3.3 Wrapping Up Addition and Subtraction Within 1,000

Unit Goals

  • Students use place value understanding to round whole numbers and add and subtract within 1,000. They also represent and solve two-step word problems using addition, subtraction, and multiplication and assess the reasonableness of answers.

Section A Goals

  • Fluently add within 1,000 using algorithms based on place value and properties of operations.
  • Use place value understanding to compose and decompose numbers.

Section B Goals

  • Fluently subtract within 1,000 using algorithms based on place value, properties of operations, and the relationship between addition and subtraction.

Section C Goals

  • Round whole numbers to the nearest multiple of 10 and 100.

Section D Goals

  • Assess the reasonableness of answers.
  • Solve two-step word problems using addition, subtraction, and multiplication.
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Section A: Add Within 1,000

Problem 1

Pre-unit

Practicing Standards:  2.MD.B.6

Which number could be labeled on the number line?

Number line. Scale 0 to 100 by 100's. No tick marks. Point between 0 and 100.
A: 23
B: 45
C: 77
D: 92

Solution

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Problem 2

Pre-unit

Practicing Standards:  2.OA.A.1

There are 85 students on the playground. There are 57 fewer students in the classroom than on the playground. How many students are in the classroom? Explain or show your reasoning.

Solution

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Problem 3

Pre-unit

Practicing Standards:  2.NBT.B.9

Jada says she can find \(87 - 59\) by taking away 60 from 87 and adding 1 so it is the same as \(27 + 1\) or 28. Explain or show why Jada’s method to calculate \(87-59\) makes sense.

Solution

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Problem 4

Pre-unit

Practicing Standards:  2.NBT.B.7

Find the value of \(316 + 514\). Explain or show your reasoning.

Solution

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Problem 5

Pre-unit

Practicing Standards:  2.NBT.A.4

Put a < or > in the blank to make each statement true.

  1. \(197\, \underline{\hspace{1.05cm}}\, 311\)
  2. \(567\, \underline{\hspace{1.05cm}}\, 555\)
  3. \(908\, \underline{\hspace{1.05cm}} \,809\)

Solution

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Problem 6

Pre-unit

Practicing Standards:  2.NBT.B.7

Find the value of each expression.

  1. \(206 + 543\)
  2. \(327 + 181\)
  3. \(674 - 129\)

Solution

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Problem 7

Select all representations of the number four hundred twenty-three.

A: 324
B: 423
C: \(400 + 30 + 2\)
D:  
Base ten diagram. 4 hundreds, 2 tens, and 3 ones.
E:  

Solution

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Problem 8

The height of the Empire State Building in New York City is 443 meters. The tallest building in the world is 830 meters. How many meters taller than the Empire State Building is the tallest building in the world?

Solution

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Problem 9

Find the value of each sum in any way that makes sense to you. Explain or show your reasoning.

  1. \(456 + 231\)
  2. \(372 + 165\)

Solution

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Problem 10

Here are three different ways to find the value of \(157 + 436\).

ATwo base ten diagrams. Top diagram, 1 hundred, 5 tens, 7 ones. Bottom diagram, 4 hundreds, 3 tens, 6 ones.
BAddition. One-hundred plus fifty plus seven, plus four-hundred plus thirty plus six, equals five-hundred plus eighty plus thirteen.
CAddition. One-hundred fifty-seven, plus four-hundred thirty-six, equals thirteen plus eighty plus five-hundred, equals five-hundred ninety-three.

How are the methods alike? How are they different? Explain your reasoning.

Solution

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Problem 11

Here is Elena's algorithm for finding \(273 + 481\).

Addition. Step one. Two-hundred seventy-three plus four-hundred eighty-one, equals four.
Addition. Step 2. Two-hundred seventy-three, plus four-hundred eighty-one, equals 54.
Addition. Step 3. Two-hundred seventy-three plus four-hundred eighty-one equals seven-hundred fifty-four.
  1. Where does the 100 that Elena wrote in step 2 come from?
  2. Use Elena's method to find \(255 + 372\).

Solution

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Problem 12

  1. What do the 1s above the 2 and 5 in 253 mean in this calculation?

  2. Use an algorithm or another strategy to find the value of each sum.

    1. \(572 + 268\)
    2. \(726 + 199\)

Solution

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Problem 13

Exploration

Here is Lin’s strategy to find the value of \(596 + 385\): “I added 600 and then took away 4.”

  1. Explain why Lin’s strategy works. Then, use it to find the value of \(596 + 385\).

  2. For which of these expressions would you use Lin’s strategy? Explain or show your reasoning.

    1. \(436 + 173\)
    2. \(517 + 255\)
    3. \(787 + 135\)
    4. \(247 + 395\)

Solution

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Problem 14

Exploration

Write an addition problem with 3-digit numbers that you think is well suited for each of the following methods. Then, find the value of the sum using that method.

  1. mental strategies
  2. base-ten blocks
  3. an algorithm

Solution

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Section B: Subtract Within 1,000

Problem 1

Find the value of \(472 - 155\) in a way that makes sense to you.

Solution

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Problem 2

Here is a subtraction calculation.

Subtraction. Five-hundred plus forty plus five, minus three-hundred plus sixty plus three, equals one-hundred plus eighty plus two.
  1. Explain what the 400 above the 500 means.
  2. Explain what the 140 above the 40 means.
  3. Explain how the calculation works to find \(545 - 363\).

Solution

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Problem 3

  1. Write 518 and 346 in expanded form.
  2. Use the expanded form to find the difference of the two numbers.

Solution

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Problem 4

  1. Use an algorithm of your choice to find the value of \(316 - 154\).
  2. Use an algorithm of your choice to find the value of \(647 - 285\).

Solution

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Problem 5

Use an algorithm of your choice to find the value of each difference.

  1. \(218 - 136\)
  2. \(473 - 258\)

Solution

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Problem 6

Use a strategy or algorithm of your choice to find the value of each difference.

  1. \(573 - 299\)
  2. \(653 - 341\)
  3. \(371 - 158\)

Solution

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Problem 7

Exploration

Here is Noah's way to find the value of \(523 - 371\).

\(371 + 100 = 471\)
\(471 + 30 = 501\)
\(501 +20 = 521\)
\(521 + 2 = 523\)

The answer is \(100+30+20+2=152\).

  1. Explain why Noah’s method works.
  2. Use Noah’s method to calculate \(618 - 266\).

Solution

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Problem 8

Exploration

  1. Find the value of \(600 - 253\). Explain or show your reasoning.
  2. How is this problem different from other subtraction problems you have solved?

Solution

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Section C: Round Within 1,000

Problem 1

  1. Locate and label 539 on one of the number lines.

    Number line. Scale 500 to 600 by 100's.
  2. What is the closest multiple of 100 to 539?

Solution

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Problem 2

Find the nearest multiple of 10 and the nearest multiple of 100 for:

  1. 537
  2. 661

Solution

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Problem 3

  1. What are all the numbers that round to 350 when rounded to the nearest 10?
  2. Which numbers round to 350 when rounded to the nearest ten and round to 400 when rounded to the nearest hundred?

Solution

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Problem 4

  1. What is 346 rounded to the nearest ten? Explain or show your reasoning.
  2. What is 346 rounded to the nearest hundred? Explain or show your reasoning.

Solution

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Problem 5

Round each number to the nearest ten and to the nearest hundred. Explain or show your reasoning.

  1. 254
  2. 145

Solution

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Problem 6

Jada rounds 145 to the nearest ten and gets 150. Then she rounds 150 to the nearest hundred and gets 200. Jada says 145 rounded to the nearest hundred is 200. Do you agree with Jada? Explain or show your reasoning.

Solution

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Problem 7

Exploration

It is 234 miles from New York City to Boston. Tyler says, “That's about 200 miles, so it's about 400 miles to travel back and forth between New York City and Boston.” Do you agree with Tyler? Explain or show your reasoning.

Solution

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Section D: Solve Two-Step Problems

Problem 1

There are 708 students at the school. Three hundred ninety-four students are in the cafeteria and the rest are in class. Han estimates that 400 students are in class. Do you agree with Han’s estimate? Explain or show your reasoning.

Solution

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Problem 2

Select all equations that match the tape diagram.

Diagram. One rectangle split into 6 parts. Total length, 110. 1 part, labeled question mark. Other 5 parts labeled 6.
A:  \(110 + 5 \times 6 = {?}\)
B:  \({?} + 5 \times 6 = 110\)
C:  \(110 - {?} = 5 \times 6\)
D:  \(110 + {?} = 5 \times 6\)
E:  \(110 - 30 = {?}\)

Solution

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Problem 3

There are 240 connecting cubes in the box. Five students each take 9 connecting cubes from the box. How many connecting cubes are left in the box?

  1. Write an equation to represent the situation.  Use a letter for the unknown quantity.
  2. Solve the problem. Explain or show your reasoning.

Solution

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Problem 4

Andre has 245 cards. He bought 7 more packages of cards. How many cards does he have now?

  1. What information do you need to know to answer the question?
  2. Write an expression to represent the situation. Use a letter for the unknown quantity.

Solution

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Problem 5

Exploration

For each equation, draw a diagram and write a situation with a question.

  1. \(3 \times n + 163 = 187\)
  2. \(b - (4 \times 10) = 89\)

Solution

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Problem 6

Exploration

  1. A question in a subtraction situation can be answered with an estimate of “about 200.” What could the subtraction situation be?
  2. A question in a situation that uses addition and multiplication could be answered with an estimate of “about 300.” What could the situation be?

Solution

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