In this activity, students solve problems involving tenths and hundredths, in a context about coins. Given information about the thickness of some Mexican coins, students compare the heights of different combinations of stacked coins. To complete the task, students write equivalent fractions, add tenths and hundredths, and compare fractions. Some students may choose to use multiplication to reason about the problems. Though the mathematics here are not new, the context and given information may be novel to students. Students have a wide variety of approaches available for these problems, with no solution approach suggested (MP1). For example, to compare the peso (PAY-soh) coins of Diego and Lin, students could reason that each person has a 5-peso coin and a 20-peso coin, and then compare the remaining coins, a 1-peso coin and 2-peso coin on the one hand and a 20-peso coin on the other. This method would require minimal calculations. Other students may add the thicknesses of Lin's coins and Diego's coins and compare these values. 

To help students visualize stacked coins, prepare some coins of different thicknesses, or include an image of stacked coins. (Access to Mexican coins would be interesting to students but is not essential.) Some students may be curious about the equivalents of centavos (sen-TAH-vohz) or pesos (PAY-sohz) in U.S. dollars. Consider checking the exchange rates before the lesson.

• Invite groups to share their responses and their reasoning. Highlight the different approaches students took to solve the same problems.
• If no students mention using multiplication to find the height of Diego and Lin’s centavo stacks, ask if any of the heights could be found using multiplication.

The purpose of this activity is for students to practice finding sums of three or more fractions in tenths and hundredths and applying properties of operations to facilitate that addition. (Students are not expected to use the terms “commutative property” or “associative property,” but should recognize from the work in earlier grades that numbers can be added in different orders and in different groups.)

This activity can be done in the format of a Gallery Walk. Ask students to visit at least three of six posters (or as many as time permits). The last three expressions include one or more mixed numbers. In the last expression, the fractional parts add up to a sum greater than 1, which needs to be decomposed into a whole number and a fraction before being added to the whole number. Consider assigning this as a starting expression for students who could use an extra challenge.

• See Lesson Synthesis.