Open Middle®
Directions: Daniel was making chocolate cookies. He had _ _ cookies in each row and _ _ many rows. There were a total of 84 cookies. How many cookies were there in each row and how many rows of cookies were there? Draw a model to support your answer.
You may use the digits 0-9 once in any of the blank boxes. (The answer of 84 does not eliminate the 8 or the 4.)
Hint
How many ways can you make 84?
Answer
There are multiple answers due to the factors that make 84.
12 x 07 = 84
06 x 14 = 84
04 x 21 = 84
02 x 42 = 84
12 x 07 = 84
06 x 14 = 84
04 x 21 = 84
02 x 42 = 84
Source: Daniel Rocha
Nice question Daniel.
Should the directions be changed from “You may use the numbers 0-9” to “You may use the digits 0-9”?
I don’t like it you should have to fill in the blanks to look at the answer
This app sucks cuz you can’t fill in the blanks
You can just do it on paper, dude.
“You may use the numbers 0-9 once in any of the blank boxes. (The answer of 84 does not eliminate the 8 or the 4.)”
My class just worked through this Open Middle problem. We noticed that you included 02 x 42 as a possible answer. We read the directions as meaning that we could only use 0-9 once in the equation. Did we read too deeply into it? Also, do 01 x 84 work and 03 x 28 work?
Thank you so much!
I agree. 02 x 42 should not be included as an answer that fits the clues.
We also came up with 03 x 28 by working with 3, 4, and 7.
Where’s the student worksheet with the boxes?
This is the second problem I’ve seen on this website, and both have “trick” solutions using nonstandard notation. I think putting such an emphasis on trick questions is counter-productive. There are plenty of problems to pose that are _tricky_ but not _tricks_, that rely on deep mathematical reasoning not playing games with superficial notation.
One of my students said 10 and a half x 8. What a fabulous answer. Would you accept it?
There isn’t any boxes
2 rows x 42 cookies = 84 cookies
4 rows x 21 cookies =84 cookies
6 rows x 14 cookies = 84 cookies
[8 rows x 10 cookies ] +[1 row x 4 cookies] =84 cookies
14 x 6 = 84
84 x 1 = 84
21 x 4 = 84
esa es mi respuesta de la materia✌😎✌
4 rows of 21 = 84.
I think the answer is 2 rows x 42 cookies = 84 cookies
4 rows x 21 cookies =84 cookies
6 rows x 14 cookies = 84 cookies
(8 rows x 10 cookies ) +(1 row x 4 cookies) =84 cookies
2 x 42= 84
4 x 21= 84
7 x 12= 84
6 x 14= 84
Is there a new google sheet for this week?
Why did you not eliminate the 4 and 8 to make it hard for us.
Why did you not eliminate the 4 and 8 to make it hard for us its to easy.
7rows of 12 cookies each
i agree with Ayesha 7 rows and 12 c cookies each
Me too. 7 rows of 12 cookies each.
12 X 7=84
12X7=84
84 X 01= 84
84×1
12×07=84.
12×7=84
12 x 07 = 84
06 x 14 = 84
04 x 21 = 84
02 x 42 = 84
2 rows 42 cookies.
When first introducing multiplication, you could change the product to a much lower number like 36 or 24 or even 12 to make the problem more accessible to students just learning about multiplication! I love this!