The document discusses the use of bar models in teaching mathematics. Bar models are visual representations that allow students to depict word problems as diagrams rather than abstract ideas. They can show relationships between quantities by using bars for each number or variable. The document provides guidelines for constructing bar models step-by-step and examples of how bar models can represent addition, subtraction and multiplication problems. It promotes bar models as an effective tool to help students understand and 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