# Lesson 11

Place Value Comparisons (Part 2)

## Warm-up: True or False: Greater Than or Less Than (10 minutes)

### Narrative

The purpose of this True or False is to elicit strategies and understandings students have for working with the value of the digits in a three-digit number. These understandings help students consider place value when comparing three-digit numbers. This will be helpful later when students compare three-digit numbers without visual representations.

### Launch

• Display one statement.
• “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategy.
• Repeat with each statement.

### Student Facing

Decide if each statement is true or false. Be prepared to explain your reasoning.

• $$86 > 80 + 4$$
• $$400 + 40 + 6 < 846$$
• $$330 < 300 + 3$$
• $$500 + 50 > 505$$

### Activity Synthesis

• “How could expanded form help you decide whether the expression $$330 < 300 + 3$$ is true or false?” (I knew that 30 is 3 tens and 3 is only 3 ones, so 330 is greater than 303.)

## Activity 1: Compare and Explain (15 minutes)

### Narrative

The purpose of this activity is for students to compare three-digit numbers based on their understanding of place value. They are invited to explain or show their thinking in any way that makes sense to them. A number line is provided. Students may revise their thinking after locating the numbers on the number line, or may choose to draw diagrams to represent their thinking. During the activity synthesis, methods based on comparing the value of digits by place are highlighted.

For the last problem, students persevere in problem solving as there are many ways to make most of inequalities true but students will need to think strategically in order to fill out all of them. In particular, 810 can be used in the first, second, or fourth inequality but it needs to be used in the fourth because it is the only number on the list that is larger than 793.

Representation: Develop Language and Symbols. Represent the problem in multiple ways to support understanding of the situation. For example, have one group member place the numbers on a number line to verify which number is greater. Another option is to have one group member make the numbers using base-ten blocks to prove which is greater.
Supports accessibility for: Conceptual Processing, Organization

### Launch

• Groups of 2
• “In the warm-up, you saw that different forms of writing a number can help you think about the value of each digit.”
• Write $$564\phantom{3} \boxed{\phantom{33}}\phantom{3}504$$ on the board.
• “What symbol would make this expression true? Explain.” (>, because they both have 500, but the first number has 6 tens or 60 and the second number has 0 tens.)

### Activity

• “Today you will be comparing three-digit numbers by looking at place value.”
• “If it helps, you can use base-ten diagrams or expanded form to help you think about place value.”
• “Try it on your own and then compare with your partner.”
• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who compare the numbers without drawing base-ten diagrams or using a number line.

### Student Facing

Compare the numbers.

1. $$>$$, $$=$$, or $$<$$

521

$$\boxed{\phantom{33}}$$

523

Explain or show your thinking. If it helps, use a diagram or number line.

2. $$>$$, $$=$$, or $$<$$

889

$$\boxed{\phantom{33}}$$

878

Explain or show your thinking. If it helps, use a diagram or number line.

3. Place the numbers in the blanks to make each comparison true. Use each number only once. Use base-ten diagrams or a number line if it helps.

810

529

752

495

1. $$\underline{\hspace{1 cm}} > 519$$
2. $$687 < \underline{\hspace{1 cm}}$$
3. $$\underline{\hspace{1 cm}} < 501$$
4. $$\underline{\hspace{1 cm}} > 793$$

### Student Response

If students write comparison statements that are not true, consider asking:

• “Could you read each statement aloud?”
• “How did you know your statement is true?”
• “How could you use the base-ten diagram or number line to help you show whether your statement is true or false?”

### Activity Synthesis

• Display $$564 > 504$$ .
• Display $$500 + 60 + 4 > 500 + 4$$.
• “We decided that this was a true statement. How does the expanded form of these numbers help justify our thinking?” (We can see the value of each place, so we can compare each digit.)
• Invite previously selected students to share how they compared numbers without drawing diagrams or using the number line.

## Activity 2: Play Greatest of Them All (20 minutes)

### Narrative

The purpose of this activity is for students to learn stage 2 of the Greatest of Them All center. Students use digit cards to create the greatest possible number. As each student draws a card, they choose where to write it on the recording sheet. Once a digit is placed, it can’t be moved. Students compare their numbers using $$<$$, $$>$$, or $$=$$. The player with the greater number in each round gets a point.

Students should remove cards that show 10 from their deck.

MLR2 Collect and Display. Synthesis: Direct attention to the words collected and displayed on the anchor chart from the previous lessons. Invite students to borrow place value language from the display as needed.

### Required Materials

Materials to Gather

Materials to Copy

• Greatest of Them All Stage 2 Recording Sheet

### Launch

• Groups of 2
• Give each group a set of number cards and each student a recording sheet.
• “Now you will be playing the Greatest of Them All center with your partner.”
• “You will try to make the greatest three-digit number you can.”
• Display number cards and recording sheet.
• Demonstrate picking a card.
• “If I pick a (2), I need to decide whether I want to put it in the hundreds, tens, or ones place to make the largest three-digit number.”
• “Where do you think I should put it?” (I think it should go in the ones place because it is a low number. In the hundreds place, it would only be 200.)
• 30 seconds: quiet think time
• Share responses.
• “At the same time, my partner is picking cards and building a number, too.”
• “Take turns picking a card and writing each digit in a space.”

### Activity

• “Now play a few rounds with your partner.”
• 15 minutes: partner work time

### Activity Synthesis

• Select a group to share a comparison statement. For example: $$654 > 349$$ and $$349 < 654$$.
• “I noticed that partners had different comparison statements for the same numbers. How can they both be true?”
• “If I draw an 8, where should I choose to place it and why?” (I would put it in the hundreds place since it’s almost the highest number I could draw. I might not get 9. With 800, I have a good chance for my number to be larger than my partner’s.)

## Lesson Synthesis

### Lesson Synthesis

“Today we compared numbers by looking at the digits and thought about how to use digits to make the greatest number possible.”

Display digits 2, 0, and 9 (in a vertical list).

“Using these digits, what is the greatest number you can make?” (920)

“Using these digits, what is the smallest three-digit number you can make?” (209, because a three-digit number cannot start with zero.)