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).

### Hint

What is the distributive property?

What could you multiply to get 30x and then 12?

What could you multiply to get 30x and then 12?

### Answer

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)

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

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

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.

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

Thanks Alisan. I see your point. I added 7.EE.1 as a standard.

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

6 (5x – 2)