Illustrative Mathematics (2024)

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Task

1. How many ten-dollar bills equal a hundred-dollar bill?
2. Jem had 20 ten-dollar bills. How many hundred-dollar bills can she trade them for?
3. Dan had 6 hundred-dollar bills. How many ten-dollar bills can he trade them for?

IM Commentary

People often use pennies, dimes, and dollars as a context for thinking about bundling by ten. However, using one, ten, and one-hundred dollar bills is easier for students to understand initially because the names of the bundles match the names of the numbers. While dimes are bundles of ten pennies and dollars are bundles of ten dimes, the translation between base-ten numbers and pennies, dimes, and dollars is more complex because of the name differences. Furthermore, there is the potential for confusion since a penny can be thought of as both 1/100 of a dollar and as 1 cent. As a result students may require more support from the teacher to understand contexts involving e.g. dimes and dollars than they would for this task context.

Solution

1. 10 ten-dollar bills equal 1 hundred-dollar bill.
2. Jem can trade 20 ten-dollar bills for 2 hundred-dollar bills.
3. Dan can trade 6 hundred-dollar bills for 60 ten-dollar bills.