Bar Model BasicsAn Introduction to the Bar Model

Strategy: Fractions

Lyndsey KlempaySusan 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:

readunderstand (translate)

strategizecompute

check workStudents 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 MethodWork 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 ModelStudents 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.

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Step-by-Step Model DrawingChar 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 restOf 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 = ?2 x 3 = ?

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 WebsitesThinkingblocks

SchooltubeLearnzillion divide

Learnzillion multiplyVimeo

MathplaygroundThinkingblocks Index

GreatSourceThinkingblocks Fractions

TheSingaporeMaths-Great Questions

What AKS have we covered today?

Turn and talk to your neighbor about what you think we covered today.