Readings for Session 11 – (Continued)  

More Examples of Division Problems and Models

Identify the sets and the model used in each division problem.

 

Example:  Three children are to share 12 pencils equally, how many pencils should each child receive?

Each child is the recipient of a set and the pencils are the elements. The question may be rewritten as “How many elements should each set receive?” This is the partition model.

Note that 12 ÷ 3 = 4 and 3(4) = 12.     Each child would receive four pencils.

 

Example:  Twenty-one trees are to be planted in four equal rows, how many trees are to be planted in each row?

Each row represents a set and the trees are the elements. The question may be rewritten as “How many elements are to be put into each set?” This is the partition model.

Note that 21 ÷ 4 = 5 R1 and 4(5) + 1 = 21. Five trees would be planted in each row with one tree left over.

 

Example:  Each child is to receive 3 pencils from a box containing 12 pencils. How many children will get pencils?

Each child is the recipient of a set and the elements are the pencils. The question may be rewritten as “How many sets will get three elements?” This is the repeated-subtraction model.

Note that 12 – 3  – 3 – 3 – 3 = 0, so 12 ÷ 3 = 4 and 4(3) = 12.
Four children will receive pencils.

 

Example:  A car is at mile marker 200 on I-94. If the car is traveling west at 50 mph, how long will it take the car to reach the state border?

Each hour can be associated with a set and the elements are the miles. The question may be rewritten as “How many sets will take 50 elements?” This is the repeated-subtraction model.

Note that 200 – 50  – 50 – 50 – 50 = 0, so  200 ÷ 50 = 4 and 4(50) = 200.
It will take the car four hours to reach the border.

 

Example:  A wagon will hold 150 bushels of wheat. How many wagon loads will it take to fill a bin that holds 900 bushels?

Each wagon is a set and the elements are the bushels. The question may be rewritten as “How many sets will hold 150 elements?” This is the repeated-subtraction model.

Note that 900 – 150  – 150 – 150 – 150 – 150 – 150 = 0, so 900 ÷ 150 = 6 and 6(150) = 900.

Six wagon loads are needed to fill the bin.

    

      

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