Make it Equal

Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to create a true statement.

Hint

Are there numbers that are helpful to use first or save for last?
What would a drawing/model look like to match this equation?

Answer

Number of Unique Solutions: 48 (allowing for permutations)
1: 8 = 2+6 = 1+3+4
2: 8 = 2+6 = 1+4+3
3: 8 = 2+6 = 3+1+4
4: 8 = 2+6 = 3+4+1
5: 8 = 2+6 = 4+1+3
6: 8 = 2+6 = 4+3+1
7: 8 = 6+2 = 1+3+4
8: 8 = 6+2 = 1+4+3
9: 8 = 6+2 = 3+1+4
10: 8 = 6+2 = 3+4+1
11: 8 = 6+2 = 4+1+3
12: 8 = 6+2 = 4+3+1
13: 9 = 1+8 = 2+3+4
14: 9 = 1+8 = 2+4+3
15: 9 = 1+8 = 3+2+4
16: 9 = 1+8 = 3+4+2
17: 9 = 1+8 = 4+2+3
18: 9 = 1+8 = 4+3+2
19: 9 = 2+7 = 1+3+5
20: 9 = 2+7 = 1+5+3
21: 9 = 2+7 = 3+1+5
22: 9 = 2+7 = 3+5+1
23: 9 = 2+7 = 5+1+3
24: 9 = 2+7 = 5+3+1
25: 9 = 4+5 = 1+2+6
26: 9 = 4+5 = 1+6+2
27: 9 = 4+5 = 2+1+6
28: 9 = 4+5 = 2+6+1
29: 9 = 4+5 = 6+1+2
30: 9 = 4+5 = 6+2+1
31: 9 = 5+4 = 1+2+6
32: 9 = 5+4 = 1+6+2
33: 9 = 5+4 = 2+1+6
34: 9 = 5+4 = 2+6+1
35: 9 = 5+4 = 6+1+2
36: 9 = 5+4 = 6+2+1
37: 9 = 7+2 = 1+3+5
38: 9 = 7+2 = 1+5+3
39: 9 = 7+2 = 3+1+5
40: 9 = 7+2 = 3+5+1
41: 9 = 7+2 = 5+1+3
42: 9 = 7+2 = 5+3+1
43: 9 = 8+1 = 2+3+4
44: 9 = 8+1 = 2+4+3
45: 9 = 8+1 = 3+2+4
46: 9 = 8+1 = 3+4+2
47: 9 = 8+1 = 4+2+3
48: 9 = 8+1 = 4+3+2

Source: Molly Rawding

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11 comments

  1. Okay, I am going to be THAT person right now. But I just noticed that the second example answer uses the digit 1 twice. Just attending to precision, over here. 🙂
    This is such an awesome activity. My students blow me away with their engagement and perseverance in looking for multiple ways to solve! Thanks, as always, for sharing these fantastic resources.

  2. The first answer is wrong . It should be 9=7+2=5+3+1

  3. Yes, definitely mistakes! Thank for catching that!
    8 = 6 + 2 = 4 + 3 + 1
    9 = 8 + 1 = 4 + 3 + 2

  4. In the Framework Chapter for California, it states that we should use the language “the same as” before introducing “equals” for the = symbol. What are your thoughts for changing the title of this task?

  5. I just love these! I thought there were some in Spanish too. Are there prompts in Spanish or only the recording sheet?

    Thank you!
    Jacquelyn

  6. Thanks for this task! I really love it. I used it today in a year 3-4 class. I think your idea of hints is great (in Australia we call them enabling prompts). I think you could add another hint before your first one. I assisted some students by asking “what numbers can’t go in the first box?” This helped some students in starting their thinking. Thanks again.

  7. 8= 6+4+3+2+1
    9 = 8 + 1 = 4 + 3 + 2

  8. This was really fun and I cannot wait to use these Open Middle problems in class. I came up with 8=6+2=1+3=4

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