At a small board game company, some employees assemble board games in their boxes. Part of the assembly requires sorting small pieces into the boxes. Since this is a board game company, the manager prefers that the employees make a game out of the mathematics needed to distribute the pieces, so calculators are not allowed, no matter how many pieces need to be sorted.

Nadirah needs to sort pieces into boxes. Here is her strategy.

pieces would be in each box, so pieces would be in each box and pieces would be in each box. I’ve got pieces left. I can put pieces in each box to use up pieces, so I’ll have pieces left over. So my answer is pieces in each box with leftover pieces.

Explain why Nadirah’s strategy is correct for calculating how many pieces are in each box. Be sure to address the following.

  • What division problem is Nadirah solving, and why?
  • What interpretation of division is Nadirah using, and how do you know? (How many groups, or how many in each group?)
  • Describe Nadirah’s steps in your own words and explain how these steps fit with the interpretation of division that you chose.
  • How does Nadirah get the answer, and how do you know it’s correct?
Nadirah wrote down the following equations to explain her calculations to her math teacher the next day. \begin{align*} 70 + 70 + 70 + 49 + 2 &= 261 \\ 10 \times 7 + 10 \times 7 + 10 \times 7 + 7 \times 7 + 2 &= 261 \\ (10 + 10 + 10 + 7) \times 7 + 2 &= 261 \\ 37 \times 7 + 2 &= 261 \\ \end{align*}

How does each expression in the first line correspond to one of Nadirah’s steps? What properties does Nadirah use to simplify the first equation into the last one? How does the last line of the equation tell Nadirah the answer to her division problem?

La’tasha needs to sort pieces into boxes. Here is her strategy.

I start with pieces used, then double that to get , then , then , then , then and I can’t double again. That was , , , , , and I have plus plus pieces left. That’s pieces. I can use the which was nines, and have one leftover, so I get nines and one leftover, or each box gets pieces and I have one leftover piece.

Explain why La’tasha’s strategy is correct for calculating how many pieces are in each box. Be sure to address the following.

  • What division problem is La’tasha solving, and why?
  • What interpretation of division is La’tasha using, and how do you know?
  • Describe La’tasha’s steps in your own words and explain how these steps fit with the interpretation of division that you chose.
  • How does La’tasha get the answer, and how do you know it’s correct?
  • Can you write equations that represent La’tasha’s strategy?
Monique needs to sort pieces into boxes. Here is her strategy.

If I had pieces to sort, that would be in each box, so pieces would be in each box. Now if I had pieces to sort, that would be per box. And pieces would be per box. So all together I’ll put pieces in each box and have piece left over.

Explain why Monique’s strategy is correct for calculating how many pieces are in each box. Be sure to address the following.

  • What division problem is Monique solving, and why?
  • What interpretation of division is Monique using, and how do you know?
  • Describe Monique’s steps in your own words and explain how these steps fit with the interpretation of division that you chose.
  • How does Monique get the answer, and how do you know it’s correct?
  • Can you write equations that represent Monique’s strategy?
Imagine that you are working at this board game company and need to sort pieces into boxes. How many pieces will fit in each box? How many different ways can you solve this problem?
2025-10-15 14:03:22