The purpose of this activity is for students to add decimals in a way that makes sense to them.

Monitor for and select students with the following approaches to share in the Activity Synthesis:

• Add on to one of the numbers by drawing a diagram using hundredths grids or equations.
• Add by place value by drawing a diagram using hundredths grids or equations.

The approaches are sequenced from more concrete to more abstract to help students build on their work with equivalent decimal values in the previous section as well as their work with whole numbers in previous grades. Students should be encouraged to use whatever strategies make sense to them. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven’t shared recently. For an example for each approach, look at the Student Responses.

• “Can you explain your representation to me?”
• “Is the sum greater or less than 4? How do you know?”

• Invite previously selected students to share in the given order. Record or display their work for all to see.
• Connect students’ approaches by asking:
  • “What is the same and what is different between the strategies?” (Some use diagrams to show the numbers and add them and some use equations. They both have to think about making a new whole out of the decimals.)
• Connect students’ approaches to the learning goal by asking them to relate diagrams and equations that use place value reasoning. 
  • Display a diagram that uses place value reasoning from the student work (or draw a diagram to show if students use place value reasoning with equations, but not with diagrams).
  • Display equation:
  • “How does the diagram show this equation?” (I can move two shaded rows from 2.26 to complete the partly shaded square in 1.87.)
  • Display equation:
  • “How does the diagram show this equation?” (I can put together all of the single shaded squares that don’t fill a full row from the two diagrams and I get 1 tenth and 3 hundredths.)

In the previous activity, students added decimals in a way that made sense to them. The purpose of this activity is for students to play a game that requires them to consider place value while adding decimals (MP7). This is Stage 8 of the Target Numbers center. Students played previous stages of this game with whole numbers in earlier grades.

• “What could you have done differently to change the outcome of the game?” (I picked too many tenths and went over. I did not get close to 1 because I was worried about going over. I picked too many hundredths.)
• Give students a chance to write their reflection.
• “Look back at the questions you wrote in the last activity about adding decimals. Discuss with your partner whether you are able to answer any of your questions.”