2.7 Adding and Subtracting within 1,000

Unit Goals

  • Students use place value understanding, the relationship between addition and subtraction, and properties of operations to add and subtract within 1,000.

Section A Goals

  • Add and subtract numbers within 1,000 without composition or decomposition, and use strategies based on the relationship between addition and subtraction and the properties of operations.

Section B Goals

  • Add numbers within 1,000 using strategies based on place value understanding, including composing a ten or hundred.

Section C Goals

  • Subtract numbers within 1,000 using strategies based on place value understanding, including decomposing a ten or hundred.
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Section A: Add and Subtract within 1,000 without Composition or Decomposition

Problem 1

Pre-unit

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

Select all representations of the number 318.

A:
Base ten diagram. 1 hundred, 3 tens, 8 ones.

B:
Base ten diagram. 3 hundreds, 1 ten, 8 ones.

C: \(300 + 10 + 8\)

D: \(100 + 30 + 8\)

E: Three hundred eighteen

F: Three hundred eighty-one

Solution

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Problem 2

Pre-unit

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

Write a number for each representation.

  1. Five hundred twenty-seven

    ______________

  2. \(300+60+8\)

    ______________

  3.  
    Base ten diagram. 2 hundreds, 3 tens, 5 ones.

    ______________

  4. \(5 + 40 + 700\)

    ______________

Solution

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Problem 3

Pre-unit

Practicing Standards:  2.NBT.B.5

Find the value of each sum or difference. Show your thinking.

  1. \(52 - 43\)
  2. \(65 - 19\)
  3. \(36 + 47\)

Solution

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Problem 4

Pre-unit

Practicing Standards:  1.NBT.C.5, 1.NBT.C.6

Find the value of each difference.

  1. \(77 - 10\)
  2. \(77 - 20\)
  3. \(90 - 70\)

Solution

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Problem 5

Find the value of each difference. Show your thinking.

  1. \(53 - 50\)
  2. \(285 - 281\)
  3. \(90 - 88\)

Solution

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Problem 6

  1. Here are Kiran's blocks.
    Base ten diagram. 3 hundreds, 2 tens, 6 ones.

    He gives 2 tens to Priya.

    What is the value of Kiran's blocks now? Show your thinking.

  2. Then Priya gives Kiran 4 hundreds.

    What is the value of Kiran's blocks now? Show your thinking.

Solution

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Problem 7

Find the value of each difference. Show your thinking. Use a number line or base-ten blocks if it helps.

  1. \(648 - 25\)

  2. \(535 - 24\)

Solution

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Problem 8

  1. Find the value of \(600 - 289\). Show your thinking.
  2. Find the value of \(245 + 612\). Show your thinking.

Solution

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Problem 9

Find the value of each expression. Explain your reasoning.
  1. \(365 + 214\)
  2. \(365 - 214\)

Solution

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Problem 10

Exploration

Here is Han's work finding the value of a difference.

Number line.

  1. What difference did Han find? Show your reasoning.
  2. Write an addition and a subtraction equation that match Han's work.

Solution

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Problem 11

Exploration

Tyler says he can find the value of \(438 - 275\) using what he knows about differences of two-digit numbers.

“First I find \(43 - 27\) and then I find \(8 - 5\) and that gives me the answer.”

Use Tyler's reasoning to find the value of \(438 - 275\).

Solution

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Section B: Add within 1,000 using Place Value Strategies

Problem 1

Find the value of each sum. Show your thinking.

  1. \(238 + 52\)
  2. \(252 + 38\)
  3. \(119 +61\)

Solution

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Problem 2

Find the value of each sum. Explain your reasoning.

  1. \(395 + 77\)
  2. \(417 + 532\)

Solution

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Problem 3

Find the value of each sum. Show your thinking.

  1. \(238 + 54\)
  2. \(345 + 77\)

Solution

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Problem 4

Here is how Jada found the value of \(741 + 179\).

\(741 + 9 = 750\)

\(750 + 100 = 850\)

  1. Explain Jada's error.
  2. Correct Jada's work and find the value of \(741 + 179\).

Solution

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Problem 5

  1. Find the value of \(382 + 479\).

  2. Find the missing digit that makes the equation true. Explain how you know.

    \(534 + 4 \underline{\hspace{.5cm}} 6 = 1,\!000\)

Solution

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Problem 6

Exploration

Here is how Han likes to add.

Addition algorithm. Four-hundred forty-eight plus three-hundred, ninety-six, equals 7 and 13 and 14, equals eight-hundred forty-four.
  1. Explain why Han's method works.
  2. What do you think of Han's method?
  3. Use Han's method to find the value of \(388 + 259\).

Solution

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Problem 7

Exploration

Here is an equation with several digits missing.

\(\underline{\hspace{.5cm}} \ \underline{\hspace{.5cm}}5 + 63 \underline{\hspace{.5cm}} = 823\)

  1. What digits can you put in the blanks to make the equation true?
  2. Can you complete the numbers in more than one way to make the equation true?

Solution

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Section C: Subtract within 1,000 using Place Value Strategies

Problem 1

  1. Find the value of each difference.

    \(325 - 19\)

    \(437 - 115\)

  2. Jada drew this picture to find the value of a difference. What difference did Jada calculate? Explain how you know.

    Base ten diagram. 2 hundreds, 1 crossed out. 5 tens, 2 crossed out, one with arrow pointing to 10 ones, 1 crossed out. 7 ones, all crossed out.

Solution

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Problem 2

Find the value of each difference. Show your thinking.

  1. \(936 - 428\)

  2. \(352 - 181\)

Solution

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Problem 3

Jada is finding the value of \(571 - 385\). She says that she can take the ones from the ones, tens from the tens, and hundreds from the hundreds, with no decomposing. Do you agree with Jada? Explain your reasoning.

Solution

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Problem 4

Find the value of each difference. Show your thinking.

  1. \(216 - 88\)
  2. \(803 - 564\)

Solution

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Problem 5

Find the value of each difference in a way that makes sense to you. Show your thinking.

  1. \(747 - 295\)
  2. \(811 - 255\)
  3. \(600 - 378\)

Solution

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Problem 6

Exploration

Here is how Kiran found the value of \(543 - 276\)

\(500 - 200 = 300\)

\(300 - 30 = 270\)

\(270 - 3 = 267\)

  1. Explain why Kiran's method works.
  2. Use Kiran's method to find \(325 - 276.\)

Solution

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Problem 7

Exploration

  1. Choose a three-digit number so that subtracting by place value is a good strategy for finding the value of \(637 - \boxed{\phantom{8}} \boxed{\phantom{8}} \boxed{\phantom{8}}\). Explain your reasoning and find the value of the difference.
  2. Choose a three-digit number so that adding on to the smaller number is a good strategy for finding the value of \(637 - \boxed{\phantom{8}} \boxed{\phantom{8}} \boxed{\phantom{8}}\). Explain your reasoning and find the value of the difference.
  3. Choose a three-digit number so that decomposing two different units is a good strategy for finding the value of \(637 - \boxed{\phantom{8}} \boxed{\phantom{8}} \boxed{\phantom{8}}\). Explain your reasoning and find the value of the difference.

Solution

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