Open Middle®
Directions: Use the digits 0 to 9, at most one time each, to fill in the boxes so that the sum is as close to 10 as possible.
Hint
How can we get close to 10 by adding digits in the ones place?
Answer
8.2 + 1.3 + 0.49
8.3 + 1.2 + 0.49
8.2 + 1.4 + 0.29
8.3 + 1.4 + 0.29
8.3 + 1.2 + 0.49
8.2 + 1.4 + 0.29
8.3 + 1.4 + 0.29
Source: Giselle Garcia
thank you for the task. Please edit the name.
Sorry, I’m not seeing it. What part needs to be edited?
I don’t know what to do here anyways.
The directions say only digits 1 to 9. Please correct if you are using the digit zero (0). My solution was 5.6 + 1.4 + 2.98 using your allowed digits.
Good catch. I’ll fix it.
5.7+1.8+2.49
My 6th graders said you could not use 0 in the directions 🙂
Good catch. I’ll fix it.
Here is the beauty of Open – middle: discussions about what you didn’t think about.
I think in the original problem you could replace the box for the numbers place with a zero.
OR you could allow zero to be used, then?
5.9 + 2.3 + 1.80 !
Technically my answer is incorrect because the original problem says “”…as close to…” not to actually reach 10, so: 6.9 + 2.3 + 0.81 ! (You didn’t say we couldn’t go over 10)
I’m sure there is more!
Totally Franco. Lots of possibilities.
Such a great problem for even your 7th and 8th graders. The decision for a student to work the problems by stacking and adding as rearrangement is essential the flexible math thinking. So many students do not go there until it is brought up in discussion or presented as another student’s work.
In your hint, do you mean, “How can we get close to ten by adding digits in the ones place?”
Yes. Thank you for catching this error, which has now been fixed.
Eso es el mimo dijito porque 5 .8 + 1.8 + 2 .49
So, do the directions specifically imply that the sum cannot actually BE 10?
If not, 5.9 + 2.3 + 1.80 – thanks to my student Jennifer M.
I have another answer that equals 9.99- thanks to my student Anthony B
6.8 + 2.4 + 0.79
Eso es el mimo dijito porque quiere decir que es el mismo dijito
what do you do? its to confusing
4.6+3.5+1.27=9.37
I cant even use the picture if just shows a photo can you put a text box on the boxes so we can write?
The boxes just come as a picture can you put text boxes so we can type our answers ?
One of my students did 4.7+3.5+1.80
1.8+3.2+5.4=10.4
I got 10.27 by adding 4.1+3.5+2.67 sigh almost got it 🙁
1: 7.6+2.3+0.14 = 10.04
2: 6.5+3.4+0.12 = 10.02
One of my students, Sophia, found another solution that gives a sum of exactly 10!
4.8 + 3.7 + 1.50 = 10
I got 4.1 + 3.0 + 2.89=9.99
4,5 + 3,6 + 1,90 = 10
5.7+2.1+2.1=9.9
Our class came up with
5.9 + 2.4 + 1.70 = 10
4.5 + 3.6 + 1.90= 10
8.4+1.3+.29
1.3 + 2.8 + 5.90 = 10.00
4 unique solutions exactly equal to 10 (you can swap the tenth places (in 6 ways) or the wholes (again in 6 ways) of any addend) or swap the two first addends to get all the other solutions:
1.3 + 2.8 + 5.90 = 10.0
1.4 + 2.7 + 5.90 = 10.0
1.5 + 3.6 + 4.90 = 10.0
1.5 + 3.7 + 4.80 = 10.0
14 solutions off by 0.01 (again, it’s possible to swap around the tenth places or the wholes of the three addends and end up with the same sum):
0.1 + 2.3 + 7.59 = 9.99
0.1 + 4.2 + 5.69 = 9.99
0.2 + 1.3 + 8.49 = 9.99
0.4 + 2.7 + 6.89 = 9.99
0.4 + 3.7 + 5.89 = 9.99
0.5 + 1.6 + 7.89 = 9.99
1.0 + 2.4 + 6.59 = 9.99
1.4 + 2.7 + 5.89 = 9.99
1.5 + 3.6 + 4.89 = 9.99
2.0 + 3.1 + 4.89 = 9.99
0.3 + 2.8 + 6.91 = 10.01
0.4 + 2.7 + 6.91 = 10.01
0.4 + 3.7 + 5.91 = 10.01
0.5 + 2.7 + 6.81 = 10.01
If you cannot use the digit 0, then the closest solutions to 10 are therefore:
1.4 + 2.7 + 5.89 = 9.99
1.5 + 3.6 + 4.89 = 9.99
BRUHHHHHHHH