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Baking Cookies

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

Source: Daniel Rocha

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23 comments

  1. Nice question Daniel.
    Should the directions be changed from “You may use the numbers 0-9” to “You may use the digits 0-9”?

  2. “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.

  3. 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.

    • There isn’t any boxes

    • Daniela Diamond Hatziiliades

      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. 4 rows of 21 = 84.

    • You will never know

      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

  5. 2 x 42= 84
    4 x 21= 84
    7 x 12= 84
    6 x 14= 84

  6. Is there a new google sheet for this week?

  7. Why did you not eliminate the 4 and 8 to make it hard for us.

  8. Why did you not eliminate the 4 and 8 to make it hard for us its to easy.

  9. 7rows of 12 cookies each

  10. i agree with Ayesha 7 rows and 12 c cookies each

  11. Scarlett Salaz

    12X7=84

  12. Zoe Savvoulides

    84 X 01= 84

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