Directions: Use the digits 1 to 9, at most one time each, to create two equations: one where x has a positive value and one where x has a negative value.

### Hint

How does the value of the number being added to x affect the value of x?

How does the value of the sum affect the value of x?

How does the value of the sum affect the value of x?

### Answer

There are many answers. To get a positive solution, the number being added to x should be less than the sum. To get a negative solution, the number being added to x should be greater than the sum.

Source: Robert Kaplinsky

Could you extend this by asking: ” Using the same digits, create an equation where x has a negative value. What do you notice?”

Sure. That’s a fine hint.

I love the critical thinking required in these questions, but this particular question isn’t a sixth grade Common Core standard. The standard, 6.EE.7, asks students to solve multiplication and addition equation with numbers that are all “nonnegative rational numbers”. Is there a way to align this question to the standard better while still preserving the DOK level? Students do not learn operations with negative numbers until the seventh grade.

X is positive:

1 x 3 + x = 2 x 6

3 + x = 12

x = 9

X is negative:

3 x 6 + x = 2 x 5

18 + x = 10

x = -8

Interesting that you interpreted the two boxes next to each other as multiplication. I was thinking they are two digit numbers.

Some positive solutions are:

13 + x = 25

24 + x = 35

Some negative solutions are:

25 + x = 13

35 + x = 24

Is it possible to do this and have x equal the same number in both equations? That’s originally what I thought I needed to do! 🙂