Singapore Primary Math Explained sc-math

Solving math problems with model diagrams

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Part-whole model Comparison model Solving model diagrams

Comparison model

comparison model

The comparison model is used for problems where there is a need to compare (more/less, before/after, difference, etc) two or more variables. Two or more bars are used to represent the problem.

Examples

Mark bought a pen and a book. The book cost $30. If the book costs 3 times as much as the pen, how much did Mark pay for both items?

model diagram

    3 units = $30
    1 unit  = $30 ÷ 3   = $10
    4 units = 4 × $10   = $40
    Mark paid $40 for the pen and the book.

Mark bought a pen and a book. The book costs 3 times as much as the pen. If the book costs $30 more than the pen, how much did Mark pay for both items?

model diagram

    2 units = $30
    1 unit  = $30 ÷ 2   = $15
    4 units = $4 × $15   = $60
    Mark paid $60 for the pen and the book.

2 pens and a book cost $36. The book cost $6 more than a pen. Find the cost of the book.

model diagram

    3 units + $6 = $36
    3 units = $36 - $6   = $30
    1 unit  = $30 ÷ 3   = $10
    1 unit + $6 = $16
    The book costs $16.

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