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Bar Modeling: Using Models to Help Solve Word Problems

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• Provide problem context

• Use of concrete objects

• Represent concepts and problems pictorially

• Use of graphic models

• Represent and solve problems numerically

• Use mental math strategies

Abstract

Pictorial

Concrete

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5 Problems in Math Instruction

• Reading

• Reading the problem

• Comprehension

• Comprehending what is read in the problem

• Transformation

• Writing and setting up a problem with the correct mathematical strategy

• Process skills

• Apply the correct skills to process and understand the mathematics of the problem

• Encoding

• Writing the answer in an acceptable and understandable form

Newman's prompts: Finding out why students make mistakes. (n.d.). Newman's Prompts: Finding out Why Students Make Mistakes. Retrieved November 24, 2015, from http://www.schools.nsw.edu.au/learning/7-12assessments/naplan/teachstrategies/yr2014/img/newman.pdf

60 %

of

errors

Page 4: Bar Modeling: Using Models to Help Solve Word Problems

• Draw a diagram/model

• Use prior knowledge

• Look for patterns

• Work backwards

• Restate the problem in another way

• Simplify the problem

• Make assumptions/guesses

• Guess and Check

• Use manipulatives

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When a student is reading and processing a word problem, having a “tool kit” of skills to solve it will make them more comfortable. Bar models, or similar drawings, allow students to create a visual model to represent their word problem. The numbers in the problem are no longer just ideas, students are looking at a representation. For example, they can see a bar showing that Greg has 24 apples and Lisa has 10. They can easily depict that 24 is more than 10, allowing these concrete examples to be in front of us, instead of ideas floating around in our heads!

Greg

Lisa

24

10

Page 6: Bar Modeling: Using Models to Help Solve Word Problems

Steps for Good Model Drawing

1. Read the problem.

2. Identify variables Who and what?

3. Draw unit bar (in young grades use manipulative/pictures) a rectangle or shape that gets added to subtracted from or divided.

4. Reread the problem, chinking information , and adjust bars to match information

5. Decide on your question mark (what the problem is asking for and draw in appropriate place).

6. Work the computation (work horizontally and group in tens as often as possible)

7. Write a grammatically correct sentences to answer the question mark .Singapore math: A visual approach to word problems. (n.d.). Retrieved November 24, 2015, from http://www.hmhco.com/~/media/sites/home/education/global/pdf/white-papers/mathematics/elementary/math-in-focus/mif_model_drawing_lr.pdf?la=en

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PART PART

WHOLE

This model makes sense to us, and it will make sense to our students too! This is a model for basic addition. Part + Part = Whole. We use the same basic principal for subtraction problems, too!

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Bar models are awesome for multiplication, too!

Ex. 3 X 2 = 6

3

Add one unit to your bar at a time! Count with students while adding each one ex. There were three times as many

Say “now let’s start with 1 times as many because the our models are equal. Now add 2 times as many (one more bar), etc.

6

This model is a great visual representation of multiplication without drawing an array or using another more time consuming strategy.

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Bar Models – Summing it up!Like any other strategy or school of thought, bar models are a tool we can use to help our mathematics leaners across grade levels. Math in Focus and Singapore math recommend bar models begin as early as second grade. They are a great tool to supplement your current mathematical instructional practices.

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References

Giblin, P. (2012, April 20). Math steeplechase. Retrieved November 24, 2015, from

https://flic.kr/p/bPbpHk

K. (2010, August 20). Math board addition. Retrieved November 24, 2015, from

https://flic.kr/p/8u2g7R

Math notebooking clock. (n.d.). Retrieved November 24, 2015, from https://flic.kr/p/6dyv8Y

(Originally photographed 2009, April 1)

Newman's prompts: Finding out why students make mistakes. (n.d.). Newman's Prompts: Finding

out Why Students Make Mistakes. Retrieved November 24, 2015, from

http://www.schools.nsw.edu.au/learning/7-

12assessments/naplan/teachstrategies/yr2014/img/newman.pdf

9th grade student Shahnoza School. (2004, June 21). Retrieved November 24, 2015, from

https://flic.kr/p/4ahAgw

P. (2008, April 18). Math homework. Retrieved November 24, 2015, from

https://flic.kr/p/4GYUNU

Segrott, J. (2015, November 22). Long multiplication. Retrieved November 24, 2015, from

https://flic.kr/p/BmJ8Ln

Singapore math: A visual approach to word problems. (n.d.). Retrieved November 24, 2015, from

http://www.hmhco.com/~/media/sites/home/education/global/pdf/white-

papers/mathematics/elementary/math-in-focus/mif_model_drawing_lr.pdf?la=en