An Introduction to the Bar Model
Strategy: Fractions
Lyndsey Klempay
Susan Kuehn
www.barmodelbasics.weebly.com
Jia earned money babysitting. She spent 1/4 of
the money on lunch. She spent 1/2 of the
money on a DVD, and she saved $4. How
much money did Jia spend on the DVD?
What are bar models?
Bar models are visual representations of word problems.
They help students describe relationships between items
(variables) in a problem.
Bar models are not intended as a replacement for all other
important and effective problem solving approaches. Bar
model drawing is a valuable tool to supplement your
problem solving tool box.
Word problems require students to:
read
understand (translate)
strategize
compute
check work
Students learn to draw bar models first using
numbers and computations they have already
mastered.
Why Bar Models?
*Maximize student understanding
*Help students visualize complex relationships
*Teach students to think analytically
*Provide an important transition between concrete
(actual objects) and abstract (algorithm)
“Pictorial bridge to abstract thinking”
*Help students organize thoughts to make the
problem manageable or approachable.
*Develops and transfers to algebraic thinking
Learning Model Drawing
1st Process – how to use model drawing to solve
word problems.
2nd Application – apply process independently
Discrete Method
Work with the discrete method of model drawing first.
Draw one square to represent each object in the
problem.
Reinforce one-to-one correspondence.
The student moves from using manipulatives to using
symbols to represent the objects.
Continuous Model
Students write the appropriate number inside
the unit bar, instead of drawing one unit for
each object.
Draw a unit bar, adjust it, and add values.
Most problems we will practice will use the
continuous model.
4
Step-by-Step Model Drawing
Char Forsten
1. Read the entire problem.
2. Rewrite the question in sentence form, leaving a space for
the answer.
3. Determine who and/or what is involved in the problem.
4. Draw the unit bar(s).
*5. Chunk the problem, adjust the unit bars, and fill in the
question mark.
*6. Correctly compute and solve the problem.
7. Write the answer in the sentence, and make sure the
answer makes sense.
I have 3 red M&M’s and 6 yellow
M&M’s. How many M&M’s do I have?
Discrete:
Continuous:
I have 12 red color tiles and 14 blue color
tiles. How many color tiles do I have?
Discrete:
Continuous:
There are 109 boys and 85 girls in the fifth
grade. How many students are there?
Discrete:
Continuous:
Important
*Follow a consistent approach.
*Chunk information.
*Provide explicit, guided instruction from the
beginning.
* Embed problem solving throughout all
standards using ANY problem solving methods.
Let’s Try!
Use your journal and manipulatives if
needed.
Feel free to use colored pencils or
crayons to develop your solution.
If 2/3 of a number is 4, what is the
number?
Marissa spent 2/3 of her money at the
mall and had $10 left. How much
money did she spend at the mall?
A pie was cut into 6 equal pieces. Luke
ate 1/3 of the pie. How many pieces
were left?
There is 1/2 of a candy bar that needs
to be divided evenly among 3 children.
What fraction of the total candy bar will
each child receive?
There was 1/2 of a chocolate cake left
over after dinner. Four people shared it
equally the next day. What fraction of
the whole chocolate cake did each
person eat?
Terra’s monthly allowance is $48. She puts
1/2 of her allowance into savings and
gives 3/4 of the remaining money to a local
charity. How much money does Terra have
left for herself each month?
Marcus wrote 3 pages of his science report
on Monday. He wrote 2/3 of the remainder
on Tuesday. He still needed to write 2
more pages. How many total pages was
Marcus’s science report?
Angela baked cookies. She gave 1/3
of them to her sister, and she put 5/8 of
the remaining cookies in the freezer. If
she had 1 dozen cookies left, how
many cookies did she bake?
Kathy had fun baking lots of cookies. She left them
on a plate to cool while she went shopping with her
dad. Her brother saw the cookies and took 1/2 of
them to his Scout meeting. Her sister took 2/3 of the
remaining cookies to share with her friends. Finally,
her mom took 1/2 of the remaining cookies to her
Book Club meeting. When Kathy and her dad got
home, there were only 5 cookies left on the plate.
Danny loved candy, especially chocolate bars.
He loved them more than football and his favorite cars.
He loved them more than video games and the rest
Of all the things he loved, chocolate was the best.
For a special treat he was given a huge bar for free.
It was so very big. It measured twelve squares by three.
Though he loved his chocolate, he thought it was fair,
If with his friends, he decided to share.
Danny broke up the bar and half of it he took.
He shared the other half with Ted, Joe, and Brooke.
Of the half share the three friends took a third.
They gobbled chocolate so fast, no one said a word.
If Danny took half, how many squares did he get?
This answer is easy, there’s no need to fret.
His friends received 1/3 of 1/2 of the bar.
So how many squares do they have so far?
So here’s the big question, its answer you’ll find.
What fraction of the big bar did the friends get from Danny so kind?
Jia earned money babysitting. She spent 1/4 of
the money on lunch. She spent 1/2 of the
money on a DVD, and she saved $4. How
much money did Jia spend on the DVD?
1. Read the entire problem.
If 2/3 of a number is 4, what is the number?
Reflectively read the problem.
Read the problem without reading the numbers.
Visualize the problem without the numbers interfering
with thoughts.
Reread the problem again with the numbers.
2. Rewrite the question in sentence form,
leaving a space for the answer.
The number is _____ .
Focus on the question to strengthen understanding of
the problem and to guide thinking and modeling.
3. Determine who and/or what is involved
in the problem.
The number
4. Draw the unit bar(s).
The number
5. Chunk the problem, adjust the unit bars,
and fill in the question mark.
The number
44
?
6. Correctly compute and solve the
problem.
Step One: 4 ÷ 2 = ?
Each box is 2.
Step Two: 2 + 2 + 2 = ?
2x3=?
7. Write the answer in the sentence, and
make sure the answer makes sense.
The number is _____.
Ask students to write their own
questions related to the original
problem.
Great homework assignment!
TIPS
*Provide graph paper
to help with spacing and alignment.
*Create a daily word problem.
Use strips of paper or sticky labels for the math notebook.
*Use “proof” sheets or show evidence,
NOT “scratch” or “scrap” paper.
*Create your own problems.
Change names, numbers, circumstances, or questions using previous practice
problems.
* Work backwards.
Once students have mastered model drawing, give a solution to the class and
ask them to create a story problem.
Practice makes permanent!
Char Forsten
Model drawing is a picture of success!
Remember:
Solve each problem yourself before assigning it to
students. 
Great Websites
Thinkingblocks
Schooltube
Learnzillion divide
Learnzillion multiply
Vimeo
Mathplayground
Thinkingblocks Index
GreatSource
Thinkingblocks Fractions
TheSingaporeMaths-Great Questions
What AKS have we covered today?
Turn and talk to your neighbor about what you think we
covered today.