# 2.5 Numbers to 1,000

## Unit Goals

• Students extend place value understanding to three-digit numbers.

### Section A Goals

• Read, write, and represent three-digit numbers using base-ten numerals and expanded form.
• Use place value understanding to compose and decompose three-digit numbers.

### Section B Goals

• Compare and order three-digit numbers using place value understanding and the relative position of numbers on a number line.
• Represent whole numbers up to 1,000 as lengths from 0 on a number line.

### Problem 1

#### Pre-unit

Practicing Standards:  1.NBT.B.2

1. 35 has $$\underline{\hspace{0.9cm}}$$ tens and $$\underline{\hspace{0.9cm}}$$ ones.
2. 52 has $$\underline{\hspace{0.9cm}}$$ tens and $$\underline{\hspace{0.9cm}}$$ ones.

### Solution

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### Problem 2

#### Pre-unit

Practicing Standards:  1.NBT.B.3, 2.NBT.A.4

Write $$<$$, $$=$$, or $$>$$ in each box to make the statement true.

1. $$90 + 5$$ $$\,\boxed{\phantom{\frac{aaai}{aaai}}}\,$$ $$70 + 10 + 10 + 10 + 5$$

2. $$116$$ $$\,\boxed{\phantom{\frac{aaai}{aaai}}}\,$$ $$100 + 10 + 6$$

3. $$10 + 10 + 20 + 3$$ $$\,\boxed{\phantom{\frac{aaai}{aaai}}}\,$$ $$38$$

### Solution

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### Problem 3

#### Pre-unit

Practicing Standards:  1.NBT.A.1, 1.NBT.C.5

Select all pictures that show 100.

A:

B:

C:

D:

E:

### Solution

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### Problem 4

Explain how you see each of these in the picture.

1. 100 ones
2. 10 tens
3. 1 hundred

### Solution

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### Problem 5

1. How many hundreds are the same as 50 tens? Explain your reasoning.
2. How many tens are the same as 6 hundreds? Explain your reasoning.

### Solution

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### Problem 6

Here is a base-ten diagram.

1. Draw another base-ten diagram to represent the same total value with the fewest number of each unit.
2. Write the number represented by the diagram as a three-digit number. __________
3. Can you make the same number with more base-ten blocks? Show your thinking using drawings, numbers or words.

### Solution

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### Problem 7

1. What three-digit number has 5 hundreds, 1 ten, and 6 ones?
2. What three-digit number has 6 tens, 1 hundred, and 5 ones?
3. What three-digit number has 1 one, 5 tens, and 6 hundreds?

### Solution

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### Problem 8

1. Represent each sum as a three-digit number.

$$300 + 80 + 6$$

$$40 + 7 + 600$$

2. Represent each number as the sum of hundreds, tens, and ones.

823

407

### Solution

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### Problem 9

Represent the number 235 in these ways.

1. a base-ten diagram
2. expanded form
3. words

### Solution

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### Problem 10

#### Exploration

1. Can you represent the number 218 without using any hundreds? Explain your reasoning.
2. Can you represent the number 218 without using any tens? Explain your reasoning.
3. Can you represent the number 218 without using any ones? Explain your reasoning.

### Solution

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### Problem 11

#### Exploration

Here are base-ten diagrams for two numbers.

1. Which diagram represents a greater number? Explain how you know.
2. For which diagram is it easier to figure out the number it represents? Why?

### Solution

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### Problem 1

1. What number is represented by the point on the number line?
2. Locate and label 738 on the number line.

### Solution

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### Problem 2

1. Estimate the location of 247 and 274 on the number line. Mark each number with a point. Label the point with the number it represents.

2. Use $$<$$, $$>$$, or $$=$$ to compare 247 and 274. Explain your reasoning.

### Solution

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### Problem 3

Here are diagrams for two numbers.

1. Which two numbers are pictured in the diagrams.
2. Which number is larger? How do you know?
3. Use $$<$$ or $$>$$ to compare the numbers.

### Solution

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### Problem 4

1. Find one number that goes in the blanks to make both equations true.

$$\underline{\hspace{1.5cm}} < 513$$

$$\underline{\hspace{1.5cm}} > 479$$

2. Can you find one number that goes in the blanks to make both equations true? Explain or show your reasoning.

$$\underline{\hspace{1.5cm}} > 718$$

$$\underline{\hspace{1.5cm}} < 709$$

### Solution

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### Problem 5

1. Locate 441, 418, 481, 487, and 429 on a number line. Mark each number with a point. Label each point with the number it represents.

2. Order the numbers from greatest to least.

### Solution

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### Problem 6

#### Exploration

Mile markers are markers on the road with numbers listed in order. During a trip, Mai first saw this mile marker. The last mile marker she saw was Mile 173.

1. Show on the number line the first and last mileage markers Mai went by on the road.

2. Which mile markers with 0 in the ones place did Mai pass? Explain your reasoning and label these on the number line.

### Solution

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### Problem 7

#### Exploration

1. What is the largest three-digit number you can make with the numbers 2, 3, 6, 7, and 9 ? (You can use each number at most once.) Explain your reasoning.
2. What is the smallest three-digit number you can make with the numbers 6, 3, 9, 7, and 2? (You can use each number at most once.) Explain your reasoning.

### Solution

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