The purpose of this activity is for students to subtract decimals in a way that makes sense to them. Students should be encouraged to use whatever strategies make sense to them, including using place value understanding and the relationship between addition and subtraction. Strategies students may use include

• Using hundredths grids. (MP5)
• Using place value and writing equations.

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.

• Refer to visual displays that students created.
• “What is the same and what is different about the strategies used to find the value of the difference?” (They all pay close attention to place value and the meaning of each digit in the numbers. Some of the displays use subtraction while some of them use addition. They add and subtract different pieces sometimes in different order. Some of the displays have diagrams and some don’t.)
• Display an image from a student's solution.
• “How does the diagram show the difference ?” (It shows 2.26 and then it takes away 1.32. What’s left is the difference.)
• “How is the diagram different from using equations?” (The 1 and 32 hundredths can be crossed out anywhere that’s convenient and then you just count what’s left. You don't have to think as strategically about what to take away or in what order.)

The purpose of this activity is for students to practice subtracting decimals to the hundredth. Students play a new stage of the center Target Numbers. Students played a previous stage that involved adding tenths or hundredths. Students take turns picking a number card, deciding to subtract that number of hundredths or tenths from their starting number for the round, and writing an equation. Students start their first equation at 2 and then the difference becomes the first addend in the next round. The player who gets closest to 1 in 6 rounds, without going below 1, is the winner. Students make strategic choices about which value to assign the number card and adapt their strategy throughout the game. For example, here is a sample record of a game.

Some students may notice that the strategy of this game is identical to the addition game they played in an earlier lesson. The only difference is they start at 2 and subtract whereas with the addition game they start at 0 and add (MP8).

• Ask previously selected students to share their reflections on the game.
• Recall the addition game students played three lessons earlier, choosing tenths or hundredths with a target number of 1.
• “How is the subtraction game the same as the addition game?” (I have 6 turns and I get to choose tenths or hundredths each time. The strategy is the same because in both cases I want the 6 decimals to add up to close to 1 without going over.)
• “How is the subtraction game different from the addition game?” (Instead of adding the decimals starting with 0, I am subtracting them starting with 2. Sometimes, I have to break up a 1 or a tenth. In the addition game I sometimes made a 1 or a tenth.)
• “Which game did you prefer?” (I liked the addition game because it was easier to add the decimals than to subtract.)