Re- Thinking Fact Families

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2 Warm- up Rethinking Fact Families Mutliple choice questions from 2nd grade Released Test Questions, California Standards Test 1 [Sophie did this subtraction problem. Which addition problem shows that she got the right answer?] 2 [Look at the two problems in the box. The same number is missing in both of them. What is the missing number?] = = 60 A B C D Prove your answer is correct using three different methods. 2 NS 2.1 A B C D 60 + = Show how a student could show their work using an open number line. 2NS [Which of these can be used to check the answer to the problem in the box?] = 7 4 [Which number sentence is an opposite number sentence for eight plus six equals fourteen?] = 14 A = 10 B 7 4 = 3 C = 7 D 10 3 = 7 Explain why you think students would choose the incorrect answers. 2 NS 2.1 A = 14 B = 14 C 8 2 = 6 D 14 8 = 6 Show two ways students could prove they are correct. 2 NS 2.1 Page 2 of 16 12/01/11

4 "When I put together 7 black dots and 3 white dots I have 10 dots altogether. Kalil has 10 marbles." Write the sum = 10 "I wonder what would happen if we changed the order of the numbers? How many marbles will Kalil have then?" Write and show with counters, then record in a 10- frame as you tell the story. "This time let s say Kalil started with 3 marbles and he won 7 more marbles. How many marbles does he have altogether? I can represent Kalil s marbles with counters. I represent the 3 marbles he started with, with 3 yellow counters, and put together 7 red counters to represent the counters he won. I can also show what happened with a 10- frame. (Use a different 10- frame so you ll have them to compare.) I show 3 white dots and then 7 black dots = Counters: Ten Frame: "When I put together 3 and 7 they make 10 dots altogether. How many marbles does Kalil have altogether?" Choral response: [10] Write the sum = 10 Show 10- frames side by side for students to compare. "When I look at these 10- frames I see the sum, the answer, is the same. It didn't matter if we started with 7 and added 3, or started with 3 and added 7, we always had 10 when we put them together. Mathematicians call the numbers we add together addends. Say that with me: Numbers we add together are addends. Page 4 of 16 12/01/11

7 Students whisper to partner then T. pulls stick for non- volunteers. Check for class agreement using silent signals for yes and no. Then have students justify their answers. Connect to Commutative Property of Addition. "Let's show it with a bar model and an open number line. Write and show with a bar model and an open number line next to your previous examples as you tell the story. "Jameesha drew 5 butterflies. She drew 2 more. How many butterflies did she draw altogether?" How many should I draw for my first bar this time? Choral Response [5] How many should I draw for my second bar? Choral Reponse: [2] How many altogether? Choral Response: [7] bar model: What s my first jump this time? Choral Response: [5] What s my second jump? Choral Response: [2] How many altogether? Choral Response: [7] open number line: = 7 "We showed that the Commutative Property of Addition is true again! Tell your partner what that Property says is always true. Call on non- volunteers for answers. [It doesn t matter which order we add the numbers, or addends, we always get the same sum. Have students repeat in Choral Response. Students write on whiteboard with teacher - and show with bar models, open number lines, and equations. Give students 2 addends and have them show the rest of their work. Page 7 of 16 12/01/11

8 1) = 5 and = 5 2) = 9 and = 9 You Tries: Students may work the first problem with their partner. Have them work independently for second problem to check for understanding. During the next Independent Practice time below, post examples of all the methods we've used and provide coaching to those who need extra support or clarification. Note students who may need small group reteaching. Independent Practice: Closure: 3) = 10 and = 10 4) = 8 and = 8 Now we know 5 ways to show the Commutative Property of Addition: Counters, 10- Frames, Bar Models, Open Number Lines, and Equations. For these next problems you will choose any two ways to show your work, and write the equations. Give students the 2 addends: 5) = 10 and = 10 6) = 12 and = 12 7) = 14 and = 14 8) = 15 and = 15 Show a few examples of student work to note the different strategies and the Commutative Property of Addition at work. How did you decide which ways to show your work? What did you have to do to show the work correctly? What patterns do you notice? (Be sure that students note how each pair of equations reflects the same addends and sum, but that the order of the addends is changed). Tomorrow we will use what we learned today with greater numbers. Remember, the Commutative Property of Addition is always true, no matter how large or small the numbers are. " What is the Math Property we learned about today? Choral Response: [Commutative Property of Addition] Page 8 of 16 12/01/11

10 I make a group of 3 cubes of one color for Maria s 3 carrots and a group of 4 cubes for the 4 more her mom gave her. When I put them together how many do I have? Choral Response: [7] = 7 Yes. When we put 3 and 4 together we get 7. "I wonder how many carrots Maria would have if her mom took those 4 carrots back from her?" "Let's try it." Write equation and show with linking cubes as you tell the math story. "Now Maria has 7 carrots and her mom needs her to give 4 back. How many carrots does Maria have after she gives 4 back to her mom?" Linking Cubes: I take the 7 bar I made and I take the four cubes off. How many carrots does Maria have now? Student Choral Response: [3] 7 4 = 3 Yes she s back to having the 3 carrots she started with. First we added and then we undid our adding when we subtracted and we had the same number we started with. "We can show this using an open number line too." Record hops on open number line as you retell the story problem. We start on 3 because that s how many carrots Maria started with. Then we jump 4 to show she got that many more. What number did we end on? Choral Response: [7] Yes, she had 7 carrots. But then she had to give four carrots back to her mom. I can show that on another open number line. I start on 7 and jump back 4. What number am I on now? Choral Response: [3] Open Number Lines: Page 10 of 16 12/01/11

14 Closure: What do notice about these equations? What helped you to find the sum or difference when you were undoing the first operation? Do you see a pattern? K notes: When working on adding and subtracting with manipulatives, note this relationship and have students show that it is true. 1 st and 2nd: Students need multiple opportunities to practice seeing this relationship. Use as a small group or center activity. 1 st and 2 nd : Next steps: Connect patterns and understandings discovered in this lesson with equations with greater numbers. Page 14 of 16 12/01/11

15 Side- By- Side Comparison for Commutative Property of Addition Strategies = 8 and = 8 Counters 10- Frames Bar Models Open Number Lines Page 15 of 16 12/01/11

16 Side- By- Side Comparison for the Inverse Relationship of Addition and Subtraction = 6 and 6 1 = 5 Linking Cubes Open Number Lines Page 16 of 16 12/01/11

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