# Lesson 12

Order Numbers

## Warm-up: Number Talk: Subtract Tens (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for mentally subtracting a multiple of 10 from a number. Building on their understanding of place value, students subtract tens from tens. These understandings help students develop fluency and will be helpful in later lessons when students will need to be able to subtract using strategies based on place value.

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Record answers and strategies.
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$80 - 50$$
• $$87 - 50$$
• $$76 - 40$$
• $$66 - 30$$

### Activity Synthesis

• “How could the third expression help you find the value of the last expression?” (76 is 10 more than 66 and 30 is 10 less than 40, so the difference between the two numbers is the same.)

## Activity 1: Who is Out of Order? (15 minutes)

### Narrative

The purpose of this activity is for students to analyze a mistake in ordering numbers (MP3). When placing numbers in order from least to greatest, students can compare using their understanding of place value. However, they see that, unlike comparing just two numbers, when comparing sets of numbers, there is more to keep track of. Students learn that a number line provides a linear representation to help organize numbers in sequence and visualize the relative distance between numbers.

MLR8 Discussion Supports. Display sentence frames to support partner discussion: “I agree with _____ because . . . “ and “I disagree with _____ because . . . .”

• Groups of 2

### Activity

• “Kiran and Andre put some numbers in order from least to greatest.”
• “Andre disagreed with Kiran, so he used a number line to justify his answer. Whom do you agree with?”
• 3 minutes: independent work time
• “Discuss with a partner using what you know about place value or the number line to justify your reasoning.”
• 5 minutes: partner work time
• Monitor for students who:
• use precise place value language to describe the correct placement of 269 and 272 in the list
• use the number line to explain that a list of numbers from least to greatest should match the placement of the numbers on the number line from left to right

### Student Facing

Kiran and Andre put a list of numbers in order from least to greatest.

Kiran

207, 217, 272, 269, 290

Andre

207, 217, 269, 272, 290

Andre disagreed with Kiran, so he used a number line to justify his answer.

Who do you agree with? Why?

Be prepared to explain your thinking. Use what you know about place value or the number line to justify your reasoning.

### Activity Synthesis

• Invite previously selected students to share using precise place value language.
• Invite a student to explain using the number line.
• “When we order numbers, we can use what we know about place value. We can also think about the counting sequence and use a number line to help us see the numbers in order.”

## Activity 2: Order Numbers (20 minutes)

### Narrative

The purpose of this activity is for students to order numbers. Students estimate the location and label numbers on a number line, and then write them in order from least to greatest or greatest to least. For the third set of numbers, students may order the numbers using any method that makes sense to them. Students reflect on how the number line can help us organize numbers (MP5). Throughout the activity, monitor for the way students explain their reasoning based on place value and the relative position of numbers on the number line.

Representation: Access for Perception. Use index cards, clothespins, and string to demonstrate the number line. Give students the numbers on the index cards and have them physically act it out by finding their place on the number line.
Supports accessibility for: Memory, Organization, Conceptual Processing

• Groups of 2

### Activity

• “Now you will have a chance to order numbers.”
• “Sometimes you will put them in order from least to greatest, and sometimes it will be from greatest to least.”
• 10 minutes: independent work time
• “Compare with a partner. Explain your thinking.”
• 5 minutes: partner discussion
• Monitor for students who order the last set of numbers by:
• explaining their reasoning using precise place value language
• placing each number on the number line before ordering the numbers

### Student Facing

1. Estimate the location of 839, 765, 788, 815, and 719 on the number line. Mark each number with a point. Label the point with the number it represents.

Order the numbers from least to greatest.

_______, _______, _______, _______, _______

2. Estimate the location of 199, 245, 173, 218, and 137 on the number line. Mark each number with a point. Label the point with the number it represents.

Order the numbers from greatest to least.

_______, _______, _______, _______, _______

3. Order the numbers from least to greatest.

545, 454, 405, 504, and 445

_______, _______, _______, _______, _______

Explain or show your thinking. Use the number line if it helps.

4. Was it more helpful for you to put the numbers in order first or put them on the number line first? Explain.

### Advancing Student Thinking

If students locate the numbers on the number line, but reverse the order given in the problem, consider asking:

• “How did you decide the order of your numbers?”
• “Does your list show the numbers in order from least to greatest or greatest to least?”

### Activity Synthesis

• Invite previously identified students to share their reasoning.
• “How are the numbers you labeled on the number line the same as the list of numbers you wrote? How are they different?” (For least to greatest, its the same. The difference is the number line shows the distance between each number, but the list of numbers shows them right next to each other.)

## Lesson Synthesis

### Lesson Synthesis

“During this unit we have used different representations to help us think about large numbers. Think about all the work we did with numbers up to 1,000.”

“Which representations help you make sense of large numbers and compare them to one another? Using a base-ten diagram, looking at the digits, or using a number line?”

Share and record responses.

“I noticed some students prefer one representation for place value, but a different one when comparing or ordering numbers. It is good to know what works best for you and when to use it.”

## Student Section Summary

### Student Facing

In this section, we learned how to compare three-digit numbers. We used number lines, base-ten diagrams, and the value of the digits in base-ten numerals to help us compare and explain our thinking.

Diagrams are helpful when comparing numbers because you can see and compare hundreds to hundreds, tens to tens, and ones to ones. We learned that you can do this with the digits too.

The number line shows the numbers in order, so we can see which number is the largest based on its location.

We also wrote expressions using the $$>$$, $$<$$, and $$=$$ symbols.

$$432 > 424$$

432 is greater than 424

$$424 < 432$$

424 is less than 432