# Lesson 4

Does the Number Change?

## Warm-up: Notice and Wonder: Lots of Dots (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the idea that collections may be arranged in different ways, which will be useful when students rearrange collections in a later activity. While students may count the dots, it is not expected for this activity. The purpose of the synthesis is to consider which arrangements would be easiest to count.

### Launch

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• 1 minute: partner discussion
• Share and record responses.

### Student Facing

What do you notice?
What do you wonder?

### Activity Synthesis

• “Which arrangements do you think would be easiest to count? Why?” (The lined up dots would be easy to count. I could count one line and then the other line.)

## Activity 1: Counting Collections (10 minutes)

### Narrative

The purpose of this activity is for students to count their collection in a way that makes sense to them. Students are provided with 10-frames and counting mats to help them organize their collections. Students use appropriate tools strategically as they choose which tools help them count their collections (MP5). The purpose of the activity synthesis is to highlight that collections can be arranged in different ways, which will be useful in a future activity when students rearrange objects and notice that the total number of objects remains the same.

### Required Materials

Materials to Gather

### Required Preparation

• Each student needs a collection of 11–20 objects.

### Launch

• Groups of 2
• Give each student a collection of objects and access to 10-frames and a counting mat.
• “How many objects are in your collection?”

### Activity

• 3 minutes: independent work time
• 30 seconds: partner discussion
• “Switch collections with your partner. Do you agree with your partner about how many objects are in the collection?”
• 3 minutes: independent work time
• Monitor for students who arrange their objects in different ways to count them.

### Activity Synthesis

• Invite previously identified students to demonstrate how they arranged and counted their collections.
• “What do you notice about how they counted?”
• If needed, “Each person arranged their objects in a different way, but they all counted each object one time.”
• After each student shares, write or display the number and say “There are _____ objects in their collection.”

## Activity 2: Count, Rearrange, Recount (15 minutes)

### Narrative

The purpose of this activity is for students to rearrange and determine how many there are in the same collection of objects multiple times, to build their understanding that the arrangement of objects does not affect the number (MP8). As students share how many objects are in their collection, write or display the number to record their count.

MLR8 Discussion Supports. Use multimodal examples to clarify what it means to rearrange the objects. Use verbal descriptions along with gestures or drawings to show the meaning of the word rearrange.
Action and Expression: Develop Expression and Communication. Synthesis: Make a connection between the two different strategies used to count the cubes. Ask students if there is only one strategy to count the total number of cubes. Reiterate to students that there are different strategies that can be used to count a collection but we always end up with the same number of cubes.
Supports accessibility for: Organization, Conceptual Processing

### Required Materials

Materials to Gather

### Required Preparation

• Each student needs a collection of 11–20 objects.

### Launch

• Groups of 2
• Give each group of students a collection of 11–20 objects and access to connecting cubes.
• “We just saw different ways that we can arrange, or organize, dots. You can use this picture for ideas about how to rearrange the objects in your collection.”
• “Choose who will go first. Figure out how many objects are in the collection. If your partner is counting, watch your partner to make sure that they count each object one time.”
• 3 minutes: partner work time
• “Once your partner has counted, rearrange the objects. You can use the picture for ideas.”
• 1 minute: independent work time
• “Figure out how many objects are in your collection now.”
• 2 minutes: partner work time
• Invite students to switch roles and repeat the steps.
• “Trade collections with another group. Then take turns figuring out how many objects there are and rearranging them.”

### Activity

• 5 minutes: partner work time
• Monitor for students who know that the number of objects is the same after they’ve been rearranged without counting.

### Activity Synthesis

• Select previously identified students who knew that the number of objects was the same without recounting to share.
• “What did you notice each time that the objects were rearranged?” (We always got the same number. The number of objects stayed the same.)
• “Count out a collection of 12 cubes.”
• Write or display the number 12.
• 1 minute: independent work time
• “How many cubes are there?” (12 cubes).
• “Arrange the cubes so they are easy to count.”
• 30 seconds: independent work time
• “How many cubes are there?” (There are still 12 cubes.)
• “Now arrange the cubes so that they are more difficult to count.”
• 30 seconds: independent work time
• “How many cubes are there?” (There are still 12 cubes.)
• “We have been rearranging objects to make them easier to count. Moving the objects around does not change how many objects there are.”

## Activity 3: Introduce Tower Build, Count and Build to 20 (20 minutes)

### Narrative

The purpose of this activity is for students to learn stage 2 of the Tower Build center. Students practice counting out objects, counting to 20, and counting on from a given number. Students may start counting their connecting cubes from 1 each time or may remember how many cubes were in the tower and count on to determine the total number of cubes.

After they participate in the center, students choose from any stage of previously introduced centers.

• Find the Pair
• Number Race
• Subtraction Towers
• 5-frames

### Required Materials

Materials to Gather

Materials to Copy

• Number Mat 1-10

### Required Preparation

• Create a tower with 16 cubes for the activity synthesis.
• Gather materials from:
• Find the Pair, Stage 1
• Number Race, Stages 1 and 2
• Subtraction Towers, Stage 1
• 5-frames, Stages 1 and 2

### Launch

• Groups of 2
• Give each group of students a number mat and access to connecting cubes.
• “We are going to learn a new way to play the Tower Build center.”
• “Your goal is to make a tower with 20 cubes. The first partner who has 20 cubes in their tower wins.”
• “Take turns rolling a cube onto the mat to figure out how many cubes to add to your tower. After each round, check to see if you or your partner have 20 cubes in your tower.”
• “If you have more than 20 cubes in your tower, use those cubes to start a new tower.”

### Activity

• 8 minutes: partner work time
• “Now you can choose another center. You can also continue playing Tower Build.”
• Display the center choices in the student book.
• Invite students to work at the center of their choice.
• 10 minutes: center work time

### Student Facing

Choose a center.

Tower Build

Find the Pair

Number Race

Subtraction Towers

5-frames

### Activity Synthesis

• Display a tower of 16 connecting cubes.
• Count the cubes in the tower or invite a student to count the cubes.
• “Noah has a tower of 16 cubes. He rolled a 3. Is he going to win? How do you know?” If needed, ask “Is his tower going to get to 20 cubes?” (He is not going to win. His tower will have 19 cubes.)
• “How many more connecting cubes does he need to have 20 in his tower now?” (He needs 1 more. 20 is 1 more than 19.)

## Lesson Synthesis

### Lesson Synthesis

Display 20 objects in a line.

Count the objects as a class or invite a student to count them. Write or display the number 20.

“There are 20 objects in a line. If I move all of the objects into a circle, how many objects will I have?” (You will still have 20 objects.)

If needed, move the objects into a circle and invite a student to count the objects to confirm that there are still 20 objects.

## Student Section Summary

### Student Facing

In this section, we counted groups of up to 20 objects.

We kept track of the objects that we counted.

We used a 10-frame or a counting mat to help us.

We realized that the number of objects stayed the same even when we rearranged them.