Open Middle®
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to create a true statement.
Hint
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
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.
The first answer is wrong . It should be 9=7+2=5+3+1
Yes, definitely mistakes! Thank for catching that!
8 = 6 + 2 = 4 + 3 + 1
9 = 8 + 1 = 4 + 3 + 2
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?
That could work. The titles are more for teachers than for students so this makes it easier to search for.
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
We’re still working on getting problems translated. It’s slow going.
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.
8= 6+4+3+2+1
9 = 8 + 1 = 4 + 3 + 2
6= 3+3= 2+3+1
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