Product of Distributive Property

Directions: Decide if 30x – 12 could be a result of using the distributive property. If it is, find the possible combinations of factors whose product would be 30x – 12 (using integer coefficients and constants).


What is the distributive property?
What could you multiply to get 30x and then 12?


30x – 12 could be a product of the distributive property.
Possible solutions include:
1(30x – 12)
2(15x – 6)
3(10x – 4)
6(5x – 2)
considering negatives:
-1(-30x + 12)
-2(-15x + 6)
-3(-10x + 4)
-6(-5x + 2)

Source: adapted from Nathan Charlton

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  1. Oh, negatives in distributive property! That will really challenge student’s thinking.

  2. Why not 0.1(300x-120) ? etc. etc….

    • With most Open Middle problems, we try to create a clear guideline as to the direction of the problem. Most of our work for this is providing students with a list of digits that is acceptable to use. This allows great work for the problem, with various approaches- to get to a single or small set of solutions. Using decimals (while challenging and interesting for this problem) would create an unlimited amount of solutions. I changed the initial wording to compensate for that oversight in this problem.

  3. With the negative constant, I really think this belongs in 7.EE.1 rather than 6.EE.3.

  4. It could have been 42x – 28 + 16 – 12x –> 30x – 12

  5. 6 (5x – 2)

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