3.3 Wrapping Up Addition and Subtraction Within 1,000

Which number could be labeled on the number line?

A: 23

B: 45

C: 77

D: 92

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.

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.

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

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. \(908\, \underline{\hspace{1.05cm}} \,809\)

Find the value of each expression.

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

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

A: 324

B: 423

C: \(400 + 30 + 2\)

D:  

E:  

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?

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

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

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

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

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

1. Where does the 100 that Elena wrote in step 2 come from?
2. Use Elena's method to find \(255 + 372\).

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. \(726 + 199\)

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. \(247 + 395\)

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

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

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 \(545 - 363\).

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

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 \(647 - 285\).

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

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

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

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

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

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

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?

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

   

   

   

   

   

   

2. What is the closest multiple of 100 to 539?

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

1. 537
2. 661

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?

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.

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

1. 254
2. 145

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.

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.

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.

Select all equations that match the tape diagram.

A:  \(110 + 5 \times 6 = {?}\)

B:  \({?} + 5 \times 6 = 110\)

C:  \(110 - {?} = 5 \times 6\)

D:  \(110 + {?} = 5 \times 6\)

E:  \(110 - 30 = {?}\)

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.

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.

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

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

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?