# Lesson 23

Two-Digit Numbers in Our World (optional)

## Warm-up: Estimation Exploration: Beans (10 minutes)

### Narrative

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.

### Launch

• Groups of 2
• Display the image.
• “The circled group shows 10 beans.”
• “What is an estimate that’s too high?” “Too low?” “About right?”
• 1 minute: quiet think time

### Activity

• 1 minute: partner discussion
• Record responses.

### Student Facing

How many beans are there?

Record an estimate that is:

too low about right too high
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Select one “about right” estimate.

## Activity 1: Count the Objects (15 minutes)

### Narrative

The purpose of this activity is for students to have an opportunity to apply their place value understanding to estimate quantities of objects and accurately count familiar objects.

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs a bag of a collection of small objects.

### Launch

• Groups of 2
• Display for all to see approximately 15–25 beans or other small objects.
• “How many objects do you think are in this pile?”
• 1 minute: partner discussion
• Share responses.
• “How could we find out exactly?” (Count them.)

### Activity

• “How many objects are in 2 handfuls? Let's do an experiment.”
• Give each group a bag of objects.
• “Take turns and grab a handful. Estimate how many objects you both grabbed altogether. Then find out how many you have exactly.”
• “You will do this experiment three times.”
• 5 minutes: partner work time
• Monitor for students who:
• count by ones
• group the objects into groups of 10 and then count the tens and ones

### Student Facing

Experiment 1: How many objects are in 2 handfuls?
Record an estimate that is:
too low about right too high
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$

Now find the exact number. ____________

Experiment 2: How many objects are in 2 handfuls?
Record an estimate that is:

too low about right too high
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$

Now find the exact number. ____________

Experiment 3: How many objects are in 2 handfuls?
Record an estimate that is:

too low about right too high
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$
Now find the exact number. ____________

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite previously identified students to share.
• “Did your estimates get better with practice?”
• “Imagine I have 72 objects. How many would you have if you have 10 fewer than I do? What if you had 10 more?”
• “If you had 72 objects, how could they be arranged in piles of 10 and ones? Are there any other ways?" (7 tens and 2 ones, 6 tens and 12 ones)

## Activity 2: Quantities Card Sort (20 minutes)

### Narrative

The purpose of this activity is for students to consider the number of objects in a group and represent numbers in as many ways as possible. Students should be encouraged to think about the number in terms of tens and ones. Students sort pictures based on the number of objects they estimate to be in each group.

Students should be encouraged to estimate quantities rather than try to count them. Some students may not have a reasonable estimate, but can be successful in this activity if they categorize the photograph based on whatever estimate they consider is “about right.”

MLR8 Discussion Supports. Students should take turns sorting cards into the different categories and explaining their reasoning to their partner. Display the following sentence frames for all to see: “I noticed _____, so I matched . . . .” Encourage students to challenge each other when they disagree.
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches.
Supports accessibility for: Attention, Organization

### Required Materials

Materials to Copy

• Estimating Quantities Card Sort

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.

### Launch

• Groups of 2
• Give each group a set of cards.

### Activity

• “There is a different picture on each card. Sort the cards based on the number of objects you think are in each picture.”
• 8 minutes: partner work time
• As students work, consider asking:
• “What is an estimate that is too low, about right, and too high?”

### Student Facing

1. Estimate and sort the pictures based on the amount of items you see.
Sort into these groups.
1. Less than 20
2. 20 to 50
3. More than 50
2. Select 1 picture from each group.
Show the number of items you think are in the picture in as many ways as you can.

Less than 20

20 to 50

More than 50

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite students to share what object they selected and its representation.
• Record responses.
• Select two estimates that have the same digit in the ones place.
• “How do we know which estimate is bigger?”
• Highlight the use of ones and tens.

## Lesson Synthesis

### Lesson Synthesis

“Today we made estimates and counted groups of objects. How did you use your understanding of tens and ones in two-digit numbers to help you with your work?”