Using bar models in math instruction to help solve word problems.

1. https://flic.kr/p/bPbpHk

2. • 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
https://flic.kr/p/6dyv8Y

3. 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

4. • 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
https://flic.kr/p/4GYUNU

5. 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

6. 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

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

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

9. 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.
https://flic.kr/p/4ahAgw

10. 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