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Counting Mats Help Build a Foundation of Understanding for Division

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Placing Counters Helps Students Understand Division.
Counting Mats Help Build a Foundation of Understanding for Division

A division mat, a simple template for distributing counters into equal groups.

Jerry Webster

Counting mats for division are incredible tools to help students with disabilities understand division.

Addition and subtraction are in many ways easier to understand than multiplication and division, since once a sum exceeds ten, multi-digit numbers are manipulated using regrouping and place value. Not so with multiplication and division. Arrays are powerful ways to illustrate both multiplication and division, but even these may not help students with disabilities understand division. They may require more physical and multi-sensory approaches to "get it into their fingers."

Use the pdf templates or create your own to make division mats. Each mat has a number by which you are dividing in the upper left corner. On the Mat are the number of boxes. Give each student a number of counter (in small groups, give each child the same number, or have one child help you by counting out the counters.) Use number you know will have multiple factors, i.e. 18, 16, 20, 24, 32. Write the number sentence on the board: 32 / 4 = , and have students divide their numbers into equal amounts in the box by counting them out, one at a time into each box. You will see some ineffective techniques: let your students fail, because in correcting their counting, they will gain a stronger understanding of division.

I am only providing counting mats from 2 to 6: for ones, just draw a big square in the middle of a whiteboard slate. By the time a students has divided numbers up through 48 by 6, your students should have a strong understanding of the operation: if not, repetition works as well with divisors from six and under as 7 and over.

2 Division Mat pdf

3 Division Mat pdf

4 Division Mat pdf

5 Division Mat pdf

6 Division Mat pdf

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