Section A: Practice Problems Add Within 1,000

Section Summary

Details

In this section, we learned that an algorithm is a set of steps that works every time as long as the steps are carried out correctly. Then, we learned algorithms to add numbers within 1,000.

We also learned that we can choose to add using a strategy or an algorithm based on the numbers being added.

Addition. Three-hundred plus sixty plus two, plus three-hundred plus fifty plus nine, equals six-hundred plus one-hundred ten plus eleven.

Addition. Three-hundred sixty-two plus three-hundred fifty-nine equals eleven plus one-hundred ten plus six-hundred equals seven-hundred twenty-one.

Addition. Three-hundred sixty-two plus three-hundred fifty-nine equals seven-hundred twenty-one.

Problem 1 (Pre-Unit)

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.

$23$
$45$
$77$
$92$

Problem 2 (Pre-Unit)

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.

Problem 3 (Pre-Unit)

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.

Problem 4 (Pre-Unit)

Find the value of $316 + 514$ . Explain or show your reasoning.

Problem 5 (Pre-Unit)

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

$197$ $311$
$567$ $555$
$908$ $809$

Problem 6 (Pre-Unit)

Find the value of each expression.

$206 + 543$
$327 + 181$
$674 - 129$

Problem 7 (Lesson 1)

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

$324$
$423$
$400 + 30 + 2$

Problem 8 (Lesson 3)

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?

Problem 9 (Lesson 4)

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

$456 + 231$
$372 + 165$

Problem 10 (Lesson 5)

Here are three different ways to find the value of $157 + 436$ .

Two base ten diagrams. Top diagram, 1 hundred, 5 tens, 7 ones. Bottom diagram, 4 hundreds, 3 tens, 6 ones. — A

Addition. One-hundred plus fifty plus seven, plus four-hundred plus thirty plus six, equals five-hundred plus eighty plus thirteen. — B

Addition. One-hundred fifty-seven, plus four-hundred thirty-six, equals thirteen plus eighty plus five-hundred, equals five-hundred ninety-three. — C

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

Problem 11 (Lesson 6)

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.

Where does the 100 that Elena wrote in step 2 come from?
Use Elena’s method to find $255 + 372$ .

Problem 12 (Lesson 7)

What do the 1s above the 2 and 5 in 253 mean in this calculation?
Use an algorithm or another strategy to find the value of each sum.
- $572 + 268$
- $726 + 199$

Problem 13 (Exploration)

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

Explain why Lin’s strategy works. Then, use it to find the value of $596 + 385$ .
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. $247 + 395$

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.

mental strategies
base-ten blocks
an algorithm