Choose manipulatives that are a similar as possible. If you want to use candy, try to sort them out by color so that you use all of the same color for each number you intend to divide. This will help when you want to begin looking at more complicated concepts like common factors.
Choose the same number of manipulatives (I'm using yellow tiles) as your number.
If my number is 6, here are my tiles:
Note that I have them ungrouped. They should not be piled on top of each other, so each is easy to see.
Now, if my problem says 6 ÷ 2, that means two groups:
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| 6 ÷ 2 = 3 |
Each group gets 3 tiles, so 3 is the answer to 6 ÷ 2.
If, instead, the problem says 6 ÷ 3, that's 3 groups:
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| 6 ÷ 3 = 2 |
8 ÷ 4, that's 4 groups:
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| 8 ÷ 4 = 2 |
Each group gets 2 notes, so the answer is 2.
Another way that often makes this sort of thing clearer is to use a manipulative that has actual value, and some characters, such as dollars for the manipulatives and muppets for the characters. We'll use Elmo, Jesse, and Rosita as our characters.
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| Left to Right: Elmo, Jesse, and Rosita *See below for image attribution. |
I would tell my student, "Okay, I have $9.00," and let my student count the dollars. "I want to give Elmo, Jesse, and Rosita each the same amount." I would let my student divide the dollars like handing out cards. "How much money does each muppet get?" And the answer is $3.00. For some reason anchoring the problem in money or something else of value, like candy or another treat, taps into a student's sense of fair play. We should divide fairly--and therefore each character will get the same amount in the end. That can help a student otherwise struggling with the concept of division to grasp what's going on.
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* This image is a work of a U.S. military or Department of Defense employee, taken or made as part of that person's official duties. As a work of the U.S. federal government, the image is in the public domain in the United States.
