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Structures for Addition and Subtraction Problems Outcomes B1: Find sums and differences involving decimals to thousandths B8: Solve and create addition and subtraction problems involving whole numbers and/or decimals

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4 Structures for Addition and Subtraction Problems Join (gain) Separate (loss) Part-Part-Whole (no action) Comparison

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JOIN: an action suggesting gain After reading the problem, ask yourself 3 questions: a)What is the resulting value? b)What is the change? c)What was the starting value? The stated problem will provide you with two answers to the above questions. It is your responsibility to solve the remaining question. Vocabulary: win, deposit, buy, increase, receive

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Examples: John had 20 marbles. He won 7 marbles. How many does he now have? John had 30 marbles after recess. At recess, he won 6 marbles. How many marbles did he have before recess? John had 20 marbles before recess. At the end of recess he had 30 marbles. How many did he win at recess time? StartChangeResult 20727 StartChangeResult 30 6 24 StartChangeResult 203010

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SEPARATE: an action suggesting loss After reading the problem, ask yourself 3 questions: a)What is the resulting value? b)What is the change? c)What was the starting value? The stated problem will provide you with two answers to the above questions. It is your responsibility to solve the remaining question. Vocabulary: lose, withdraw, decrease, give away

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Examples: John had 20 marbles. He lost 7 marbles. How many does he now have? John had 30 marbles after recess. At recess, he lost 6 marbles. How many marbles did he have before recess? John had 30 marbles before recess. At the end of recess he had 20 marbles. How many did he lose at recess time? StartChangeResult 20713 StartChangeResult 30 6 36 StartChangeResult 302010

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PART-PART-WHOLE: no action After reading the problem, ask yourself 2 questions: a)What is the whole? b)What is the missing part? If the problem provides you with the whole, then you must find the missing part. If the problem provides you with both parts, then you must find the whole.

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Examples: John has 3 pets while his cousin Mark has 4 pets. How many pets do they have altogether? There are 7 cattle on John’s farm. Altogether John has 15 farm animals including cattle and pigs. How many pigs does he have on the farm? Part 1Part 2Whole 347 Part 1Part 2Whole 158 7

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COMPARISON After reading the problem, you may ask yourself the following questions: a)What is the difference? b)What is larger? c)What is smaller? With these problems, solutions are found by comparing the size or amounts of select quantities/measurements/probabilities/etc.

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Examples: John has 12 fewer marbles than his cousin Mark. If Mark has 20 marbles, how many does John have? John has 7 marbles. This is 6 fewer than his cousin has. How many does his cousin have? JohnMarkmore/less 820John has 12 less JohnMarkmore/less John has 6 less or Mark has 6 more 13 7

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Label the Structure Sarah’s candle was 2.3 cm tall when the electricity came back on. During the power outage, the candle melted 4.7 cm. How tall was the candle before the power went out? The perimeter of Eric’s rectangular garden is 6.8 m. One side of the garden is 2.2 m long. What are the lengths of the other three sides? Halie had $65.40 in her bank account. Halie received and promptly deposited the $35.50 she received in birthday money. How much money does Halie now have in her bank account? Separate Part-Part-Whole Join

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Label the Structure Bart has $35.65 and Millhouse has $64.15. How much money does Martin have if together they can buy the ultra rare $100 Radioactive-man issue #1 comic book? Stephanie’s snowperson is 0.64 m shorter than Demetri’s snowperson. If Demetri’s snowperson is 1.87 m tall, how tall is Stephanie’s snowperson? Part-Part-Whole Comparison

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Creating problems Create 4 problems using the structures we discussed. The problems should contain decimals. –Remember: each structure can be presented in more than one form.

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6.3 Systems with a Vengeance!! Alg Con. 1. One number is 6 less than five times another. Their difference is 22. Find the numbers. Answer : One number.

6.3 Systems with a Vengeance!! Alg Con. 1. One number is 6 less than five times another. Their difference is 22. Find the numbers. Answer : One number.

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