CCSS.MATH.CONTENT.3.OA.B.5: Candy Counting Using Chunking

Counting can be stressful.

When the brain is presented a lot of information at the same time, the filtering process may become overwhelming. This is when cognitive strategies are useful, and these skills are part of any good math test preparation program.

Let us try to count all the candy in the following photo:

It is difficult. And a little stressful. The direction of counting may feel random, and the multiple colors and positions may be very distracting. Also, if students with disabilities have attention problems, counting the candy in the photo is nearly impossible without some cognitive strategy.

Perhaps we can help improve the counting process by grouping the candy by color. We do that, and try counting again.


However, this grouping may still be putting pressure on working memory. The brain is still making decisions about where to start counting and which direction to follow. That bandwidth is taking “processing power” away from our main counting task.

If we could break up the candy into smaller groups, the chunking process could make counting much easier.

Let’s find out.

Much better.

We can now count the smaller groups of candy using the chunking facility in our working memory. We can see the groups at a glance, and we can count the number of groups with minimal effort.

Grouped by color, we can now take a running tally of the candy without overwhelming the working memory.

Red2 groups of 4, 1 group of 5
(4 x 2) + (5 x 1)
Green2 groups of 5
(5 x 2)
Blue1 group of 3, 1 group of 4, 1 group of 5
(3 x 1) + (4 x 1) + (5 x 1)
Brown1 group of 4
(4 x 1)
Yellow1 group of 4, 1 group of 3
(4 x 1) + (3 x 1)
Orange2 groups of 5
(5 x 2)

In Wolfram Alpha, type this:
(4 * 2) + (5 * 1) + (5 * 2) + (3 * 1) + (4 * 1) + (5 * 1) + (4 * 1) + (4 * 1) + (3 * 1) + (5 * 2) (view)

OR type this:
SUM(4*2,5*1,5*2,3*1,4*1,5*1,4*1,4*1,3*1,5*2) (view)

CCSS.MATH.CONTENT.3.OA.B.5: Apply properties of operations as strategies to multiply and divide.

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