This task is ideal for exploring different interpretations of a remainder. I’ve done this task with lots of different audiences from second graders to adults. With every group, there are at least 3 possible answers that come up and the conversations about them are very powerful.
Play the clip and ask students what they notice and wonder. Record all of their suggestions. If the question, “How many bills are in the roll?” does not come up naturally in the discussion, suggest that question as the one they will explore for this task.
There are two choices for Act 2. You may use the measurements with cubes or the measurements with the ruler and tape measure. I prefer the cubes because the dollar is slightly larger than 8 cubes. This will bring up a lot of discussion about the remaining amount after students solve the problem. Also, there are often questions people ask related to the roll that might need to be addressed. Here are the common questions:
- Are there gaps or overlaps between the bills? No, the bills are taped end-to-end.
- What denominations are the bills? They are all $1.00.
- How are the bills connected? I used Scotch tape to hold them together.
- Is there a bill that has been cut at the end? No, the whole roll is made of complete one-dollar bills. No bills were harmed in the creation of this task.
It’s not uncommon to have a range of answers to this task from 20 – 24 bills. The reason for the variation comes from different interpretations of how to handle the extra amount when people notice that one bill is slightly more than 8 cubes long. The correct answer of 22 can be seen in the video where Mike counts out the total number of bills. However, the image below the video is also helpful because it shows the end of the roll with the 3 remaining cubes. The entire money roll was measured in different colored stacks of 8 cubes. There were 22 stacks of 8 with 3 remaining cubes that covered the 22 bills.
Money Roll 3 Act Task by Mike Flynn is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Based on a work at http://mathleadership.org/.
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