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Why Bar Models? - Makes an abstract word problem or equation pictorial. (Concrete → Pictorial → Abstract) - Allows for deeper analysis and understanding of the problem by teaching students to: Identify all information given and its relationship to other pieces of information Identify missing information that needs to be found Understand what mathematical operation needs to take place - Bar modeling is a very versatile strategy! It can be used for problems involving: Addition, subtraction, multiplication, division, fractions, decimals, percentages, ratios - Bar modeling trains students to think algebraically. “develops students’ visual thinking capabilities and algebraic thinking and reinforces higher level thinking.”

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9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement.

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Try a problem! One number is 1/3 of another number. If the difference between the numbers is 26, find the two numbers.

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**? 14 8 6 9 Steps to Model Drawing 1st Grade**

Mike had 8 big blocks and 6 small blocks in a basket. How many blocks are there in the basket? 14 There are ________ blocks in the basket. 8+6=14 9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement. Mike’s Blocks ? 8 6 Big Small

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1st Grade John has 15 marbles. 4 of them are outside the bag. How many marbles are there in the bag? 11 There are ________ marbles in the bag. 15-4=11 9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement. John’s marbles 4 ? 15 in out

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1st Grade Mary has 11 storybooks. She has 2 more storybooks than Sally. How many storybooks does Sally have? 9 Sally has ________ storybooks. 11 11-2=9 9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement. Mary’s storybooks ? 2 Sally’s storybooks ?

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3rd Grade Pam has 4 times as much money as Kurt. If Pam has $30 more than Kurt, how much money do they have in all? They have ________ money in all. $50 a) 1 unit, 30 ÷ 3=10 b) Pam+ Kurt, = 50 9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement. Pam’s money 10 10 10 10 ? $30 Kurt’s money 10

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5th Grade Peter has twice as many stickers as Joe. Joe has 20 less stickers than Emily. They have 300 stickers altogether. How many stickers does Peter have? Peter has ________ stickers. a) 300 – 20 = 280 b) 280 ÷ 4 = 70 (1 unit) Peter’s stickers ? 70 70 9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement. C) Peter 70 x 2 = 140 Joe’s stickers 300 70 Emily’s stickers 70 20

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5th Grade There are 3 pieces of rope. Rope A is 3 times as long as Rope B. Rope C is 10.4 cm longer than Rope A. The total length of all 3 ropes is cm. How long is Rope C? 55.7 Rope C is ________cm long. a) = 105.7 b) ÷ 7 = 15.1 (1 unit) Rope A 15.1 15.1 15.1 c) Rope c = (15.1x3) = 55.7 9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement. 116.1 Rope B 15.1 ? Rope C 15.1 15.1 15.1 10.4

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5th Grade Betsy made cupcakes for the class party. 1/3 of the cupcakes were chocolate. 2/5 of the remaining were vanilla and the remaining 12 cupcakes were strawberry. How many cupcakes did Betsy make in all? 30 Betsy made ________cupcakes in all. 20 a) 12 ÷ 3 = 4 b) 5 x 4 = 20 Betsy’s cupcakes ? 10 10 10 9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement. c) 10 x 3 = 30 4 chocolate 4 4 4 4 4 Vanilla Strawberry

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5th Grade The ratio of Carla’s postcards to Juan’s postcards was 2:5. If together they had a total of 35 postcards, how many more postcards did Juan have than Carla? 15 Juan had ________ more postcards than Carla. a) 35 ÷ 7 = 5 (1 unit) b) 5 x 3 = 15 ? Carla’s postcards 5 5 9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement. 35 Juan’s postcards 5 5 5 5 5

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**One number is 1/3 of another number**

One number is 1/3 of another number. If the difference between the numbers is 26, find the two numbers. 13 The two numbers are ________ and _________. 39 a) 26 ÷ 2 = 13 (1 unit) Num. 1 = 13 Num . 2 (13x3 =39) Number 1 13 9 Steps to Model Drawing 1. READ the entire problem. 2. REPHRASE the question into a statement. 3. WHO is involved in the problem? 4. WHAT is involved in the problem? 5. Draw BAR(s). 6. Read each sentence ONE at a time. 7. LABEL bar(s) and write a question mark for the unknown. 8. Write an EQUATION and a NUMBER BOND. 9. Write the answer in the blank to complete the statement. 26 Number 2 13 13 13

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