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2 mathematics Grade 1 Adding to Situational Tasks: Solving for Unknowns in All Positions A SET OF RELATED S UNIVERSITY OF PITTSBURGH

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6 mathematics Grade 1 Introduction Adding to Situational Tasks: Solving for Unknowns in All Positions A SET OF RELATED S

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15 14 Introduction

16 mathematics Grade 1 Tasks and Lesson Guides Adding to Situational Tasks: Solving for Unknowns in All Positions A SET OF RELATED S

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18 Tasks and Lesson Guides 17 Name Three Collections TASK 1 Three friends have collections. Use counters or create a picture to show each collection. Try to write an equation that shows each friend s collection. Juan collects marbles. He has 6 marbles and he gets 5 more marbles. Martha collects blocks. She has 5 blocks and she gets 6 more blocks. Jasmine collects books. She has 5 books and she gets 3 more books. Then later in the day, she gets 3 more books. Which friend has the most items in their collection? Be prepared to explain to the class how you know who has the most in their collection.

22 Tasks and Lesson Guides 21 EU: Two quantities can be combined in any order and the whole quantity will remain the same. (Commutative property; = 5 + 4) Who has the most items in their collection? Martha and Juan only had two parts in their collections and Jasmine has three parts? So Jasmine has the most, right? (Challenging) How can Juan and Martha have the same amount in their collections if Juan starts with 6 and Martha starts with 5? (Challenging) So if = 11 and = 11, can we write = 5 + 6? Is this okay? Why or why not? When we are adding, we are allowed to switch the order of the numbers because the sum remains the same. (Recapping) 1 Application What is = What is = What is = What is = What is = What is = Summary Quick Write When we add two addends, we get a sum. We can switch the order of the addends and we will still get the same sum because we add the same amounts. We did not take any away from the collection. Write an equation to describe each part-part-whole map and explain how you know they will have the same sum.

27 26 Tasks and Lesson Guides 2 Quick Write Explain how you know these two equations will have the same sum = = Supports 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.

28 Tasks and Lesson Guides 27 Name Order of Groups 1. Solve each set of equations TASK 3 A = = B = = C = = D = = 2. Look at each set of equations. What do you notice about the sets? 3. Omar claims that you can add the numbers in an addition equation in any order. Do you agree or disagree with Omar s claim? Make a picture and be prepared to explain to the class why you agree or disagree with Omar.

32 Tasks and Lesson Guides 31 Application No application. Summary So what do we notice about all the sets of expressions? What s the pattern? - They are all addition equations. - The equations in each set have the same sum. - The equations in each set have the same numbers, but in different orders. Are we permitted to switch the numbers? What will always be true when we switch the numbers of two addition problems? This is called the commutative property. It says that numbers can be added in any order and it won t change the sum. 3 Quick Write Write an equation for each part-part-whole map. Which two part-part-whole maps show that parts can be added in any order without changing the sum? Be prepared to tell how you know.

33 32 Tasks and Lesson Guides TASK 4 Name Picking Apples Javon and Kya are picking apples at the orchard. Javon picks 9 apples in the morning and 6 apples in the afternoon. How many apples did Javon pick at that orchard? Kya picked 7 apples in the morning. She picked more apples in the afternoon. Now she has 15 apples. How many apples did Kya pick in the afternoon? Javon says he has more apples than Kya. Is he right? Explain your thinking using counters, pictures, or words. Try to write equations to show Javon s apples and Kya s apples.

37 36 Tasks and Lesson Guides 4 EU: 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; = 9, 9 5 = 4) We said that = 15 describes Kya s apples. Did anyone write a different equation to describe Kya s apples? (Call on a student who wrote a subtraction equation.) You used subtraction to think about Kya s apples. Come up and show us how you did that. (Marking) Can we write 15 7 =? to think about Kya s apples? How would we solve that equation? When we know the whole and one part, we can find the unknown part by subtracting. (Recapping) Application Solve for the missing number in each problem. What do you notice about these problems? = 3 + = = Summary When we know the whole and a part, we can subtract the part from the whole to find out what changed. Addition is when groups come together and subtraction is when groups are taken apart; they do the opposite things. Quick Write Solve each equation and draw a picture. How are the pictures similar? 4 + = =

38 Tasks and Lesson Guides 37 Name Collecting Stickers TASK 5 Aaron likes to collect stickers. He has animal stickers and sports stickers. Aaron wants to know if he has more animal stickers or more sports stickers. Aaron starts with 13 animal stickers. He gets 7 more animal stickers. Aaron starts with 7 sports stickers. Then he gets some more sports stickers. He now has 19 sports stickers. Does Aaron have more animal stickers or more sports stickers? Be prepared to share your thinking with the class. You can draw pictures to show and try to write an equation to describe each type of sticker.

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

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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