Open Middle®
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to create two true number sentences. You may reuse all the digits for each number sentence.
Hint
What does the equal sign tell you?
How do we know if both sides of the equal sign have the same value?
How do we know if both sides of the equal sign have the same value?
Answer
There are many answers to this problem including:
1 + 6 = 9 – 2
2 + 3 = 6 – 1
What students MIGHT think is correct, but is NOT correct is:
1 + 6 = 7 – (any number other than 0)
2 + 3 = 5 – (any number other than 0)
This would be because 1 + 6 = 7 and 2 + 3 = 5. However, both sides of the equal sign must have the same value, and they do not when you subtract another number other than zero.
Source: Robert Kaplinsky
I’m confused on the directions for this problem. The sample answer uses the digit 6 twice and the digit 2 twice. Are they only supposed to worry about repeating digits within one equation?
Thanks in advance for clarifying this!
I think we’d expect students to give one of those sample answers. Within a student’s one equation, we wouldn’t see repeated digits.
Sorry, yes, you can reuse all the digits again for each equation. Alternatively you could not reuse digits and that would be even more challenging.
2+3=6-1