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2 mathematics Grade 2 Put Together & Compare Situational Tasks: Missing Addend Addition as Subtraction A SET OF RELATED S UNIVERSITY OF PITTSBURGH

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16 Tasks and Lesson Guides 15 Name Picking Flowers Read about the flowers that Evie and Maria pick. Evie picks 8 red flowers and 9 yellow flowers. Maria picks 15 flowers. She picks 9 red flowers and the rest are yellow. TASK 1 1. Who picks more flowers, Evie or Maria? Make a diagram and write an equation to explain how you know who has more flowers. 2. Who picks more yellow flowers, Evie or Maria? Make a diagram and write an equation to explain how you know she has more flowers. 3. Look at your diagrams and equations for Evie s flowers and Maria s flowers. What do you notice about these two situations? How are they alike? How are they different?

18 Tasks and Lesson Guides 17 Essential Understandings Materials Needed Mapping devices and tools can help you gain a sense of the quantities involved, to notice increases and decreases, and consider the doing and undoing related to addition and subtraction. Problems can be solved by counting all, counting on from a quantity, counting on from the largest set, or using derived facts when solving for the whole amount or the missing part of the whole. Addition and subtraction are inverse operations because two or more quantities can come together and then the whole amount of objects can be taken apart, but the composition of the whole quantity remains the same. (Doing and Undoing, Inverse Operations) Counters or other appropriate manipulative, 25 per student. Part-part-whole map, 1 per student. Student task reproducible, 1 per student. 1

19 18 Tasks and Lesson Guides 1 SET-UP PHASE Listen as I read the task. Follow along on your paper. Work by yourself for a few minutes. Use the counters and part-part-whole map or create a diagram to show Evie s and Maria s flowers. Write equations to tell about the flowers. (Teachers may choose to engage students in the Explore and Share, Discuss, and Analyze phase of the problem for the first problem and then follow the same cycle for the second problem.) EXPLORE PHASE Possible Student Pathways Can t get started. Uses counters and partpart-whole-map to build a model. Assessing Questions What do you know about Evie s (Maria s) flowers? Tell me what you are showing here. Advancing Questions How can you show Evie s (Maria s) flowers with counters? Write an equation that describes the story problem. Has a correct sum for each collection but has not shown equations. Writes equations. Evie: = 17 Maria: = 15, possibly 15 9 = 6 Tell me how you arrived at the total number of flowers. What do the equations tell about Evie s (Maria s) flowers? Write an equation that describes Evie s (Maria s) flowers. Who has the most flowers? How do you know? Who has the most yellow flowers? How do you know?

22 Tasks and Lesson Guides 21 Name Fruit Pies TASK 12 Marcus makes two fruit pies. There are 20 pieces of fruit in each pie. The first pie has 12 pears and the rest are apples. The second pie has 10 pears, 2 oranges, and the rest are apples. 1. Marcus s dad claims there are more apples in the first pie. Do you agree or disagree with his dad? Explain in words and make diagrams to show why you agree or disagree with Marcus s dad. 2. What do you notice about these two situations? How are they alike? How are they different?

26 Tasks and Lesson Guides 25 Repeat this sequence of EUs and prompts for the second fruit pie. Application Write each addition problem as a subtraction problem and then solve: 9 +? = ? = ? = Summary Quick Write See recapping above What is the same between each diagram? What is different in each diagram? Diagram 1 shows 8 +? = 11 Diagram 2 shows 11 8 = Support for students who are English Learners (EL): 1. Bring in actual real-world items for students identified as English Learners so they associate the words with the items. 2. Ask students who are identified as English Learners to physically point to the counters or act out the situation as they talk through the situational problem.

27 26 Tasks and Lesson Guides TASK 31 Name What s the Unknown? Solve the story problems. Make a diagram and write an equation to describe each situation. 1. There are 7 black marbles in the bowl. There are some white marbles in the bowl. There are 19 marbles in the bowl. How many white marbles are there in the bowl? 2. There are 6 strawberries and 8 grapes in the bowl. The rest of the fruit in the bowl are bananas. There are 17 pieces of fruit in the bowl. How many bananas are there in the bowl? 3. There are 18 pencils in the box. Some of the pencils in the box are red. There are 12 blue pencils in the box. How many of the pencils in the box are red? 4. There are some books on the shelf. There are 7 books in the basket. Together there are 20 books. How many books are on the shelf?

29 28 Tasks and Lesson Guides 13 Essential Understandings Mapping devices and tools can help you gain a sense of the quantities involved, to notice increases and decreases, and consider the doing and undoing related to addition and subtraction. Addition and subtraction are inverse operations because two or more quantities can come together and then the whole amount of objects can be taken apart, but the composition of the whole quantity remains the same. (Doing and Undoing, Inverse Operations) Problems can be solved by counting all, counting on from a quantity, counting on from the largest set, or using derived facts when solving for the whole amount or the missing part of the whole. Two quantities can be combined in any order and the whole quantity will remain the same. (Commutative Property) Materials Needed Counters or other appropriate manipulative, 25 per student. Part-part-whole map, 1 per student. Student task reproducible, 1 per student.

33 32 Tasks and Lesson Guides TASK 41 Name Addition and Subtraction 1. Destiny and Malik solve 9 + = 16. Destiny draws the diagram below. She starts with 9 circles and draws more circles until she gets to 16. She adds on 7 circles. She writes the equation = 16. Malik solves 9 + = 16 a different way. He draws the diagram below. He starts by drawing 16 circles. Then he crosses out 9 circles. He writes the equation 16 9 = What do you notice about Destiny s diagram and Malik s diagram? How are they similar? How are they different? 2. Solve this story problem. Choose either Destiny s strategy or Malik s strategy to solve the problem. Make a diagram and write an equation to describe the situation. There are 20 dogs in the park. There are 9 black dogs and the rest are white dogs. How many are white dogs? 3. Solve this story problem. Choose the strategy that you did not use yet to solve this problem. Make a diagram and write an equation to describe the situation. There are 6 pepper plants and 9 tomato plants in the garden. The rest of the vegetable plants are carrots. There are 20 vegetable plants in the garden. How many carrot plants are there in the garden? 4. Four addition equations are shown below. Shelly claims that she can write a subtraction equation to solve each equation. Write a subtraction equation and make a diagram to show how subtraction can be used. 7 + = = = = 17

35 34 Tasks and Lesson Guides 14 Essential Understandings Mapping devices and tools can help you gain a sense of the quantities involved, to notice increases and decreases, and consider the doing and undoing related to addition and subtraction. Addition and subtraction are inverse operations because two or more quantities can come together and then the whole amount of objects can be taken apart, but the composition of the whole quantity remains the same. (Doing and Undoing, Inverse Operations) Problems can be solved by counting all, counting on from a quantity, counting on from the largest set, or using derived facts when solving for the whole amount or the missing part of the whole. Materials Needed Counters or other appropriate manipulative, 25 per student. Part-part-whole map, 1 per student. Student task reproducible, 1 per student.

Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number

Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number

Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number

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