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.
MLR8 Discussion Supports. Synthesis: Display sentence frames to agree or disagree. Examples: “Estoy de acuerdo porque . . .” // “I agree because . . . ,” and “Estoy en desacuerdo porque . . .” // “I disagree because . . . .”
Advances: Speaking, Conversing
Representation: Access for Perception. Invite students to model the situation using sticky notes or scrap paper to represent the coins. Students can label each sticky note with the thickness, value, and owner of the coins, and then move the sticky notes around as they model and solve each problem. Encourage students to use the sticky notes to solve problems strategically. For example, they might group like denominators before adding, or layer repeated fractions to represent multiplication.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Memory