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Model Drawing(Basics)

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• Models are pictorial representations (i.e. bar diagrams) drawn to represent the data in a problem sum.

• It allows us to visualize the relationship between the parts and/or whole in a problem sum.

Model Drawing

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Problem Solving Tips

• Read the question carefully.

• Underline important information.

• Transfer the information/data into a model.

• Use a ? to represent the unknown data.

• Label the model with names of the people/things in the question.

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Types of Models• Part-whole (i.e. for one person)

Ali

Ali

Don

• Comparison (i.e. for comparison between two people)

30 stamps

?

30 stamps

?

Don has as

many stamps as Ali.

3

2

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Part-whole model

• A box of cereal costs $7. How many such boxes of cereal can Kelly buy with $42?

$42

$7

• $42 ÷ $7 = 6

She can buy 6 boxes of cereal.

? boxes

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Comparison Model

• Bala has the amount of money Alyssa has.

Bala has thrice the amount of money Catherine has. If the total amount of money they have is $50, how much money does Alyssa have?

2

1

B

C

A

$50

?

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10 units $50

1 unit $50 ÷ 10

= $5

B

C

A

$50

?

6 units $5 x 6

= $ 30

She has $30.

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Other models

• ‘Stack Up’ Model

• ‘Constant Difference’ Model

• Before & After Model

These models are improvisation of the part-whole and/or comparison models.

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‘Stack Up’ Model• 2 dictionaries and 4 novels cost $90.

Each dictionary cost thrice as much as each novel. How much did each dictionary cost?

D

$90

?

N

D

NNN

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N

D

$90

?

D

NNN

10 units $90

1 unit $90 ÷ 10

= $9

3 units $9 x 3

= $ 27

Each dictionary cost $27.

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‘Constant Difference’ Model

• There was 14 kg of rice in Box A and 2 kg of rice in Box B. Tommy added an equal amount of rice into each box. Now there are 5 times as much rice in Box A as in Box B. How much rice is there in Box A in the end?

Box A

14 kg

Box B

2 kg 12 kg

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There is 15 kg of rice in Box A.

4 units 12 kg

1 unit 12 kg ÷ 4

= 3 kg

Box A

14 kg

Box B

2 kg 12 kg

14 kg – 2 kg = 12 kg 5 units 3 kg x 5

= 15 kg

?

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Before & After Model

John

?

Ivan

• John and Ivan had an equal number of sweets. After John gave away 36 sweets, Ivan had 5 times as many stamps as John. How many stamps did Ivan have?

36

John

IvanBefore

After

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John

Ivan

?

36

Ivan had 45 sweets.

4 units 36

1 unit 36 ÷ 4

= 95 units 9 x 5

= 45