Open Middle®
Directions: Use only the digits 1 to 7, at most one time each, fill in the boxes to create a true equation.
Hint
What place value would you like to start with? What digits “go” together?
Answer
Number of Unique Solutions: 20 (40 with commutative property)
1: 43 = 16 + 27
2: 43 = 17 + 26
3: 47 = 32 + 15
4: 47 = 35 + 12
5: 57 = 21 + 36
6: 57 = 31 + 26
7: 61 = 34 + 27
8: 61 = 37 + 24
9: 62 = 15 + 47
10: 62 = 45 + 17
11: 67 = 14 + 53
12: 67 = 54 + 13
13: 71 = 25 + 46
14: 71 = 26 + 45
15: 74 = 23 + 51
16: 74 = 53 + 21
17: 75 = 12 + 63
18: 75 = 13 + 62
19: 76 = 41 + 35
20: 76 = 45 + 31
Source: Eric Appleton
62=59+43
12 +15 =27
You are not supposed to use the same digit twice!
59+42= 102 (not 62)
50=40+10
Zero is not a choice of digits.
17+8=25
90=14+76
90=67=23
90=34+56
90=27+63
Can’t use 0 or 9.
76=52+24
15=7+8
76=35+41
97=76+21
94=74+20
45=35+10
74=39+45
76=35+41
97=76+21
94=74+20
45=35+10
74=39+45
43=17+25
57=21+36
74=21+53
67=13+54
100=10+90
How are you supposed to explain this to a 2nd grader to solve?
I would use cards on which I would write the digits 1 to 7. Then you have to ask them questions about additions. I will try it out with my students on Zoom next Monday. I know they will enjoy. I think I’m going to make a little explanation on Explain Everything.
60=40+20
43 = 16 + 27
43=27+16
49 = 17 + 32
76 = 45 + 31
57 = 21 + 36
79 = 56 + 23
57 = 37 + 20
Who on earth is writing these questions for second graders? I am three years through my math degree and had trouble with this, let alone explaining it to my little sister.
20+20=40
30+30=60
90+80=170
180+160=250
56+32=88
86+14=100
63+34=97
47+52=99
70=40+30
43=20+23
20=10+10
64=50+14
80=35+45
40=35+5
68=45+23
39=15+24
50=26+24
70=35+35
40=35+5
67=45+22
37=15+22
50=26+24
43 = 16+27
61 = 14+47
14=12+26
16=19+35
62=43+19
71=26+45
2000 = 2x 1000
5000 = 3000 + 2000
600000000000 = 2×300000000000
17+6=23
15+6=21
43 = 16 + 27
43 = 17 + 26
47 = 32 + 15