Open Middle®
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)
There’s a task on Open Middle called “Distributive Property” that should link to “https://www.openmiddle.com/distributive-property-2/” and has “Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make a true equation. Source: Adrianne Burns” as the preview text, but instead it links to this exercise.