have to do to make sure School A has more students than School C? What do you have to do to make sure School A has fewer students than School C? How can you make sure Schools C and D are close in the number of students they have?”

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for supporting the intentional development of MP6: Attend to precision, in connection with grade-level content standards, as expected by the mathematical practice standards.

Students across the K-2 grade band engage with MP6 throughout the year. MP6 is found in the three-part lesson structure as students develop precision in communicating their mathematical thinking and justifying their solution approaches. Action Tasks provide opportunities for students to explain their reasoning and use mathematical language accurately. The Student Experience Book includes journal prompts that support reflection and articulation of ideas with clarity. During the Consolidate phase, students share strategies and refine explanations, while the teacher supports, Dr. Marian Small’s coaching videos, the Teacher Assistance Panel, “And the Point Is” sections, and “Probing and Extending” questions, guide them to use precise vocabulary, attend to details, and connect strategies to mathematical ideas.

Across the grades, students engage in tasks that support key components of MP6. These include formulating clear explanations, using grade-level appropriate vocabulary and conventions, applying definitions and symbols accurately, calculating efficiently, and specifying units of measure. Students are also expected to label tables, graphs, and other representations appropriately, and to use precise language and notation when presenting mathematical ideas. Teachers support this development by modeling accurate mathematical language, ensuring students understand and apply precise definitions, and providing feedback on usage. Lessons include opportunities for students to clarify the meaning of symbols, evaluate the accuracy of their own and others’ work, and refine their communication. Teachers are encouraged to facilitate discussions and structure tasks that promote attention to detail in both reasoning and representation.

An example in Kindergarten includes:

• Topic 4: Comparing Quantities, Lesson 4, Student Experience Book, students use pan balances and connecting cubes to explore balance and equality. Student Experience Book, Action Task states, “1. Will it balance if you put 5 green cubes on this side? 2. Will it balance if you put 1 blue cube and 4 green cubes on this side? 3. How could you describe that using the word ‘equals’? 4. Are there other ways to make it balance?” Teacher Experience Guide, Action states, “Present the activity digitally. Set up a similar situation in the classroom, perhaps in response to an observation of a student during play, asking the same questions. Provide connecting cubes of the same size and pan balances. Show students that the pan balance does not balance if there are 5 blue cubes on one side and 4 green cubes on the other side. Point out that you can tell that it is not balanced because one side goes down farther than the other side.” Teacher Experience Guide, Planning states, “Students accurately compare quantities.” Teacher Experience Guide, Probing and Extending states, “Suppose there are 5 cubes on one side of the balance. How many must be on the other side? Do they have to all look the same? Suppose I add a cube to one side. What do I have to do to the other side? What if there were 3 red cubes and 4 blue cubes on one side. What could be on the other side? What would happen if I used big cubes on one side and small cubes on the other side?” Teacher Experience Guide, Providing Feedback: Responding to What Students Do or Say states, “You can gain insight into what students are thinking by asking questions based on what they do or say. For example, a student calls something balanced that is close, but not quite, you might respond by adding a cube to one side to make it balanced and asking: Is it balanced now that I have added a cube? Could it have been balanced before?”

An example in Grade 1 includes:

• Topic 3: Comparing Numbers within 100, Lesson 3, Student Experience Book, students use their comparing skills to make a series of number statements all true at the same time. Student Experience Book, Action Task states, “Imagine you are swimming deep in the ocean and a parade of sea creatures swims by. What do you see? Read these rules. Then, put a two-digit number in each blank to make all of the statements true: At least one number is close to 10. At least one number is close to 60. At least one number is close to 80. There are fewer manta rays than dolphins. There are more seahorses than pufferfish. There are only a few more starfish than pufferfish. I see a group of __________ seahorses. I see a group of __________ starfish. I see a group of __________ dolphins. I see a group of __________ manta rays. I see a group of __________ pufferfish. 2. Imagine that a huge group of angelfish swim by. There are more angelfish than seahorses. How many angelfish might there have been?” Teacher Experience Guide, Action states, “Students are careful to select numbers that accurately reflect the required relationships.” Teacher Experience Guide, Using the Action Task states, “Students can work together to figure out what numbers to put into each statement to make it true. You may want to print the descriptions and/or the rules about group size. Encourage students to use base-ten blocks to help them. Encourage them to compare numbers by thinking about the tens digits when they can.” Teacher Experience Guide, Conversation Starters states, “What sorts of numbers do you think are close to 60? What numbers are not? How can you make sure that the number of seahorses is the greatest? Could there be fewer than 10 of any creature?”

An example in Grade 2 includes:

• Topic 9: Length, Lesson 1, Student Experience Book, students search for objects that are about 1 foot long or 1 yard long. Student Experience Book, Action Task states, “1. Find objects in the room that are about 1 foot long. 2. Find objects in the room that are about 1 yard long”. Teacher Experience Guide, Action states, “Students use the most appropriate tool for yards and the most appropriate tool for feet.” Teacher Experience Guide, Using the Action Task states, “Provide measuring tools for students. Encourage them to work in small groups to look for the required items. It may be necessary to plant some items around the room to ensure students can find a variety of items about 1 foot long or 1 yard long. For example, you might plant a water bottle, a baseball bat, or a couple of large shoes.” Teacher Experience Guide, Conversation Starters states, “Might part of your arm be 1 foot long? Do you think the door is 1 yard wide? Is there a part of this drawing that is about 1 foot long?”

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for supporting the intentional development of MP7: Look for and make use of structure, in connection with grade-level content standards, as expected by the mathematical practice standards.

Students across the K-2 grade band engage with MP7 throughout the year. MP7 is found in the three-part lesson structure as students look for and make use of structure to identify patterns and mathematical relationships. Action Tasks provide opportunities for students to recognize regularities in repeated calculations, geometric configurations, and algebraic expressions that support problem solving. The Student Experience Book highlights Essential Understandings that help students connect new ideas to broader mathematical structures. During the Consolidate phase, students share strategies and explain how patterns or structures informed their reasoning. Teacher supports, including Dr. Marian Small’s coaching videos, the Teacher Assistance Panel, “And the Point Is” sections, and “Probing and Extending” questions, guide students to deepen their reasoning and make connections between mathematical ideas.

Across the grades, students engage in tasks that support key components of MP7. These include looking for and describing patterns, identifying structure within mathematical representations, and decomposing complex problems into simpler, more manageable parts. Students are encouraged to analyze problems for underlying structure and to consider multiple solution strategies. They make generalizations based on repeated reasoning and use those generalizations to solve problems efficiently. Teachers support this development by selecting tasks that highlight mathematical structure and by prompting students to attend to and describe patterns they notice. Lessons provide opportunities for students to compare approaches, justify their reasoning, and reflect on how structure helps deepen their understanding. Teachers are encouraged to facilitate discussions and structure lessons in ways that promote the recognition and use of patterns and structure in problem-solving.

An example in Kindergarten includes:

• Topic 10: Representing Numbers from 10 to 20, Lesson 1, Student Experience Book, students use spinners and ten-frames to represent teen numbers as 10 and some more ones. Student Experience Book, Action Task states, “Each teen number is 10 and some more. 1. Spin the spinner to see how much more. 2. Show the total number on two ten-frames. 3. Say the number. 4. Write the equation that shows your number as 10 and some more ones.” Teacher Experience Guide, Planning states, “Students use tools to focus on the fact that every teen number 1▢ is 10 + ▢.” Teacher Experience Guide, Using the Action Part of the Lesson states, “Use one of these ideas for the main part of the lesson: Present the activity digitally, using a digital spinner. Set up a similar hands-on activity in the classroom. Provide spinners, a ten-frame filled with counters and an empty ten-frame. Alternatively, you could provide a number rack with the first row of beads already pushed to the left. Repeat these instructions many times to give students a chance to represent several teen numbers. Leave the ten-frame representations students build set up so they can compare them.” Teacher Experience Guide, Probing and Extending states, “How do you know 17 is more than 12? Why does 15 come after 14 when you count? How do you know you will not need another ten-frame? (or another row on the number rack).” Teacher Experience Guide, Providing Feedback: Responding to What Students Do or Say states, “For example, if students spin a 4 and say ‘four,’ you might ask, What about the ten counters on the first ten-frame?”

An example in Grade 1 includes:

• Topic 7: Adding within 20, Lesson 6, Student Experience Book, students use structure to compare related addition equations. Student Experience Book, Action Task states, “1. How much more or less is the second sum than the first? Use models to show why. 7 + 3 and 7 + 5, 7 + 3 and 7 + 6. 2. How much more or less is the second sum than the first? Use models to show why. 5 + 5 and 6 + 5, 5 + 5 and 6 + 6. 3. How much more or less is the second sum than the first? Use models to show why. 6 + 6 and 6 + 8, 6 + 6 and 8 + 8, 6 + 6 and 5 + 8.”. Teacher Experience Guide, Action states, “When relating facts, students are making use of the structure of decomposing numbers as well as properties like the associative property to see how addition facts are related.” Teacher Experience Guide, In This Task… states, “Students explain how knowing one particular sum can help them figure out other sums that are of interest.” Teacher Experience Guide, And the Point Is… states, “This Action Task provides three different sorts of situations, that involve slightly different levels of complexity: one where only the second addend changes; one where facts are related to the very familiar 5 + 5; one involving potentially two changes in addends.” Teacher Experience Guide, Conversation Starters states, “Will 7 + 5 be more or less than 7 + 3? How does a model for 6 + 6 look different from one for 5 + 5? How much more should 6 + 5 be than 5 + 5? Why?”

An example in Grade 2 includes:

• Topic 1: Skip Counting, Lesson 1, Student Experience Book, students use structure to count tallies, fingers, and dots by 5s. Student Experience Book, Action Task states, “1. How could you use skip counting by 5s to tell how many tallies there are? Count by 5s. Tell how many hands you would need to see these numbers of fingers. 2. 50 fingers 3. 60 fingers 4. 80 fingers. 5. The paper is covering 35 tally marks. Count by 5s starting with the 35 tally marks under the paper to tell how many tally marks there are in all. 6. Count these dots by making groups of 5 and counting by 5s to tell how many.” Teacher Experience Guide, Action states, “Students have the opportunity to observe the pattern when counting by 5s.” Teacher Experience Guide, In This Task… states, “Students count sets of objects by 5s to figure out how many. They also count by 5s from a greater multiple of 5.” Teacher Experience Guide, And the Point Is… states, “This Action Task uses tallies and fingers, which come in 5s, for counting by 5s, since we are unlikely to count by 5s when items are not already in groups of 5 … gives students experience counting on by 5s from numbers other than 5 … gives students an opportunity to create their own groups of 5.” Teacher Experience Guide, Conversation Starters states, “Why might it make sense to count the tallies or fingers by 5s? When you count the tallies or fingers, how can you make sure you keep track of what you’ve already counted and what else you have to count? What will you do with those last two tallies? Do you need to say, ‘5, 10, 15, 20, …,’ or can you start at 35?”