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.
Section A: The Value of Three Digits
Problem 1
Pre-unit
Practicing Standards: 1.NBT.B.2
- 35 has \(\underline{\hspace{0.9cm}}\) tens and \(\underline{\hspace{0.9cm}}\) ones.
- 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.
-
\(90 + 5\) \(\,\boxed{\phantom{\frac{aaai}{aaai}}}\,\) \(70 + 10 + 10 + 10 + 5\)
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\(116\) \(\,\boxed{\phantom{\frac{aaai}{aaai}}}\,\) \(100 + 10 + 6\)
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\(10 + 10 + 20 + 3\) \(\,\boxed{\phantom{\frac{aaai}{aaai}}}\,\) \(38\)
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.
Solution
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Problem 4
Explain how you see each of these in the picture.
- 100 ones
- 10 tens
- 1 hundred
Solution
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Problem 5
- How many hundreds are the same as 50 tens? Explain your reasoning.
- 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.
- Draw another base-ten diagram to represent the same total value with the fewest number of each unit.
- Write the number represented by the diagram as a three-digit number. __________
- 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
- What three-digit number has 5 hundreds, 1 ten, and 6 ones?
- What three-digit number has 6 tens, 1 hundred, and 5 ones?
- What three-digit number has 1 one, 5 tens, and 6 hundreds?
Solution
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Problem 8
-
Represent each sum as a three-digit number.
\(300 + 80 + 6\)
\(40 + 7 + 600\)
-
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.
- a base-ten diagram
- expanded form
- words
Solution
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Problem 10
Exploration
- Can you represent the number 218 without using any hundreds? Explain your reasoning.
- Can you represent the number 218 without using any tens? Explain your reasoning.
- 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.
- Which diagram represents a greater number? Explain how you know.
- For which diagram is it easier to figure out the number it represents? Why?
Solution
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Section B: Compare and Order Numbers within 1,000
Problem 1
-
What number is represented by the point on the number line? -
Locate and label 738 on the number line.
Solution
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Problem 2
-
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.
- Use \(<\), \(>\), or \(=\) to compare 247 and 274. Explain your reasoning.
Solution
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Problem 3
Here are diagrams for two numbers.
- Which two numbers are pictured in the diagrams.
- Which number is larger? How do you know?
- Use \(<\) or \(>\) to compare the numbers.
Solution
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Problem 4
-
Find one number that goes in the blanks to make both equations true.
\(\underline{\hspace{1.5cm}} < 513\)
\(\underline{\hspace{1.5cm}} > 479\)
-
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
-
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.
- 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.
![Mile marker sign showing mile 106.](https://cms-im.s3.amazonaws.com/ltkjleef0ly9p1wpryiz2htmfz44?response-content-disposition=inline%3B%20filename%3D%22106_ds106_106milemarker-206084.jpg%22%3B%20filename%2A%3DUTF-8%27%27106_ds106_106milemarker-206084.jpg&response-content-type=image%2Fjpeg&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001521Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ad785e46525f71c51b4a8e6c25537a528be61d4767d3d7b09737236b2940e4d5)
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Show on the number line the first and last mileage markers Mai went by on the road.
- 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
- 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.
- 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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