Directions: Using the integers -3 to 3, at most one time each, fill in the blanks to make each equation true.

### Hint

What do you know about adding and subtracting integers?

### Answer

There are many possibilities. 2 + -3 = -1 and 1 – 3 = -2; 1 + 2 = 3 and -3 – (-1) = -2

Source: Jeanmarie Mullen

The second solution is incorrect. -3 – 1 = -4

It should read -3 – (-1) = -2

Thanks for pointing this out Kara. I have edited the solution.

you were correct, if you do a KCC, you get -3 + -1 = -4

zero is part of the integer set. Should the directions also state that zero can’t be used?

I let them use zero. Solutions like -2 + 1 = -1 and 0 – (-3) = 3 were found. Made for some good discussion about the meaning of 0.

I really like this activity. Thank you for coming up with it. It is fun and challenging

It is!! It was fun for my students to figure out!

-1+-2= -3

3-2=1

Does this work?

3+-3=0

1+-2=-1

2+-3=-1

1 -3=-2

I believe this is an exhaustive list of answers.

-3 + 1 = -2 and 2 – -1 = 3

-3 + 1 = -2 and 2 – 3 = -1

-3 + 2 = -1 and 1 – -2 = 3

-3 + 2 = -1 and 1 – 3 = -2

-3 + 3 = 0 and -1 – -2 = 1

-3 + 3 = 0 and -1 – 1 = -2

-3 + 3 = 0 and 1 – -1 = 2

-3 + 3 = 0 and 1 – 2 = -1

-2 + -1 = -3 and 3 – 1 = 2

-2 + -1 = -3 and 3 – 2 = 1

-2 + 1 = -1 and 0 – -3 = 3

-2 + 1 = -1 and 0 – 3 = -3

-2 + 3 = 1 and -1 – -3 = 2

-2 + 3 = 1 and -1 – 2 = -3

-1 + -2 = -3 and 3 – 1 = 2

-1 + -2 = -3 and 3 – 2 = 1

-1 + 2 = 1 and 0 – -3 = 3

-1 + 2 = 1 and 0 – 3 = -3

-1 + 3 = 2 and -2 – -3 = 1

-1 + 3 = 2 and -2 – 1 = -3

1 + -3 = -2 and 2 – -1 = 3

1 + -3 = -2 and 2 – 3 = -1

1 + -2 = -1 and 0 – -3 = 3

1 + -2 = -1 and 0 – 3 = -3

1 + 2 = 3 and -3 – -2 = -1

1 + 2 = 3 and -3 – -1 = -2

2 + -3 = -1 and 1 – -2 = 3

2 + -3 = -1 and 1 – 3 = -2

2 + -1 = 1 and 0 – -3 = 3

2 + -1 = 1 and 0 – 3 = -3

2 + 1 = 3 and -3 – -2 = -1

2 + 1 = 3 and -3 – -1 = -2

3 + -3 = 0 and -1 – -2 = 1

3 + -3 = 0 and -1 – 1 = -2

3 + -3 = 0 and 1 – -1 = 2

3 + -3 = 0 and 1 – 2 = -1

3 + -2 = 1 and -1 – -3 = 2

3 + -2 = 1 and -1 – 2 = -3

3 + -1 = 2 and -2 – -3 = 1

3 + -1 = 2 and -2 – 1 = -3