Open Middle®
Directions: Using the integers -3 to 3, at most one time each, place an integer in each box to make both equations 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