Introduction to Bar Modeling

with Singapore Math

by Beckey Townsend

Benefits of Model Drawing1. Models give students a tangible graphic to hold on to as

they compute a word problem.2. Modeling emphasizes the relationships between values in

the computation.3. It teaches students to look for the way the parts relate to

the whole.4. It provides a step-by-step road map to solving most word

problems.

3 Backbone Pieces of Singapore Math* Problem Solving* Mental Math* Intense Number Sense & Place Value Instruction

Number SenseA student’s overall understanding of a number.

Model Drawing Steps1. Read the entire problem.2. Rewrite the question in the problem as a statement, leaving underlined space for the answer.3. Identify the WHO and WHAT is involved in the problem. List these variables, ALWAYS in order.

4. Draw unit bar(s) to model each variable and place question mark.5. Read each sentence, one at a time and adjust/label your unit bars to match information. Label your question mark with words?

6. Work your computation and solve the problem correctly. Check for reasonableness. See tips.7. Write the answer in your complete sentence.

STATEMENT (2 pts) LABEL/LIST/DRAW (4 pts)

WORK (2 pts) ANSWER (2 pts)

Great article available online to give parents at orientation:Teach Kids Math with Model Method

www.teach-kids-math-by-model-method.com

Sample Problem:Mike has 21 crayons. Elisha has 7 crayons. How many more crayons does Mike have than Elisha?

Tips to TryFor Step 1

• Whole class read aloud together

• Each student copy problem & silently read

• Alternate calling on various students to read aloud

• Teacher read problem to class

• Students partner to read to each other

Step 2 - Statement:Mike has _______ more crayons than Elisha.

Step 3 - Guiding Questions for Variables:• WHO is the word problem about?• Is there anyone else?• Who knows the “WHAT” of our problem?• Does anyone have any other ideas for WHAT ?• Re-read and decide for WHAT you are solving: total crayons?

Difference in crayons?

Step-by-Step Bar Modeling for Easy Problem Solving

Example 1: Step 2 Mike has _______ more crayons.

Example 1: Step 3Mike’s crayonsElisha’s crayons

Example 1: Step 4

Mike’s crayonsElisha’s crayons

Example 1: Step 5

Mike’s crayonsElisha’s crayons difference

217

Example 1: Steps 6 & 7Comparing numbers to find the difference

21 – 7 same as 24 – 10 = 14

14 Computation Tips

1. What does this information give you?

2. Why is it important?

3. Where does the number go in the model?

4. Now what do you do?

Step-by-Step Bar Modeling for Example #2

Step 1:READ

Step 2:WRITE

Step 3:LIST

Step 4:DRAW

Step 5:ADJUST

& LABEL

Steps 6 & 7:Compute

& Answer

2. Sally has 47 jelly beans in her candy jar. She and her friend Anna ate 28 jelly beans. How many jelly beans does Sally have in left in her jar?

Sally has ______ jelly beans left in jar.

Sally’s beans

Sally’s beans

Sally’s beans

47

28

Left in jar

Total in jar

Whole to Part = find the difference 47 – 28 ORFind compliment by adding 2 to both numbers: 49-30 = 19

19

Computation Tips

1. What does this information give you?

2. Why is it important?

3. Where does the number go in the model?

4. Now what do you do?

Step-by-Step Bar Modeling for Multiplication Word Problems

Golden Rules of Multiplication Model Drawing1. When a problem says, “There were ____ times as many…” hone in on what that means.

- Add one unit at a time to your beginning unit bar (1x) = “counting method”- Example: Start with 1 times when comparing variables Jane’s cookies □ (1x)

Jim’s cookies □ (1x)2. It is usually helpful to draw a smaller unit bar to begin. Then add units as you count up # of times.3. Make sure the model mirrors the statement sentence.

Step 1:READ

Ryan had 4 times as many marbles as Jordan. If they had 60 marbles altogether, how many marbles did Ryan have?

Step 2:Write

Ryan had _______ marbles.

Step 3:List

1x 2x 3x 4x

Ryan’s marbles 60

Jordan’s marbles ? Total

Steps 4-5:Draw & Adjust

Ryan’s marblesJordan’s marbles

Steps 6 & 7:Compute

& Answer

Ryan = 4 units 5 x ___ = 60 OR 60 ÷ 5 = ____ = 12Jordan = 1 unit 1 unit = 124 units + 1 unit = 5 total units Ryan’s 4 units? 4 units = 4 x 125 units = 60 = (4 x 10) + (4 x 2)1 unit = ? = 40 + 8 = Ryan had 48 marbles.

Practice this problem in journal.

Monica had 3 times as many pens as Griffin. If they had 220 pens altogether, how many pens did Monica have?

Computation Tips

1. What does this information give you?

2. Why is it important?

3. Where does the number go in the model?

4. Now what do you do?

48

Singapore Math Strategies: Model Drawing for Grades 1-6* Addition & Subtraction/ Multiplication & Division * Rate & Travel* Part to Whole Models * Comparison Models* Mixed Operation * Fraction (Simple & Complex)

Advanced Model Drawing Grades 6-9*Complex Part to Whole * Complex Comparison* Before & After (Fractions & Ratios) * Decimals* Percents * Integers * Remainders

Bar modeling easily lends itself to leveling up or down in complexity.