# Lesson 11

Make Sense of Decimal Addition

## Warm-up: How Many Do You See: Grids (10 minutes)

### Narrative

The purpose of this How Many Do You See is for students to group common decimal values and compose new units when they describe the images they see. This helps prepare students to add decimals given in numerical form in the lesson. Students may use words, fractions, or decimals to describe how many they see.

### Launch

• Groups of 2
• “How many do you see? How do you see them?”
• Display the image.
• 1 minute: quiet think time

### Activity

• Display the image.
• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

### Student Facing

How many do you see? How do you see them?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Display the third image.
• “How many do you see? How do you see them?” (I see 95 hundredths and 7 hundredths more. I can move 5 hundredths from the second square to the first and then I have 1 full square and 2 more hundredths.)

## Activity 1: The Sum (15 minutes)

### Narrative

The purpose of this activity is for students to add decimals in a way that makes sense to them. Students may use a variety of strategies including

• drawing a diagram using hundredths grids (MP5)
• adding by place value
• adding on to the larger number

Students should be encouraged to use whatever strategies make sense to them.

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

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs a piece of chart paper and colored pencils, markers, or crayons.

### Launch

• Groups of 2
• Give each group of students a piece of chart paper, colored pencils, crayons or markers, and access to hundredths grids.

### Activity

• 5 minutes independent work time
MLR7 Compare and Connect
• “Create a visual display that shows your thinking about the first problem. You may want to include details such as notes, diagrams or drawings to help others understand your thinking.”
• 2–5 minutes: partner work time
• 5–7 minutes: gallery walk

### Student Facing

1. Find the value of the expression. Show your thinking. Organize it so it can be followed by others.

$$2.26 + 1.87$$

2. What questions do you have about adding decimals?

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

If students do not have a strategy for getting started, refer to the grids and ask, “How can we represent the sum on the grids?”

### Activity Synthesis

• Refer to the visual displays that students created or use the student solutions.
• “What is the same and what is different between the strategies?” (Some of them use diagrams to show the numbers and add them and some of them use equations. They both have to think about making a new whole out of the decimals.)
• Display equation: $$0.8 + 0.2 = 1$$
• “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: $$0.06 + 0.07 = 0.13$$
• “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.)

## Activity 2: Target Numbers: Add Tenths or Hundredths (20 minutes)

### Narrative

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 center Target Numbers. Students played previous stages of this game with whole numbers in earlier grades.

Students roll a number cube and decide whether they want the number to represent tenths or hundredths. They roll the number cube six times and try to make a cumulative sum that is as close to 1 as possible, without being greater than 1. Students make strategic choices about which value to assign the number as they roll and adapt their strategy throughout the game.

For example, here is a sample record of a game.

number
rolled
0.1 0.01

equation to
represent
the total

3 0.3 $$0+0.3=0.3$$
1 0.1 $$0.3+0.1=0.4$$
4 0.4 $$0.4+0.4=0.8$$
4 0.04 $$0.8+0.04=0.84$$
5 0.05 $$0.84+0.05=0.89$$
3 0.03 $$0.89+0.03=0.92$$
Engagement: Develop Effort and Persistence. Invite students to generate a list of shared expectations for group work. Record responses on a display and keep visible during the activity.
Supports accessibility for: Attention, Social-Emotional Functioning

### Required Materials

Materials to Gather

Materials to Copy

• Target Numbers Stage 8 Recording Sheet

### Required Preparation

• Each group of 2 needs 1 number cube.

### Launch

• Groups of 2
• Give each group one number cube and a copy of the blackline master.
• “We’re going to play a game called Target Numbers. Let’s read through the directions and play one round together.”
• Read through the directions with the class and play a round with the class:
• Display each roll of the number cube.
• Think through your choices aloud.
• Record your move and score for all to see.
• “Now, play the game with your partner.”

### Activity

• 8–10 minutes: partner work time
• Monitor for students who:
• go over 1 and describe how they could have changed the placement of a number from the tenths place to the hundredths place to impact the game
• don't come close to 1 and describe how they could have changed the placement of a number from the hundredths place to tenths place to impact the game

### Student Facing

Directions:

1. Play one round of Target Numbers.
• Partner A
• Start at 0. Roll the number cube. Choose whether to add that number of tenths or hundredths to your starting number.
• Write an equation to represent the sum.
• Take turns until you’ve played 6 rounds.
• Each round, the sum from the previous equations becomes the starting number in the new equation.
• The partner to get a sum closest to 1 without going over wins.
2. Describe a move that you could have made differently to change the outcome of the game.

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

If students are not being strategic about their placement of the number rolled, ask, “How did you decide whether to make the number you rolled worth tenths or hundredths?”

### Activity Synthesis

• “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.”

## Lesson Synthesis

### Lesson Synthesis

“Today we added decimals.”

Display a piece of chart paper titled “Decimal Addition” as you reflect on the work from today.

“How is adding decimals the same as adding whole numbers?” (You have to pay attention to place value. Sometimes you have to compose a new unit.)

“How is it different?” (You have to add tenths and hundredths. There is a decimal point.)
Record responses on poster.

“What do you still wonder about adding decimals?” (Can you add thousandths? What if there is a zero in one of the places? Can we use the algorithm like we do for whole numbers?)

Record responses on poster. Save poster to refer back to in future lessons.

## Cool-down: The Value of the Sum (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.