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MathBait™ Multiplication

Count This

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In this short activity, students authentically develop an understanding of the importance of systematic exploration in order to ensure completeness.


Resource Type


Primary Topic

Primes & Factoring







The goal of this activity is to help students see how a systematic method is helpful for organizing information.

Provide students with a collection of small items such as a handful of M&Ms, number cubes, or paperclips. We recommend providing somewhere between 25 and 50 items. Lay them out on a table and ask students to count the items. Watch for strategies such as clever grouping. (For more on this, check out Marco the Great and the History of Numberville).

Some great strategies are making groups of 5's or 10's and skip counting. Allow students to share their different strategies.

Next, provide students with a new group of objects (it can be the same items, but should be a different quantity). Make sure to scatter them a bit on the desk/table in front of students and announce they will not be able to touch the items this time. Ask students to determine how many objects are in front of them.

Students will find the task more difficult without the ability to organize the items. Allow students to share their strategies for counting the total without the ability to sort or group.

Conclude the activity by asking students the following questions:

  • How did you know you counted all the items each time?

  • What strategies made it easier to count the items?

Both parts of this activity parallel the struggle in finding factors. In the first part, when students could touch the items, organizing into smaller groups was helpful as it is easier to make sure each group has 5 or 10 and then skip count to find the total. This strategy will be important in factoring: we want to use what we know to help us find all the factors.

In the second part, we couldn't touch the items. The lesson to learn here is the importance of a systematic approach. Counting one on the top, then one on the right, then one over here, then one over there will make the task impossible! Most students will likely approach by moving in one direction as they count. Highlight the strength of this method. When we factor, it will be helpful to start with the smallest building blocks and move up systematically to ensure we counted every option.

Conclude the activity by reminding students that staying organized will help us to make sure we don't miss anything.

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