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

### Hint

How many ways can you make 84?

### Answer

### 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”?

“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?