Category: Envision Math

Envision Math 5th Grade Textbook Answer Key Topic 1.5 Problem Solving

Look for a Pattern

There are patterns in decimal number charts. Continue the pattern to label the other squares.

Answer:

Another Example
In this decimal number chart, what are the patterns in the diagonals?

Using the same system as above, you could fill in the diagonals of a decimal number chart.

Explain It

Question 1.
If the grid above were extended by 2 cells in the same design, what decimals would be used to complete the grid?
Answer:

What are the missing decimals?

What are the missing decimals?

Moving from left to right, tenths are the same in each row except for the last number; the hundredths increase by 1.

Guided Practice*

Do you know how?

In 1 and 2, determine the patterns, and then complete the grids.

Question 1.

Answer:

Question 2.

Answer:

Do you UNDERSTAND?

Question 3.
In a completed decimal chart, look at the first row, which begins 0.01,0.02. If Rene were to create a thousandths table, what two numbers would immediately follow 0.001?
Answer:

Question 4.
Write a real-world problem that you could solve by looking for a pattern.
Answer:

Independent Practice

In 5 and 6, determine the patterns, and then complete the grids.

Question 5.

Answer:

Question 6.

Answer:

Question 7.
Describe the patterns you should use to complete the following grid, then complete it.

Answer:

Question 8.
Determine the pattern, and then complete the grid.

Answer:

Question 9.
Determine the pattern, and then complete the grid.

Answer:

Question 10.
What is the missing number in the grid?

Answer:

Question 11.
Drake drew a grid of five cells in a row. The number 0.75 was in the middle cell. What did Drake’s grid look like?

Answer:

Question 12.
Determine the pattern, and then complete the grid.

Answer:

Question 13.
Juan and his family went to a movie. They bought 2 adult tickets for $8 each and 3 student tickets for $5 each. They paid with two $20 bills. How much change did they get?
Answer:

Question 14.
The greatest distance of Mercury from Earth is 136,000,000 miles. Write this number in expanded form.
Answer:

Think About the Process

Question 15.
You buy three items costing $0.37, $0.35, and $0.19, and give the clerk $1.00. Which expression shows how to find the amount of change you would get from $1.00?
A. $0.37 + $0.35 + $0.19 + $1.00
B. $1.00 – $0.37
C. $1.00 – ($0.37 + $0.35 + $0.19)
D. $1.00 + $0.37 + $0.35 – $0.19
Answer:

Question 16.
If 100 people are waiting in line to buy tickets and only 53 tickets are available, which expression would you use to find how many people won’t be able to buy tickets?
A. 100+53
B. 100 – 53
C. 100×53
D. 53 + 53
Answer:

Stop and Practice

Find the sum. Estimate to check if the answer is reasonable.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Find the difference. Estimate to check if the answer is reasonable.

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Find the product.

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Question 14.

Answer:

Question 15.

Answer:

Question 16.

Answer:

Question 17.

Answer:

Question 18.

Answer:

Error Search Find each sum or difference that is not correct. Write it correctly and explain the error.

Question 19.

Answer:

Question 20.

Answer:

Question 21.

Answer:

Question 22.

Answer:

Question 23.

Answer:

Number Sense

Estimating and Reasoning Write whether each statement is true or false. Explain your reasoning.

Question 24.
The product of 5 and 7 is 5 less than 30.
Answer;

Question 25.
The sum of 610 and 209 is less than 800.
Answer:

Question 26.
The quotient of 0 divided by 6 is zero.
Answer:

Question 27.
The difference of 619 – 271 is greater than 300 and less than 500.
Answer:

Question 28.
The sum of 196 + 435 is 4 less than 635.
Answer:

Question 29.
The quotient of 7 divided by 1 is 1.
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 1.4 Comparing and Ordering Decimals

How can you compare and order decimals?

Scientists collected and measured the lengths of different cockroach species. Which cockroach had the greater length, the American or the Oriental cockroach? Use these three steps to find out.

Answer:

Another Example
How can you order decimals?

Step 1
Write the numbers, lining up the decimal points. Start at the left. Compare digits of the same place-value.
3.576
3.432
3.582
3.432 is the least.

Step 2
Write the remaining numbers, lining up the decimal points. Start at the left. Compare.
3.576
3.582
3.582 is greater.

Step 3
Write the numbers from least to greatest.
3.432, 3.576, 3.582
In order of their lengths from least to greatest, the cockroaches are the Oriental, the American, and the Australian.

Guided Practice*

Do you know how?

Compare the two numbers. Write >, <, or=for each .

Question 1.
3.692 3.697
Answer:

Question 2.
7.216 7.203
Answer:

Order these numbers from least to greatest.

Question 3.
5.540, 5.631, 5.625, 5.739
Answer:

Question 4.
0.675, 1.529, 1.35, 0.693
Answer:

Do you understand?

Question 5.
Write a number that is greater than 4.508 but less than 4.512.
Answer:

Question 6.
Scientists measured a Madeira cockroach and found it to be 3.438 cm long. If they were ordering the lengths of the cockroaches from least to greatest, between which two cockroaches would the Madeira cockroach belong?
Answer:

Step 1
Line up the decimal points.
Start at the left.
Compare digits of the same place-value.
3.576
3.432

Step 2
Find the first place where the digits are different.
3.576
3.432

Step 3
Compare. 5 > 4
Think 0.5 > 0.4
So, 3.576 > 3.432.
The American cockroach is longer than the Oriental cockroach

Independent Practice

Copy and complete. Write >, <, or = for each .

Question 7.
0.890 0.89
Answer:

Question 8.
5.733 5.693
Answer:

Question 9.
9.707 9.717
Answer:

Question 10.
4.953 4.951
Answer:

Order from least to greatest.

Question 13.
2.912, 2.909, 2.830, 2.841
Answer:

Question 14.
8.541, 8.314, 8.598, 8.8
Answer:

Order from greatest to least.

Question 15.
5.132, 5.123, 5.312, 5.231
Answer:

Question 16.
62.905, 62.905, 62.950, 62.383
Answer:

Problem Solving

Question 17.
Writing to Explain Why do you need to line up the decimal points before comparing and ordering numbers with decimals?
Answer:

Question 18.
Judith wants to buy her mother flowers. Judith earns $4 a week doing chores. If each flower costs $2, how many flowers can Judith buy her mother if she saves for three weeks?
Answer:

Question 19.
There are five types of grains of sands: coarse, very coarse, medium, fine, and very fine. A grain of fine sand can have a diameter of 0.125 millimeters.
Which number is less than 0.125?
A. 0.5
B. 0.2
C. 0.13
D. 0.12
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 1.1 Place Value

Review What You Know

Vocabulary

Choose the best term from the box.

Question 1.
_________________________ are the symbols used to show numbers.
Answer:

Question 2.
A group of 3 digits in a number is a ______________________
Answer:

Question 3.
___________________ is the position of a digit in a number that is used to determine the value of the digit.
Answer:

Adding Whole Numbers

Question 4.
800 + 90 + 2
Answer:

Question 5.
3,000 + 400 + 50
Answer:

Question 6.
10,000 + 2,000 + 60 + 1
Answer:

Question 7.
37 + 85
Answer:

Question 8.
124 + 376
Answer:

Comparing

Compare. Use < or >.

Question 9.
869 912
Answer:

Question 10.
9,033 9,133
Answer:

Question 11.
11.1,338 1,388
Answer:

Question 12.
7,325 7,321
Answer:

Place Value

Question 13.
Writing to Explain In the number 767, does the first 7 have the same value as the final 7? Why or why not?
Answer:

Guided Practice

Do you know how?

In 1 through 3, write each number in standard form.

Question 1.
forty billion, forty-eight million
Answer:

Question 2.
90,000,000,000 + 5,000,000 + 300
Answer:

Question 3.
six billion, two hundred million, twelve thousand, six
Answer:

Do you uderstand?

Question 4.
Look at the number in the example at the top. In what place is the digit 6? What is its value?
Answer:

Question 5.
In which period does the 1 occur on the place-value chart? How does the period name help you read a large number?
Answer:

Independent Practice

Write each number in word form

Question 6.
7,123
Answer:

Question 7.
18,345
Answer:

Question 8.
10,010,468
Answer:

Question 9.
300,014,000,56
Answer:

write each number in standard form.

Question 10.
8,000,000 + 300 + 9
Answer:

Question 11.
60,000,000 + 10,000 + 20 + 3
Answer:

Question 12.
114,000,000,000 + 70,000 + 8,000 + 7
Answer:

Question 13.
50,000,000,000 + 200, 000 + 30, 000
Answer:

Write each number in expanded form.

Question 14.
670,200,640
Answer:

Question 15.
1,000,102,200
Answer:

Question 16.
85,000,011,000
Answer:

What is the value of the underlined digit in each number?

Question 17.
67,100
Answer:

Question 18.
6,800,000
Answer:

Problem Solving

Question 19.
The Milky Way Galaxy has at least two 20. Neptune is 4,498,252,900 km from hundred billion stars. Write this number in standard form.
Answer:

Question 20.
Neptune is 4,498,252,900 km from the sun. Write this number in expanded form.
Answer:

Question 21.
Janet purchased 3 T-shirts and 2 blouses. Each T-shirt cost $12 and each blouse cost $23. What was the total cost of Janet’s purchase?
Answer:

Question 22.
Number Sense Write three different 10-digit numbers that have a 7 in the millions place.
Answer:

Question 23.
In a recent U.S. Census, California’s population was 33,871,648. What is California’s population after
a. an increase of 100,000.
b. an increase of 1,000,000.
c. a decrease of 10,000
Answer:

Question 24.
Writing to Explain For the standard form of two billion, three hundred fifty thousand, four, Danielle wrote 2,350,400,0. What error did she make? What is the correct standard form of the number?
Answer:

Question 25.
Each October, millions of monarch butterflies migrate south from as far north as the Canadian Rockies, to locations in California and Mexico. About 65,000 come to stay the winter in Pacific Grove, California. Write 65,000 in word form.

Answer:

Question 26.
What is the value of the underlined digit in 90,805,001,021?
A. 5,000
B. 50,000
C. 500,000
D. 5,000,000
Answer:

Go through the enVision Math Common Core Grade 4 Answer Key Topic 2 Fluently Add and Subtract Multi-Digit Whole Numbers regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 2 Fluently Add and Subtract Multi-Digit Whole Numbers

Essential Questions:
How can sums and differences of whole numbers be estimated? What are standard procedures for adding and subtracting whole numbers?

enVision STEM Project: The World’s Fastest Vehicles
Do Research Since 1970, the speed record has been broken many times. Use the Internet or other sources to find five vehicles that can go faster than 1,000 kilometers per hour.
Journal: Write a Report Include what you found. Also in your report:

• Make a table that includes the type of vehicle, whether the vehicle moves on land, water, or in space, and the speed of the vehicle.
• Use place value to find the fastest and the slowest vehicle in your table.
• Calculate the difference between the speeds of two of the vehicles in your table.

Review What You Know

Vocabulary
Choose the best term from the box. Write it on the blank.

• equation
• estimate
• period
• rounding

Question 1.
An __________ is an approximate number or answer.
Answer:
An estimate is an apporoximate number or answer.

Question 2.
A process that determines which multiple of 10, 100, 1,000, and so on a number is closest to is called _________.
Answer:
A process that determines which multiple of 10, 100, 1000, and So on a number is closest to is called rounding.

Question 3.
A number sentence that uses the equal sign (=) to show two expressions have the same value is an __________.
Answer:
A number sentence that uses the equal sign(=) to show two expressions have the same value is an equation.

Addition Facts and Mental Math

Find each sum.
Question 4.
4 + 6
Answer:
4 + 6 = 10

Question 5.
7 + 5
Answer:
7 + 5 = 12

Explanation:
The sum of 7 and 5 is 12.

Question 6.
29 + 8
Answer:
29 + 8 = 37

Explanation:
The sum of 29 and 8 is 37.

Question 7.
14 + 5
Answer:
14 + 5 = 19

Question 8.
13 + 7
Answer:
13 + 7 = 20

Explanation:
The sum of 13 and 7 is 20.

Question 9.
37 + 7
Answer:
37 + 7 = 42

Question 10.
289 + 126
Answer:
289 + 126 = 415

Explanation:
The sum of 289 and 126 is 415.

Question 11.
468 + 329
Answer:
468 + 329 =797

Explanation:
The sum of 468 and 329 is 797.

Question 12.
157 + 211
Answer:
157 + 211 = 368

Explanation:
The sum of 15 and 211 is 368.

Subtraction Facts and Mental Math

Find each difference.
Question 13.
27 – 3
Answer:
27 – 3 = 24

Question 14.
6 – 4
Answer:
6 – 4 = 2

Question 15.
15 – 8
Answer:
15 – 8 = 7

Question 16.
11 – 8
Answer:
11 – 8 = 3

Explanation:
The difference between 11 and 8 is 3.

Question 17.
66 – 2
Answer:
66 – 2 = 64

Question 18.
17 – 8
Answer:
17 – 8 = 9

Explanation:
The difference between 17 and 8 is 9.

Question 19.
416 – 404
Answer:
416 – 404 = 12

Explanation:
The difference between 416 and 404 is 12.

Question 20.
220 – 205
Answer:
220 – 205 = 15

Explanation:
The difference between 220 and 205 is 15.

Question 21.
148 – 106
Answer:
148 – 106 = 132

Explanation:
The difference between 148 and 106 is 42.

Rounding

Question 22.
Construct Arguments Why does 843,000 round to 840,000 rather than 850,000 when rounded to the nearest ten thousand?

Answer:
The rule for rounding to the nearest ten thousand is to look at the last four digits.If the last four digits are  5000 or greater, then we round our ten thousands digit up, and if it is less than 5000, then we keep our ten thousands digit the same.
So, 843,000 rounds downs to 840000.

Pick a Project

PROJECT 2A
What are the largest cities in your home state?
Project: Map the Population of Your State’s Largest Cities

PROJECT 2B
How did the United States become a nation?
Project: Write a Report on U.S. Expansion

PROJECT 2C
How do the sizes of the planets compare to the size of Earth?
Project: Make a Model of the Solar System

PROJECT 2D
How high is high?
Project: Compare Mountain Elevations

Lesson 2.1 Finding Sums and Differences with Mental Math

Solve & Share
Luke collected 1,034 baseball cards, 1,289 football cards, and 1,566 hockey cards. Use mental math to find the number of cards in Luke’s collection. Solve this problem any way you choose.
I can … use properties and strategies to change a problem to add and subtract with mental math.

Look Back! Construct Arguments How could you use mental math to solve 1,289 + 1,566? 1,034 + 1,566? How is the thinking different?

Essential Question
How Can You Use Mental on Math to Solve Problems?

Visual Learning Bridge
Katy’s dad washes windows at one of the tallest buildings in Miami, the Four Seasons Hotel. He worked Saturdays in October and earned more money than in September. How much did he earn in the two months combined?
Find $1,985 + $2,595 with mental math.

Washing Windows Earned $1,985 in Sept. Earned $2,595 in Oct.
+5+10 +80 +500 +2,000
Make Ten

Break apart 1,985 to get a number that makes a ten, hundred, or thousand when added to 2,595. Then, use the Associative Property of Addition to change the grouping.
1,985 + 2,595
= (1,580 + 405) + 2,595
= 1,580 + (405 + 2,595)
= 1,580 + 3,000
= 4,580
Katy’s dad earned $4,580.

Add On
Break one addend apart and add on.

You can start with either addend because of the Commutative Property of Addition.

Katy’s dad earned $4,580.

Use Compensation
Add 15 to 1,985. Then subtract 15 from 2,595 to compensate. Adding 15 and subtracting 15 is the same as adding zero. Adding zero doesn’t change the sum because of the Identity Property of Addition.
1,985 + 2,595
= (1,985 + 15) + (2,595 – 15)
= 2,000 + 2,580
= 4,580
Katy’s dad earned $4,580.

Convince Me! Use Structure How could you make ten by breaking apart 2,595?

Another Example!
Subtract 2,595 – 1,985 with mental math.

Count Up
Count from 1,985 up to 2,595.

Find how much you counted up.
5 + 10 + 595 = 610

Count Down
Count down 1,985 from 2,595.

Use Compensation
Adding the same amount to both numbers in a subtraction problem doesn’t change the difference.
1,990
2,510
(2,595 + 15) – (1,985 + 15)
= 2,610 – 2,000
= 610

Guided Practice

Do You Understand?
Question 1.
Explain how to find 2,987 + 4,278 with mental math. What property does your strategy use?
Answer:
7265

Explanation:
Use Compensation
Add 13 to 2,987. Then subtract 13 from 4278 to compensate. Adding 13 and subtracting 13 is the same as adding zero. Adding zero doesn’t change the sum because of the Identity Property of Addition.
2987 + 4278
= (2987 + 13) + (4278 – 13)
= 3000 + 4265
= 7265
Therefore, the sum of 2987 and 4278 is 7265.

Do You Know How?
For 2-4, use mental math strategies to solve.
Question 2.
6,794 – 999
Answer:

Explanation:
1+794+5000=5795
The difference between 6794 and 999 is 5795.

Question 3.
4,505 + 3,515
Answer:
7620

Explanation:
Make Ten

Break apart 4505 to get a number that makes a ten, hundred, or thousand when added to 3515. Then, use the Associative Property of Addition to change the grouping.
4505 + 3115
= (4000+505) + 3115
= 4000 + (505 + 3115)
= 4000 + 3620
= 7620
Therefore, the sum of 4505 and 3115 is 7620.

Question 4.
9,100 + 2,130 + 900
Answer:
7620

Explanation:
Make Ten

Break apart 9100 to get a number that makes a ten, hundred, or thousand when added to 2130 and 900. Then, use the Associative Property of Addition to change the grouping.
9100 + 2130 + 900
=(9000+100) + 2130 + 900
=9000 + (100+900) + 2130
=9000 + 1000 + 2130
=10000 + 2130
=12130
Therefore, the sum of 9100, 2130 and 900 is 12130.

Independent Practice

For 5-10, use mental math to solve.
Question 5.
7,000 – 827
Answer:

Explanation:
3+170+6000=6173
The difference between 7000 and 827 is 6173.

Question 6.
1,225 + 975
Answer:
2200

Explanation:
Use Compensation
Add 75 to 1,225. Then subtract 75 from 975 to compensate. Adding 15 and subtracting 15 is the same as adding zero. Adding zero doesn’t change the sum because of the Identity Property of Addition.
1,225 + 975
= (1225 + 75) + (975 – 75)
= 1300 + 900
= 2200
The sum of 1225 and 975 is 2200.

Question 7.
5,491 – 2,860
Answer:

Explanation:
40+60+2491=2591
The difference between 5491 and 2860 is 2591.

Question 8.
6,686 – 1,443
Answer:

Explanation:
7+50+500+4686=5243
The difference between 16686 and 1443 is 5243

Question 9.
8,375 + 31,145
Answer:
39520

Explanation:
Make Ten

Break apart 8375 to get a number that makes a ten, hundred, or thousand when added to 31145. Then, use the Associative Property of Addition to change the grouping.
8375 + 31145
= (8000+375) + 31145
= 000 + (375 + 31145)
= 8000 + 31520
= 39520
Therefore, the sum of 8375 and 31145 is 39520.

Question 10.
23,100 + 74,900
Answer:
98000

Explanation:
Make Ten

Break apart 23100 to get a number that makes a ten, hundred, or thousand when added to 74900. Then, use the Associative Property of Addition to change the grouping.
23100 + 74900
= (23000+100) + 74900
= 23000 + (100 + 74900)
= 23000 + 75000
= 98000
Therefore, the sum of 23100 and 74900 is 98000.

Problem Solving

For 11-12, use the table at the right.

Question 11.
Precision How much greater is the area of California than Montana? Explain how to use mental math to solve.
Answer:

Question 12.
Round the land area of the state with the least number of square miles to the nearest ten thousand.
Answer:

Question 13.
The town of Worman Grove has collected 28,481 pens for a school supplies drive. Their goal is 30,000 pens. Show how to use counting on to find how many more pens they need to reach their goal.
Answer:

Question 14.
Conservationists weigh two Northern elephant seals. An adult seal weighs 6,600 pounds, and its pup weighs 3,847 pounds. What is their combined weight? Explain how to use mental math to solve.
Answer:

Question 15.
Higher Order Thinking Is Kelly’s answer correct? What mistake did she make?
Kelly’s Work
5,356 + 2,398
= (5,356 + 2) +(2,398 + 2)
5,358 + 2,400 = 7,758
Answer:
Kelly’s work is wrong.her mistake is she has to add and subtract the number if the question is to find the sum.

Explanation:
Add and subtract same number, the answer will not differ.
(5356-2) + (2398+2)
5354 + 2400
7754
Therefore 5356 + 2398 = 7754.

Assessment Practice

Question 16.
Use mental math to find 1,218 + 1,598.
A. 2,716
B. 2,720
C. 2,816
D. 2,820
Answer:
C.2816

Explanation:
1218+1598
Break apart 1218 as 1000 and 218 and and the second part with 1598.
=(1000+218)+1598
=1000+(218+1598)
=1000+1816
=2816
1218+1598=2816

Question 17.
Use mental math to find 5,280 – 1,997.
A. 3,177
B. 3,180
C. 3,277
D. 3,283
Answer:
D.3283

Explanation:
5280-1997
Adding the same amount to both numbers in a subtraction problem doesn’t change the difference
=(5280+3) – (1997+3)
=5283 – 2000
=3823
5280-1997=3823

Lesson 2.2 Estimate Sums and Differences

Solve & Share
A manufacturer in Detroit produces three new cars that weigh 6,127 pounds, 4,652 pounds, and 3,393 pounds. If these are are loaded on a truck, has the truck reached its 15,000-pound maximum? Use an estimate to decide. Solve this problem any way you choose.
I can … use rounding and place value to estimate sums and differences.

Answer:

Explanation:
When these three cars are loaded in the truck, the truck doesn’t reach the maximum limit of 15000pounds as the estimated total weight of the three cars is 14200.

Look Back! Why can you solve the problem using only an estimate rather than finding the exact weight of the three cars?

Essential Question
How Can You Estimate Sums and Differences of Whole Numbers?
Answer:
We can estimate the sums and difference of whole numbers by rounding of them to the nearest hundreds and thousands.

Visual Learning Bridge
Books, magazines, and movies were checked out of the public library. About how many more books were checked out than magazines and movies combined?

Estimate: Round to the nearest thousand.
Find the number of magazines and movies.

Subtract the number of magazines and movies from the rounded number of books.
13,000 – 6,000 = 7,000
About 7,000 more books were checked out.

Estimate: Round to the nearest hundred.
Find the number of magazines and movies.

Subtract the number of magazines and movies from the rounded number of books.
12,600 – 6,400 = 6,200
About 6,200 more books were checked out.

Convince Me! Construct Arguments The head librarian at the public library says she will establish a separate checkout desk for magazines and movies if the difference between the number of books and the number of these other materials is greater than 6,500. Which of the estimates above should you use to help her make her decision? Explain.

Another Example!
Decide if each computation is reasonable.
You can use an estimate to decide whether or not an exact answer is reasonable.
39,482 + 26,357 = 65,839
39,482 + 26,357 is about 40,000 + 26,000 = 66,000
The sum, 65,839, is reasonable because it is close to the estimate of 66,000.

8,215 – 5,852 = 3,643
8,215 – 5,852 is about 8,000 – 6,000 = 2,000
The difference, 3,643, is not reasonable because it is not close to the estimate of 2,000.

Guided Practice

Do You Understand?
Question 1.
Is 2,793 a reasonable difference for 6,904 – 4,111? Explain.
Answer:

Explanation:
Yes, 2793 is a reasonable difference for 6,904 – 4,111 as estimated difference is 2800 and 2793 is very close to 2800.

Do You Know How?
For 2-4, estimate each sum or difference.
Question 2.

Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 9400.

Question 3.

Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 88500.

Question 4.

Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 13200.

Independent Practice

Leveled Practice For 5-13, estimate each sum or difference.
Question 5.

Answer:

Explanation:
When rounded to the nearest thousands,
The estimated sum is 8000.

Question 6.

Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 515400.

Question 7.

Answer:

Explanation:
When rounded to the nearest ten thousands,
The estimated sum is 110000.

Question 8.

Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 4300.

Question 9.

Answer:

Explanation:
When rounded to the thousands
The estimated sum is 766200.

Question 10.

Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 14260.

Question 11.
485,635 – 231,957
Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 253600.

Question 12.
9,668 – 2,489
Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 7200.

Question 13.
368,545 + 114,254
Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 482800.

Problem Solving

Question 14.
The table shows the number of students at each school in the district. Is 2,981 reasonable for the total number of students at Wilson Elementary and Kwame Charter School? Explain.

Answer:

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 3000.
Therefore, as 2,981 is close to 3000, it is reasonable for the total number of students at Wilson Elementary and Kwame Charter School

Question 15.
enVision® STEM A satellite moves at a speed of 27,950 kilometers per hour. A satellite at a higher orbit travels at a speed of 11,190 kilometers per hour. About how much faster is one satellite than the other? Explain how to estimate.
Answer:

Explanation:
When rounded to nearest thousands,
The estimated difference is 17000.

Question 16.
Critique Reasoning Elle says, “When rounding to the nearest thousand, 928,674 rounds to 930,000.” Do you agree? Explain.
Answer:
No, I don’t agree with Elle as she rounded of to the nearest then thousands rather tha nearest thousand.
The nearest thousand for 928674 is 929000.
When we round of o the nearest thousand we have to look at the last three digits and if it lessthan 500 we hav eto round of to the same digit in the thousands place, if it is more than 500 then we have to roundof to the net thousand than the digit in thousands place.

Question 17.
Higher Order Thinking A football team needs to sell at least 20,000 tickets to two games to cover expenses. They sell 10,184 tickets to one game and 9,723 to the other. Estimate by rounding to the nearest thousand and by rounding to the nearest hundred. Did the team sell enough tickets? Explain your answer.
Answer:

Explanation:
The estimated sum of tickets sold when rounded to hundreds is 20900
The estimated sum of tickets sold when rounded to thousands is 20000
As both sums are same or close to 20000.
Therefore, the team could sell enough ticketsto cover their expenses.

Assessment Practice

Question 18.
Last week, Mallory flew two round trips. They were 3,720 miles and 5,985 miles. Which is the best estimate of the total distance Mallory flew?
A. 11,000 miles
B. 9,700 miles
C. 8,700 miles
D. 8,000 miles
Answer:
B.9700

Explanation:
The sum of miles Mallory flew when rounded to hundreds is 9700,
The sum of miles Mallory flew when rounded to thousands is 10000,
As the option B.9700 is close to the estimates So, rounded to hundreds is the best estimate.

Question 19.
Use estimation to decide which is a reasonable difference.
38,041 – 19,558
A. 21,374
B. 20,973
C. 18,473
D. 16,483
Answer:
C.18473

Explanation:
As the estimated difference whrn roundrev to the nearest hundreds is 18400 and as 18473 is close to 18400, 18473 is reasonable.

Lesson 2.3 Add Whole Numbers

Solve & Share
Students collect empty plastic water bottles to recycle. How many bottles were collected in the first two months? How many bottles were collected in all three months? Solve this problem using any strategy you choose.
I can … connect place-value concepts to using addition algorithms.

Look Back! When adding, how do you know when there are enough tens to make one hundred?

Essential Question
How Do You Add Whole Numbers Efficiently?

Visual Learning Bridge
The Florida Legislature set a statewide recycling goal. To help meet this goal, Kennedy Elementary school students collected newspaper. How many pounds of newspaper did they collect in all?
Add 358 + 277.
Estimate.
350 + 250 = 600

Add using partial sums.
Add using the standard algorithm.

Convince Me! Use Structure in the problem above, when you add partial sums you can add the ones first or the hundreds. Can you do the same when you add using the standard algorithm?

Guided Practice

Do You Understand?
Question 1.
When you place a 1 above the tens values, what does it mean?
Answer:
If i place 1 above the tens values it means that i regrouped ones.

Question 2.
When you place a 1 above the hundreds values, what does it mean?
Answer:
If i place 1 above the hundreds values it means that i regouped tens.

Do You Know How?
Find the sum by using partial sums and by using the standard algorithm.
Question 3.

Answer:

Explanation:
The sum of 378 and 557 is 935.

Find each sum using the strategy you choose.
Question 4
a.

Answer:

Explanation:
The sum of 678 and 253 is 931.

b.

Answer:

Explanation:
The sum of 325 and 256 is 581.

c.

Answer:

Explanation:
The sum of 185 and 253 is 438.

Independent Practice

In 5-16, find each sum.
Question 5.

Answer:

Explanation:
The sum of 148 and 157 is 305.

Question 6.

Answer:

Explanation:
The sum of 389 and 461 is 850.

Question 7.

Answer:

Explanation:
The sum of 365 and 458 is 823.

Question 8.

Answer:

Explanation:
The sum of 126 and 138 is 264.

Question 9.

Answer:

Explanation:
The sum of 371 and 454 is 825.

Question 10.

Answer:

Explanation:
The sum of 357 and 498 is 855.

Question 11.
142 + 178
Answer:

Explanation:
The sum of 142 and 178 is 320.

Question 12.
565 + 694
Answer:

Explanation:
The sum of 565 and 694 is 1259.

Question 13.
375 + 548
Answer:

Explanation:
The sum of 375 and 548 is 923.

Question 14.
718 + 865
Answer:

Explanation:
The sum of 718 and 865 is 1583.

Question 15.
909 + 624
Answer:

Explanation:
The sum of 909 and 624 is 1533.

Question 16.
129 + 587
Answer:

Explanation:
The sum of 129 and 587 is 716.

Problem Solving

Question 17.
Construct Arguments Harmony solved this problem using the standard algorithm, but she made an error. What was her error, and how can she fix it?

Answer:

Explanation:
The sum of 437 and 175 is 612.
Harmony didnot regroup tens.she should regroup tens and place 1 above the hundreds place to solve the problem.

Question 18.
Higher Order Thinking For which problems would you use a mental strategy or the standard algorithm to solve? Explain.
499 + 121
827 +385
175 + 325
Answer:
I use mental strategy to solve 499+121 and 175+325 as the number in hundreds place is small and it is easy to slove mentally, I use standard algorithm to solve 827+385 as the number in hundreds place is big.

Question 19.
A Little League team played a doubleheader (two back-to-back baseball games). The first game lasted 155 minutes. The second game lasted 175 minutes. There was a 30-minute break between games. What was the total time of the doubleheader?
Answer:

Explanation:
A Little League team played a doubleheader, The first game lasted 155 minutes. The second game lasted 175 minutes. There was a 30-minute break between games.
To find the total time of the doubleheader we need to add 155, 165 and 30.
The the total time of the doubleheader is 360.

Assessment Practice

Question 20.
Select all the correct sums.
☐ 742 + 353 = 1,095
☐ 428 + 247 = 665
☐ 604 + 684 = 1,288
☐ 735 + 298 = 1,033
☐ 912 + 198 = 1,010
Answer:

Explanation:
The marked sums are correct.

Question 21.
What is the missing digit in the addition problem?

Answer:

Explanation:
To find the missing number first subtract 1004 and 659, we get 345 as the answer.The missing tens is 4.

Lesson 2.4 Add Greater Numbers

Solve & Share
Erica’s class collected 4,219 bottles for the recycling center. Ana’s class collected 3,742 bottles. Leon’s class collected 4,436 bottles. How many bottles did the three classes collect? Solve this problem any way you choose.
I can … use the standard algorithm and place value to add multi-digit numbers.

Look Back! Generalize Which properties allow you to change the order and grouping of numbers to add? How did you use these properties?

Essential Question
baby How Do You Add Greater Numbers?

Visual Learning Bridge
Plans for remodeling a sports stadium include adding an additional 19,255 seats. How many seats will be in the remodeled stadium?
Seats in the original stadium:
20,000 + 4,595 = 24,595

Step 1
Use the standard algorithm for addition
To add 24,595 + 19,255, add the ones, then the tens, and then the hundreds. Regroup if necessary

Step 2
Add the thousands and the ten thousands. Regroup if necessary.

The remodeled stadium will have 43,850 seats.
You can add two or more numbers when you line up the numbers by place value. Add one place at a time.

Step 3
Use an estimate to check if your answer is reasonable.

43,850 is close to the estimate of 44,000, so the answer is reasonable.

Convince Me! Construct Arguments When using the standard algorithm to add 24,595 + 19,255, how do you regroup 1 ten + 9 tens + 5 tens?

Another Example!
Find 30,283 + 63,423 + 6,538.
Explain how to check that your answer is reasonable.
Estimate:
30,000 + 63,000 + 7,000 = 100,000

The sum is reasonable because it is close to the estimate of 100,000.

Guided Practices

Do You Understand?
Question 1.
When adding 36,424 and 24,482, why is there no regrouping in the final step?
Answer:

Explanation:
When 36424 and 24482 are added there is no regrouping in the final step because the sum of the final numbers donot exceed 9.

Question 2.
Science-volunteer teams catalog 7,836 species of insects and 4,922 species of spiders. How many species did the volunteers catalog?
Answer:

Explanation:
12758 species the volunteers cataloged.

Do You Know How?
For 3-6, find each sum. Check that your answer is reasonable.
Question 3.

Answer:

Explanation:
The sum of 14926 and 3382 is 18308.Answer is reasonable as the estimate 18000 is close to the answer.

Question 4.

Answer:

Explanation:
The sum of 423156 and 571607 is 994763.Answer is reasonable as the estimate 99500 is close to the answer.

Question 5.

Answer:

Explanation:
The sum of 3258 and 1761 is 5019.Answer is reasonable as the estimate 5100 is close to the answer.

Question 6.

Answer:

Explanation:
The sum of 82385 and 49817 is 132202.Answer is reasonable as the estimate 132000 is close to the answer.

Independent Practice

For 7-16, find each sum. Check that your answer is reasonable.

Question 7.

Answer:

Explanation:
The sum of 14312 and 9617 is 23929.Answer is reasonable as the estimate 24000 is close to the answer.

Question 8.

Answer:

Explanation:
The sum of 275558 and 605131 is 880689.Answer is reasonable as the estimate 881000 is close to the answer.

Question 9.

Answer:

Explanation:
The sum of 38911 and 45681 is 84592.Answer is reasonable as the estimate 85000 is close to the answer.

Question 10.

Answer:

Explanation:
The sum of 5801 and 4189 is 9990.Answer is reasonable as the estimate 10000 is close to the answer.

Question 11.

Answer:

Explanation:
The sum of 8818 and 1182 is 10000.Answer is reasonable as the estimate 10000 is close to the answer.

Question 12.

Answer:

Explanation:
The sum of 5555 and 7412 is 12967.Answer is reasonable as the estimate 13000 is close to the answer.

Question 13.

Answer:

Explanation:
The sum of 21009 and 5529 is 26538.Answer is reasonable as the estimate 26600 is close to the answer.

Question 14.

Answer:

Explanation:
The sum of 30080 and 19187 is 49267.Answer is reasonable as the estimate 49000 is close to the answer.

Question 15.
29,634 + 12,958 + 6,835
Answer:

Explanation:
The sum of 29634, 12958 and 6835 is 49427.

Question 16.
64,673 + 48,262 + 8,918
Answer:

Explanation:
The sum of 64673, 48262 and 8918 is 121853.

Problem Solving

Question 17.
Aubrey writes a blog. 29,604 people read her first post. The next week, 47,684 people read her second post. Aubrey’s third post had 41,582 readers. What is the total number of readers?
Answer:

Explanation:
The sum of 29604, 47684 and 4152 is 81440.
Therefore the total number of readers are 81440.

Question 18.
Write the number name for 21,604.
Answer:
Number name of 21604 is Twenty one thousand six hundred four.

Question 19.
Higher Order Thinking Explain the mistake made when finding the sum at the right. What is the correct sum?

Answer:
The correct sum is 872879.

Explanation:
The sum of 638528 and 234351 is 872879.
The mistake is regrouping 8 and 4 thousands as 1 tensthousand is not done in the given sum.

Question 20.
Number Sense Maria added 45,273 and 35,687 and got a sum of 70,960. Is Maria’s answer reasonable? Explain.
Answer:

Explanation:
Estimate:
45273-45000, 35687-36000
45000+36000=81000
The sum of 45273 and 35687 is 80960.Maria’s answer is not reasonable as the estimate is not close to the answer.

Question 21.
Make Sense and Persevere There were 130,453 pairs of skates rented at an ice rink in one year. The next year, 108,626 pairs were rented. The following year 178,119 pairs were rented. How many pairs were rented during the busiest two years? How many pairs were rented during all three years?
Answer:

Explanation:
308572 pairs were rented during the busiest two years.
417198 pairs were rented during all three years

Assessment Practice

Question 22.
Select all the correct sums.
☐ 5,742 + 8,353 = 14,095
☐ 9,428 + 18,247 = 27,665
☐ 29,604 + 47,684 = 77,288
☐ 66,288 + 145,280 = 211,568
☐ 235,912 + 19,847 = 434,382
Answer:

Question 23.
Select all the addition expressions that have a sum of 89,405.
☐ 78,487 + 7,998
☐ 79,562 + 9,843
☐ 2,222 + 77,183
☐ 52,514 + 36,891
☐ 6,573 + 82,832
Answer:

Lesson 2.5 Subtract Whole Numbers

Solve & Share
Carly’s parents own a motel in Orlando with 224 rooms. Last night, 176 rooms were rented. How many rooms were not rented? Solve this problem using any strategy you choose.
I can … connect place-value concepts to using the standard algorithm for subtraction

Look Back! How can you use properties to find the number of rooms not rented?

Essential Question
How Can You Subtract Whole Numbers Efficiently?

Visual Learning Bridge
The movie theater already sold 172 seats. How many seats are still available?
Subtract 358 – 172.
Estimate: 400 – 200 = 200

What You Show

What You Write

Convince Me! Use Structure How many times do you need to regroup to subtract 483 – 295? Explain.

Guided Practice

Do You Understand?
Question 1.
To subtract 859 – 583, how do you regroup 8 hundreds 5 tens?
Answer:

Explanation:
The difference of 859 and 583 is 276.
I regrouped 8hundreds 5tens as 7hundreds 15tens.

Question 2.
What do you need to regroup to subtract 753 – 489 using the standard algorithm?
Answer:

Explanation:
The difference of 753 and 489 is 264.
I need to regroup 5tens 3ones and 7hundreds 4tens.

Do You Know How?
In 3-6, subtract. Use an estimate to check that your answer is reasonable.
Question 3.

Answer:
Estimate: 154 — 150, 89 — 90
150-90 = 60

Explanation:
The difference of 154 and 89 is 65.
The difference 65 is reasonable as it is close to the estimated difference 60.

Question 4.

Answer:
Estimate: 592 — 590, 357 — 360
590-360=230

Explanation:
The difference of 592 and 357 is 235.
The difference 235 is reasonable as it is close to the estimated difference 230.

Question 5.

Answer:
Estimate: 915 — 920, 288 — 290
920-290=630

Explanation:
The difference of 915 and 288 is 627.
The difference 627 is reasonable as it is close to the estimated difference 630.

Question 6.

Answer:
Estimate: 743 — 740, 694 — 690
740-690=50

Explanation:
The difference of 743 and 694 is 49.
The difference 49 is reasonable as it is close to the estimated difference 50.

Independent Practice

In 7-18, subtract. Use an estimate to check that your answer is reasonable.
Question 7.

Answer:
Estimate: 289 — 290, 145 — 150
290-150=140

Explanation:
The difference of 289 and 145 is 144.
The difference 144 is reasonable as it is close to the estimated difference 140.

Question 8.

Answer:
Estimate: 326 — 330, 184 — 180
330-180=150

Explanation:
The difference of 326 and 184 is 142.
The difference 142 is reasonable as it is close to the estimated difference 150.

Question 9.

Answer:
Estimate: 736 — 740, 218 — 220
740-220=520

Explanation:
The difference of 736 and 218 is 518.
The difference 518 is reasonable as it is close to the estimated difference 520.

Question 10.

Answer:
Estimate: 525 — 530, 267 — 270
530-270=260

Explanation:
The difference of 525 and 267 is 258.
The difference 258 is reasonable as it is close to the estimated difference 250.

Question 11.

Answer:
Estimate: 683 — 680, 295 — 300
680-300=380

Explanation:
The difference of 683 and 295 is 388.
The difference 388 is reasonable as it is close to the estimated difference 380.

Question 12.

Answer:
Estimate: 847 — 850, 387 — 390
850-390=460

Explanation:
The difference of 847 and 837 is 460.
The difference 460 is reasonable as it is close to the estimated difference 460.

Question 13.

Answer:
Estimate: 475 — 480, 98 — 100
480-100=380

Explanation:
The difference of 475 and 98 is 377.
The difference 377 is reasonable as it is close to the estimated difference 380.

Question 14.

Answer:
Estimate: 826 — 830, 184 — 180
830-180=650

Explanation:
The difference of 826 and 184 is 642.
The difference 642 is reasonable as it is close to the estimated difference 650.

Question 15.

Answer:
Estimate: 936 — 940, 218 — 220
940-220=720

Explanation:
The difference of 936 and 218 is 718.
The difference 718 is reasonable as it is close to the estimated difference 720.

Question 16.
167 – 79
Answer:

Explanation:
The difference of 167 and 79 is 88.

Question 17.
284 – 167
Answer:

Explanation:
The difference of 284 and 167 is 117.

Question 18.
817 – 548
Answer:

Explanation:
The difference of 817 and 548 is 269.

Problem Solving

Question 19.
How much greater is the area of Hernando County than Union County?

Answer:

Explanation:
The difference of 473 and 244 is 229.
Therefore, the area of Hernando County is 229squaremiles than Union County.

Question 20.
Make Sense and Persevere How much greater is the area of Monroe County than the area of Union County and Hernando County combined? Explain.
Answer:
The area of union country and hernando country combines is 719sqmiles


Explanation:
The difference of 983 and 719 is 264.
Therefore, the area of Monroe County is 264sqmiles greater than the area of Union County and Hernando County combined.

Question 21.
Population density is measured in people per square mile. It indicates how crowded an area is. How many more people per square mile does Brevard County have than neighboring Volusia County?
Answer:

Explanation:
The difference of 535 and 449 is 86.
Therefore, Brevard County have 86more people per square mile than neighboring Volusia County .

Question 22.
Higher Order Thinking What mistake did Leon make? What is the correct difference?

Answer:

Explanation:
The difference of 793 and 576 is 217.
The correct difference is 217,The mistake made by leon is he unnecessarily regrouped hundreds.to find the differene of the above numbers their is no need of regrouping hundreds.

Assessment Practice

Question 23.
What is the difference?

A. 1,183
B. 335
C. 266
D. 265
Answer:
D.265.

Explanation:
The difference of 724 and 459 is 265.

Question 24.
What is the missing digit in the subtraction statement?

Answer:

Explanation:
The difference of 634 and 297 is 337.
Therefore, the missing number in the subtraction statement is 9.

Lesson 2.6 Subtract Greater Numbers

Solve & Share
Nevada has a land area of 109,781 square miles. Colorado has a land area of 103,642 square miles. How much larger is Nevada than Colorado? Solve this problem any way you choose.
I can … use the standard algorithm and place value to subtract whole numbers.

Look Back! Estimate the difference in the areas of the two states. Is your answer close to this estimate?

Essential Question
How Do You Subtract Greater Numbers Efficiently?

Visual Learning Bridge
Three of the country’s most scenic national parks are in Alaska. How much larger is the area of Gates of the Arctic than the combined area of Denali and Kenai Fjords?
Find the total area of Denali and Kenai Fjords.

Step 1
Find 34,287 – 21,893.
Subtract the ones. Regroup if necessary

Step 2
Subtract the tens, hundreds, thousands, and ten thousands.
Regroup if necessary

Gates of the Arctic is 12,396 square kilometers larger.

Step 3
Operations that undo each other are inverse operations. Addition and subtraction have an inverse relationship. Add to check your answer.

Convince Me! Critique Reasoning The work shown is NOT correct. What errors were made? Show how to find the correct answer.

Another Example!
Find 38,792. – 33,215.
Estimate:
39,000 – 33,000 = 6,000

Guided Practice

Do You Understand?
Question 1.
In the subtraction problem above, why was the zero in the ten thousands place not written in the answer?
Answer:

Question 2.
The total land area of New Jersey is 19,047 square kilometers. Write and solve an equation to show how to find how much more land area Gates of the Arctic has than New Jersey.
Answer:
34287-19407 sqkm = 14880 sqkm

Explanation:
The Gates of the Arctic has 14880sqkilometers more land area than New Jersey.

Do You Know How?
For 3-6, subtract. Estimate to check whether your answers are reasonable.
Question 3.
139,484 – 116,691
Answer:
Estimate: 140000-120000=20000

Explanation:
The difference of 139484 and 116691 is 22793.
The difference 22793 is reasonable as it is close to the estimate 20000.

Question 4.
2,164 – 1,398
Answer:
Estimate:2200-1400=800

Explanation:
The difference of 2164 and 1398 is 766.
The difference 766 is reasonable as it is close to the estimate 800.

Question 5.
49,735 – 25,276
Answer:
Estimate: 50000-25000=25000

Explanation:
The difference of 49735 and 25276 is 24459.
The difference 24459 is reasonable as it is close to the estimate 25000.

Question 6.
281,311 – 3,427
Answer:
Estimate: 281000-3000=278000

Explanation:
The difference of 281311 and 3427 is 277884.
The difference 277884 is reasonable as it is close to the estimate 280000.

Independent Practice

For 7-14, subtract. Estimate to check if your answers are reasonable.
Question 7.

Answer:
Estimate: 82000-47000=35000

Explanation:
The difference of 82376 and 47294 is 35082.
The difference 35082 is reasonable as it is close to the estimate 35000.

Question 8.

Answer:
Estimate: 654000-562000=92000

Explanation:
The difference of 653642 and 562410 is 91232
The difference 91232 is reasonable as it is close to the estimate 92000.

Question 9.

Answer:
Estimate: 9000-4000=5000

Explanation:
The difference of 9128 and 3753 is 5375
The difference 5375 is reasonable as it is close to the estimate 5000.

Question 10.

Answer:
Estimate: 43000-8000=35000

Explanation:
The difference of 42648 and 8169 is 34479
The difference 34479 is reasonable as it is close to the estimate 35000.

Question 11.

Answer:
Estimate: 426000-87000=339000

Explanation:
The difference of 425637 and 86942 is 338695
The difference 338695 is reasonable as it is close to the estimate 339000.

Question 12.

Answer:
Estimate: 8500-2000=6500

Explanation:
The difference of 8457 and 1946 is 6511
The difference 6511 is reasonable as it is close to the estimate 6500.

Question 13.

Answer:
Estimate: 216000-176000=40000.

Explanation:
The difference of 215714 and 176313 is 39401
The difference 39401 is reasonable as it is close to the estimate 40000.

Question 14.

Answer:
Estimate: 86000-74000=12000

Explanation:
The difference of 85968 and 74084 is 11884
The difference 11884 is reasonable as it is close to the estimate 12000.

Problem Solving

Question 15.
Reasoning A crayon company makes 87,491 blue crayons, 36,262 red crayons, and 25,063 gray crayons. How many more blue crayons are made than red and gray crayons combined?
Answer:
There are 61325 red and gray crayons combined


Explanation:
The difference of 87491 and 61325 is 26166.
Therefore there are 26166 blur crayons are made more than red and grey crayons.

Question 16.
Number Sense Patrick subtracted 4,832 – 2,322 and got 2,510. Is his difference reasonable? Explain.
Answer:
Yes, Patrick’s answer is reasonable.

Explanation:
Estimate: 4800-2300=2500
The difference 2510 is reasonable as it is close to estimate 2500.

Question 17.
Higher Order Thinking Nadia found 9,476 – 8,185 using the algorithm shown. Show how to find 1,784 – 1,339 with Nadia’s algorithm.
9,476 – 8,185 = 1,000 + 300 – 10 + 1
= 1,291
Answer:
1784-1339 = 500-100+40+5

Explanation:
Using Nadia’s algorithm i shown the difference 1784 and 1339 by adding and subtracting numbers.

Question 18.
How many more people attended the street fair in 2019 than in 2017 and 2018 combined?

Answer:
193301 people attended the street fair in 2017 and 2018 combined

Explanation:
The difference of 362839 and 169538 is 169538.
Therefore, 169538 more people attended the street fair in 2019 than in 2017 and 2018 combined.

Question 19.
On Monday, from the peak of Mount Kilimanjaro, a group of mountain climbers descended 3,499 feet. On Tuesday, they descended another 5,262 feet. How many feet did the mountain climbers descend after 2 days? How many more feet do they have to descend to reach the bottom?

Answer:
8761 feet the mountain climbers descend after 2 days

Explanation:
The difference of 19341 and 8761 is 10580.
10580 feet they have to descend to reach the bottom.

Assessment Practice

Question 20.
What is the missing digit in the subtraction statement?

Answer:


Explanation:
The difference of 365928 and 187669 is 178259.
So, the missing digit in the number 178259 in the above question is 8.

Question 21.
What is the difference 62,179 – 31,211?
A. 31,968
B. 30,986
C. 30,968
D. 30,000
Answer:
C.30968

Explanation:
The difference of 62179 and 31211 is 30968.

Lesson 2.7 Subtract Across Zeros

Solve & Share
London, England, is 15,710 kilometers from the South Pole. Tokyo, Japan, is 13,953 kilometers from the South Pole. How much farther is London than Tokyo from the South Pole? Solve this problem any way you choose.
I can … use the standard algorithm to subtract from numbers with zeros.

Look Back! Explain how you decided what operation to use to find how much farther London is than Tokyo from the South Pole.

Essential Question
How Do You Subtract Across Zeros?

Visual Learning Bridge
A music hall is hosting a concert. The hall sells 4,678 tickets to the show. How many tickets are still available?

Regroup.

Subtract.

Since the difference 1,322 is close to the estimate 1,300, the difference is reasonable.
There are still 1,322 tickets available for the concert.

Convince Me! Use Structure How would you regroup if the hall had 5,900 seats?

Guided Practice

Do You Understand?
Question 1.
Leesa used compensation to solve the problem on the previous page. She subtracted (6,000 – 1) – (4,678 – 1) = 5,999 – 4,677 = 1,322. How could you use Leesa’s approach to subtract 5,000 – 1,476?
Answer:
3524

Explanation:
Using Leesa’s approach we can solve 5000-1476 by subrtacting 1 from both the numbers as shown below
=(5000-1)-(1476-1)
=4999-1475
=3524
Therefore, the difference of 5000 and 1476 is 3524.

Question 2.
One passenger flew 11,033 kilometers from Oslo to Lima. Another passenger flew 8,593 kilometers from Oslo to Los Angeles. How many more kilometers was the flight to Lima?
Answer:

Do You Know How?
For 3-8, subtract.
Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.
101,001 – 8,915
Answer:

Question 8.
9,050 – 3,461
Answer:

Independent Practice

For 9-23, subtract.
Estimate to check if your answer is reasonable.
Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Question 14.

Answer:

Question 15.

Answer:

Question 16.

Answer:

Question 17.

Answer:

Question 18.

Answer:

Question 19.

Answer:

Question 20.

Answer:

Question 21.
6,090 – 5,130
Answer:

Question 22.
11,246 – 9,489
Answer:

Question 23.
790,008 – 643,829
Answer:

Problem Solving

Question 24.
Construct Arguments Will the difference between 44,041 and 43,876 be greater or less than 1,000? Explain.
Answer:

Question 25.
Vocabulary Define variable and give an example of how a variable is used in an equation.
Answer:

For 26-27, use the table at the right.

Question 26.
How many more hip-hop than country downloads were sold?
Answer:

Question 27.
Higher Order Thinking How many more hip-hop and Latin downloads were sold than rock and country downloads? Explain.
Answer:

Assessment Practice

Question 28.
Select all the correct differences.
☐ 5,000 – 1,856 = 3,244
☐ 10,700 – 8,243 = 2,457
☐ 64,002 – 43,178 = 20,934
☐ 98,000 – 59,214 = 38,786
☐ 600,482 – 428,531 = 171,951
Answer:

Question 29.
Find the difference.

A. 17,355
B. 20,757
C. 21,757
D. 98,243
Answer:

Lesson 2.8 Problem Solving

Reasoning
Solve & Share
A group of students collected donations for a toy drive. They collected a total of 3,288 toys one week and 1,022 toys the next week. They donated 1,560 toys to the Coal City Charity and the rest were donated to Hartville Charity. How many toys were donated to Hartville Charity? Use reasoning about numbers to show and explain how the two quantities of toys given to charity are related.
I can … make sense of quantities and relationships in problem situations.

Thinking Habits
Be a good thinker! These questions can help you.

• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Look Back! Reasoning Over three weeks, the students collected a total of 8,169 toys. How many toys did they collect in the third week? Complete the bar diagram to show your reasoning. Did the students collect more toys in the third week than in weeks 1 and 2 combined? Explain.

Essential Question
How Can You Use Quantitative Reasoning to Solve Problems?

Visual Learning Bridge
Kara and Carl join their mother on a boat off the coast of the Florida Keys. Their mother is a scientist studying blue marlins. Each child gets to help weigh two marlins. How much more did Kara’s marlins weigh than Carl’s?

How can you draw a diagram to help reason how the numbers in the problem are related?
I can represent the relationship between the numbers with a bar diagram.

How can I use reasoning to solve this problem?
I can

• identify the quantities I know.
• draw diagrams and write equations to show relationships.
• connect the solution back to the real world problem.

Here’s my thinking.
K = the total weight of Kara’s marlins, and C = the total weight of Carl’s marlins.

Kara’s marlins weighed 299 pounds more than Carl’s.

Convince Me! Reasoning Write a problem that can be solved using the bar diagram below. Write an equation to solve. Use reasoning to think about the meaning of each number before starting.

Guided Practice

Reasoning
A manufacturer shipped 12,875 fidget spinners one week and 9,843 of them were sold. The next week, they shipped 19,175 and 12,752 of them were sold. How many fidget spinners had not sold yet?

Question 1.
What quantities are given in the problem, and what do the numbers mean?
Answer:

Question 2.
Use the bar diagrams that show the relationships of the numbers in the problem. Write and solve equations which could be used to find f, the spinners not sold the first week; s, the spinners not sold the second week; and t, the total spinners not sold.
Answer:

Independent Practice

Reasoning A wall is being built with 16,351 stones. The builders have placed 8,361 stones, and they have 7,944 stones left. Do they have enough stones? How many more stones do they need?

Use Exercises 3-5 to answer the question.
Question 3.
What quantities are given in the problem, and what do the numbers mean?
Answer:

Question 4.
Complete the bar diagram to show how to find s, the number of stones the builders have in all. Then, write and solve an equation. Do they have enough? Explain.
Answer:

Question 5.
Complete the bar diagram to show how to find the difference, d, of how many more stones the builders need. Then, write and solve an equation.

Answer:

Problem Solving

Performance Task
Bird Migration Ornithology is the scientific study of birds. Every year, some birds travel great distances, or migrate, to find food and start families. The table shows the distances five species of birds flew over one year, as observed by an ornithologist. How much farther did the Arctic Tern fly than the Pectoral Short-Tailed Shearwater and the Pied Wheatear combined?

Question 6.
Reasoning What quantities are given in the problem and what do the numbers mean?
Answer:

Question 7.
Make Sense and Persevere What strategy can you use to solve the problem?
Answer:

Question 8.
Make Sense and Persevere What is the hidden question?
The hidden questions are the questions which must be answered before answering the main question asked in the problem.
Answer:

Question 9.
Model with Math Complete the bar diagrams to show how to find the answer to the hidden question and the main question. Write and solve equations.

Answer:

Topic 2 Fluency Practice Activity

Follow the Path
Shade a path from START to FINISH. Follow the sums that are correct. You can only move up, down, right, or left.
I can.. add multi-digit whole numbers.

Topic 2 Vocabulary Review

Understand Vocabulary
Word List

• add on
• algorithm
• Associative Property of Addition
• Commutative Property of Addition
• compensation
• Identity Property of Addition
• inverse operations
• variable

Question 1.
Circle the property of addition shown by 126 + 0 = 126.
Associative
Commutative
Identity
Answer:

Question 2.
Circle the property of addition shown by 21 + 34 = 34 + 21.
Associative
Commutative
Identity
Answer:

Question 3.
Circle the property of addition shown by (1 + 3) + 7 = 1 + (3 + 7).
Associative
Commutative
Identity
Answer:

Question 4.
Draw a line from each term to its example.

Answer:

Use Vocabulary in Writing
Question 5.
Rob found 103 + 1,875 = x using mental math. Use at least 3 terms from the Word List to describe how Rob could find the sum.
Answer:

Topic 2 Reteaching

Set A pages 37-40

Find 3,371 + 2,429. Use mental math.
Make Ten
3,371 + 2,429 = 3,371 + (29 + 2,400)
= (3,371 +29) + 2,400
= 3,400 + 2,400 = 5,800
S0, 3,371 + 2,429 = 5,800.

Remember to adjust the sum or difference when you use the compensation strategy.
Question 1.
4,153 + 2,988
Answer:

Question 2.
92,425 + 31,675
Answer:

Question 3.
5,342 + 1,999
Answer:

Question 4.
22,283 – 14,169
Answer:

Question 5.
47,676 – 16,521
Answer:

Question 6.
1,089 – 961
Answer:

Set B pages 41-44

Estimate the sum by rounding each number to the nearest ten thousand.

241,485 rounds to 240,000.
429,693 rounds to 430,000.

Remember that you can round numbers to any place when estimating sums and differences.

Estimate each sum or difference.
Question 1.
652,198 + 49,753
Answer:

Question 2.
8,352 – 3,421
Answer:

Question 3.
17,586 – 9,483
Answer:

Question 4.
823,725 + 44,851
Answer:

Question 5.
1,440 – 933
Answer:

Question 6.
55,748 – 28,392
Answer:

Question 7.
4,981 + 6,193
Answer:

Question 8.
995,275 + 4,921
Answer:

Set C pages 45-52

Find 72,438 + 6,854.

The answer 79,292 is close to the estimate of 79,000, so the answer is reasonable.

Remember to regroup if necessary when adding whole numbers.
Question 1.

Answer:

Question 2.

Answer:

Question 3.
215 + 8,823
Answer:

Question 4.
142,968 + 44,456
Answer:

Question 5.
2,417 + 3,573
Answer:

Question 6.
572,941 + 181,662
Answer:

Set D pages 53-60

Find 52,839 – 38,796.
Estimate: 53,000 – 39,000 = 14,000

The answer is reasonable.

Remember that you may need to regroup to subtract.

Question 1.

Answer:

Question 2.

Answer:

Question 3.
41,542 – 32,411
Answer:

Question 4.
4,978 – 2,766
Answer:

Question 5.
735,184 – 255,863
Answer:

Question 6.
44,558 – 22,613
Answer:

Set E pages 61-64

Find 60,904 – 54,832.
Estimate: 61,000 – 55,000 = 6,000

The answer is reasonable.

Remember you may need to regroup more than one place at a time to subtract across zeros.
Question 1.

Answer:

Question 2.

Answer:

Question 3.
70,000 – 25,228
Answer:

Question 4.
560,043 – 312,562
Answer:

Question 5.
8,052 – 1,205
Answer:

Question 6.
20,008 – 16,074
Answer:

Set F pages 65-68

Think about these questions to help you reason abstractly and quantitatively.
Thinking Habits

• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?
  

Remember that you can draw a bar diagram and use it to reason about a problem.

Raahil traveled 11,469 kilometers from home to visit his mother’s family in Qatar. He then traveled 12,332 kilometers from Qatar to visit his father’s family in Brisbane, Australia.
Question 1.
Draw a bar diagram that shows the distance Raahil traveled to Brisbane.
Answer:

Question 2.
Write and solve an equation for your bar diagram.
Answer:

Topic 2 Assessment Practice

Question 1.
The table shows the number of hot dogs Frank’s hot dog stand sold this weekend.

A. Estimate the number of hot dogs sold by rounding each number in the table to the nearest thousand and finding the sum.
Answer:

B. Write and solve an equation to find how many hot dogs were sold.
Answer:

Question 2.
Find 8,000 – 6,280.
Answer:

Question 3.
Enter the missing digit to complete the subtraction.

Answer:

Question 4.
Find the difference.

A. 6,811
B. 6,351
C. 6,333
D. 6,331
Answer:

Question 5.
Complete the equation to make it true. Write your answer in the box.
12,769 + 16,065 = _________ + 15,402
Answer:

Question 6.
Find the difference. Then use addition to check your work.

Answer:

Question 7.
Which of the following statements is true? Select all that apply.
☐ 12,395 + 14,609 = 27,004
☐ 76,237 – 4,657 = 42,430
☐ 67,407 – 38,227 = 29,180
☐ 69,844 + 1,014 = 70,452
☐ 34,980 – 1,999 = 32,981
Answer:

Question 8.
Find the sum.

Answer:

Question 9.
Sandra used addition properties to rewrite the equation below. Select all the equations Sandra might have written.
1,450 + 1,125 + 1,050 = n
☐ (1,400 + 1,100 + 1,000) + (50 + 25 + 50) = n
☐ 1,450 + 1,050 = n 1,125 + 1,050 + 1,450 = n
☐ 1,000 + 1,000 + 1,000 + 450 + 50 + 125 = 1
☐ (1,450 + 1,050) + 1,125 = n
Answer:

Question 10.
Joe and Sara recorded the number of birds they saw in the park over two summers.

A. Write and solve equations to find how many more total birds Joe and Sara saw this year than last year.
Answer:

B. Estimate how many more birds were seen in the park this year than last year by rounding each number in the table and solving the problem. Use the estimate to check if your answer to Part A is reasonable.
Answer:

Topic 2 Performance Task

Taking Inventory Jiao runs a wholesale art supply website. She fills bulk orders for craft and hobby stores.
Question 1.
Use the Wooden Beads table to answer the questions.
Part A
Crafts and Stuff ordered oak and ebony beads. Explain how to use mental math and properties of addition to find how many beads Jiao sent.

Answer:

Part B
Jiao sends an order of oak and bayong beads to Jill’s Crafts and an order of ash and ebony beads to Create. How much larger is the order for Create? Write and solve equations to find j, the number of beads in the order to Jill’s Crafts; c, the number of beads in the order to Create; and d, the difference.
Answer:

Question 2.
Use the Glass Beads table to answer the questions.
Part A
Write and solve an equation to show how many glass beads, b, Create will have if they order the bubble and smoky beads.

Answer:

Part B
Jiao sends the molded and stained beads to Hometown Craft Supply. Explain how to use compensation to find how many more molded beads than stained beads were sent.
Answer:

Question 3.
Use the Metal Beads table to answer the questions.
Part A
Write and solve an equation to show how many more beads, b, are in an order of gold beads than in an order of platinum beads.

Answer:

Part B
Craftology orders the brass and copper beads. After they arrive, the store sells 29,735 of them. How many beads does Craftology have left from their order? Show your computations.
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 20 Reteaching

Reteaching

Set A, pages 452-453

Construct an angle congruent to angle A.
Answer:
Draw a ray with endpoint E.
With point A as center, use your compass to draw an arc that intersects both sides of angle A. Label the points of intersection R and S. With the same compass setting, use point E as center and draw an arc that intersects the ray at point D.

Open the compass to length RS. Then, with point D as center, draw an intersecting arc.
Label the intersection F. Use a straightedge to draw ray EF.

Angle E is congruent to angle A.

Remember that a construction uses only a compass and a straightedge.

Construct an angle congruent to the given angle.
Question 1.

Answer:

Question 2.

Answer:

Set B, pages 454-456

Construct a line perpendicular to another line.
Answer:

1. Draw line AB.
2. With A as center, draw two arcs that intersect line AB. Label the points of intersection D and E.
3. Open the compass wider.
4. Using D and E as centers, draw arcs that intersect. Label the intersection C.
5. Draw Line CA.
6. Line CA is perpendicular to line AB.
   

Remember to keep the compass open to the same setting when drawing the arcs with D and E as the centers.
Question 1.
Construct a line perpendicular to another line.
Answer:

Question 2.
For the construction started below, what is the next step to construct a line perpendicular to line XY?

Answer:

Set C, pages 458-460

Construct a triangle congruent to triangle DEF.

Answer:

1. Draw a ray with endpoint G.
2. Construct angle G.
3. Congruent to angle D.
4. Construct segments GK and GL on the sides of angle G so that they are congruent to segments DE and DF.
5. Draw segment KL.
6. Triangle GKL is congruent to triangle DEF.

Construct a rectangle ABCD.
Answer:

1. Draw line AB.
2. Construct line DA perpendicular to line AB at A.
3. Construct line DC perpendicular to line DA at D.
4. Construct line CB perpendicular to line AB at B.
5. Lines DC and CB intersect at C.
   

Remember to use the compass to measure the length of the original line segments by placing the point on one endpoint and the slider on the other endpoint.
Question 1.
Construct a triangle congruent to triangle XYZ.

Answer:

Question 2.
Construct a rectangle KLMN.
Answer:

Set D, pages 462-463

When you use objects to solve problems, follow these steps.
Step 1: Choose objects that can best model what is described in the problem.
Step 2: Use the objects to make a model of what you know.
Step 3: Use the objects to act out the action in the problem. Look for patterns.
Step 4: Find the answer in your model.

Remember to state clearly at the beginning what your objects represent in the problem.
Question 1.
How many total bricks are needed if the pattern extends to 4 bricks in the middle row?

Answer:

Envision Math 5th Grade Textbook Answer Key Topic 20 Test Prep

Test Prep

Question 1.
Teresa is constructing ∠ C congruent to ∠A for her drafting class. What is the next step that Teresa should take to complete the construction? (20-1)

A. Measure the opening of arc LM with a compass.
B. Measure the opening of arc LM with a protractor.
C. Draw an arc with center at point C using the same compass setting used to draw arc LM.
D. Draw another arc that intersects arc LM.
Answer:

Question 2.
Mrs. Bradley is an architect who needs to construct \(\overline{S T}\) congruent to \(\overline{L M}\) . She has drawn a ray with endpoint S as shown. What is the next step she should take? (20-2)

A. Draw an arc above \(\overline{L M}\).
B. Draw an arc above and below \(\overline{L M}\).
C. Draw an arc on \(\overline{L M}\).
D. With point L as the center, open the compass so it lines up with point M.
Answer:

Question 3.
What is the next step in constructing a line parallel to \(\overleftrightarrow{A B}\)? (20-2)

A. Draw segment BC.
B. Construct a line perpendicular to line AC.
C. Construct a line segment congruent to line segment AB.
D. Draw a line through point G.
Answer:

Question 4.
Angelo is constructing LMN so that it is congruent to ABC. He has constructed ∠M congruenS to ∠B and \(\overline{M L}\) congruent to segment \(\overline{B A}\).
What is the next step? (20-3)

A. Measure the length of \(\overline{B A}\) with his compass.
B. Measure the length of \(\overline{B A}\) with his protractor.
C. Construct \(\overline{M N}\) congruent to \(\overline{B C}\).
D. Connect point L with \(\overrightarrow{M N}\).
Answer:

Question 5.
What is missing from the construction of a line perpendicular to \(\overleftrightarrow{D E}\)? (20-2)

A. Arc above \(\overleftrightarrow{D E}\) with center at point E.
B. Arc above \(\overleftrightarrow{D E}\) with center at point D.
C. Arc above \(\overleftrightarrow{D E}\) with center at point Y.
D. A line parallel to \(\overleftrightarrow{D E}\).

Question 6.
The first step in constructing a rectangle ABCD is to draw line AB. Which of the following choices could be the next step? (20-3)
A. Construct two lines that are parallel.
B. Construct a line segment that is congruent to segment \(\overleftrightarrow{A B}\).
C. Construct two angles that are congruent.
D. Construct a line perpendicular to AB at point A.
Answer:

Question 7.
Suppose each of the 6 squares in a hexamino represents a table which can seat one person on a side. Which arrangement of 6 tables can seat exactly 12 people? (20-4)

Answer:

Question 8.
What two tools are used to construct geometric figures? (20-1)
A. ruler and straightedge
B. straightedge and compass
C. ruler and protractor
D. compass and protractor
Answer:

Question 9.
Aidan is a graphic designer and needs to construct AS congruent to AT for one of his projects. What is the first step in the construction? (20-1)
A. Draw a ray with endpoint S.
B. Draw a ray with endpoint T.
C. Draw an arc with endpoint S.
D. Draw an arc with endpoint T.
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 20.4 Problem Solving

Problem Solving

Use Objects
Answer:
A pentomino is an arrangement of 5 identical squares in a plane. The squares must be attached to one another edge to edge.

Question.
Using 5 identical square tiles, how can you build 3 more pentominoes that have 3 squares in a row?
Answer:

Guided Practice

Do you know HOW?
Question 1.
Is the following a pentomino? Explain.

Answer:

Question 2.
Are these two pentominoes the same or different? Explain.

Answer:

Do you UNDERSTAND?
Question 3.
In the example above, how many more pentominoes can you find with 3 in a row?
Answer:

Question 4.
Write a Problem Write a real-world problem that can be solved by using objects.
Answer:

Independent Practice
In 5 and 6, tell whether the pentominoes in each pair are related by a reflection or a rotation.
Question 5.

Answer:

Question 6.

Answer:

In 7 and 8, use objects to help you solve the problem.
Question 7.
How many pentominoes can you build with 5 in a row?
Answer:

Question 8.
How many pentominoes can you build with 4 in a row?
Answer:

Read and Understand
What am I asked to find?
Three more unique pentominoes that have 3 squares in a row
Two pentominoes are the same if they can be matched together by rotating or reflecting.

Plan and Solve
I can use objects to build 3 more pentominoes with 3 in a row.

Here are 3 possible solutions.

Look Back and Check
All are attached edge to edge.
All can be rotated and reflected. None are repeated.
The 3 pentominoes I’ve made are all unique.

Question 9.
Suppose each square in a pentomino is a table that seats one person on a side. Find a table arrangement (a pentomino) that can seat 12 people.

Answer:

Question 10.
The figure below can be folded to form a box. After it is folded, which face will be parallel to Face ABDC?

Answer:

Question 11.
Maureen is buying a game that is priced at $15. She has a coupon worth $2.50 off the regular price. After Maureen gives the clerk a $20 bill, how much change does she receive?
Answer:

Question 12.
James and Kurt were paid $176 for landscaping a yard. James worked 9 hours and Kurt worked 13 hours. How much is Kurt’s fair share of the earnings? James’s share?
Answer:

Question 13.
Use objects to build pentominoes with 2 squares in a row. How many of these kinds of pentominoes can be built?
Answer:

Question 14.
Make an organized list. How many different combinations of coins can make $0.42 if one of the coins is a quarter? One possible combination: 1 quarter, 17 pennies.
Answer:

Question 15.
At the concert, Mischa, Jordan, and Elijah are sitting together in a row. Make a list of the possible orders the three could be sitting.
Answer:

Question 16.
Estimation
A great white shark can weigh 4,400 lbs. A dolphin can weigh 440 lbs. About how many times as heavy is the shark as the dolphin?
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 20.3 Constructing Shapes

Constructing Shapes

How can you construct congruent triangles?
Answer:
Triangles are rigid figures which makes them useful in constructing buildings.

Question.
Construct a triangle that is congruent to triangle XYZ.

Answer:

Another Example
How can you construct a rectangle?
A rectangle has four right angles and opposite sides that are parallel and congruent. Construct a rectangle ABCD
Step 1
Draw a line AB. Construct a line perpendicular to line AB at point A. Choose a point D on the line.

Step 2
Construct a line perpendicular to line AB at point B.

Step 3
Construct a line perpendicular to line AD at point D

Step 4
The point where the perpendicular lines you constructed in Steps 2 and 3 intersect is point C.

Explain It
Question 1.
What are the the four right angles in ABCD?
Answer:

Question 2.
Name the two pairs of parallel and congruent sides in ABCD
Answer:

Step 1
Construct ∠P congruent to ∠X.

Step 2
On one side of ∠P, construct \(\overline{P Q}\) ≅ \(\overline{X Y}\). On the other side of ∠P, construct \(\overline{P R}\) ≅ \(\overline{X Z}\)

Step 3
Draw segment QR. ∆PQR ≅ ∆XYZ

Guided Practice

Do you know HOW?
Question 1.
Copy the following triangle on another sheet of paper. Then construct a triangle.

Answer:

Question 2.
Construct a rectangle using a compass and straightedge.
Answer:

Do you UNDERSTAND?
Question 3.
When you construct a rectangle, what is the measure of each angle?
Answer:

Question 4.
How can you be sure that a triangle you construct is congruent to the original triangle?
Answer:

Independent Practice

Copy each triangle on another sheet of paper. Then construct a triangle congruent to it.
Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.
Copy the following line on another sheet of paper. Use it to construct a rectangle.

Answer:

Question 9.
Ellen studied math for 1\(\frac{1}{2}\) hours, science for \(\frac{3}{4}\) hour, and history for \(\frac{3}{4}\) hour. How many hours did she study in all?
Answer:

Question 10.
Alan bought 2 packages of tennis balls for $7.98 each. How much change will Alan get from $20?
Answer:

Question 11.
Geometry What is the measure of the third angle in the triangle?

Answer:

Question 12.
Algebra Yasmin is 6 inches taller than Burt. If b represents Burt’s height, which expression represents Yasmin’s height?
A. b + 6
B. b × 6
C. b – 6
D. b ÷ 6
Answer:

Question 13.
Reasoning Terry is arranging furniture and wants to center her 6.5-foot table against a wall that measures 15 feet. How far will the table be from each end of the wall? You can draw a picture to help you.
Answer:

Question 14.
Squares for a quilt are being cut from a piece of material that is 15 inches wide and 20 inches long. The squares are 4 inches on each side. How many whole squares can be cut from the material? Draw a picture to help you.
Answer:

Question 15.
Mr. Smith is redecorating his dining room. Tell if he needs to find the perimeter or area for each the following.
a. the amount of wallpaper border to go around the top of the room
b. the amount of carpeting needed to cover the floor
Answer:

Question 16.
Writing to Explain How can you construct a triangle that is congruent to triangle EFG formed by the roofline of the house?

Answer:

Question 17.
Let x represent the number of miles Gina ran. Paul ran 3 more than \(\frac{1}{2}\) many miles as Gina. Which expression represents the distance Paul ran?
A. \(\frac{1}{2}\)(x + 3)
B. \(\frac{1}{2}\)x + 3
C. 3x + \(\frac{1}{2}\)
D. 2(x + 3)
Answer:

Mixed Problem Solving

Question 1.
How many Kemp’s Ridley sea turtle nests were found in 2002?
Answer:

Question 2.
How many more Kemp’s Ridley nests were found in 2004 than in 2001?
Answer:

Question 3.
Is there a trend in the data for Kemp’s Ridley sea turtle nests? Explain.
Answer:

Question 4.
Between which two years did the number of Kemp’s Ridley nests increase the most?
Answer:

Question 5.
On a picture graph that shows the number of participants in rubber duck derbies, one picture equals one thousand participants. How many participants are represented by 3.5 pictures?
Answer:

Question 6.
Strategy Focus Solve using the strategy Use Reasoning. Greg, Rick, and Tom like either math, science, or art best. Tom dislikes art. Rick is not the student who likes art or math best. Which student likes each subject best?
Answer:

Question 7.
What was the high temperature on August 4?
Answer:

Question 8.
On which date was the high temperature the lowest?
Answer:

Question 9.
What was the difference between the greatest and least high temperatures for the week?
Answer:

Question 10.
A scientist is studying the types and number of plants in a small area. What kind of graph should the scientist use to present his data?
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 20.2 Constructing Lines

Constructing Lines
How can you construct perpendicular and parallel lines?
Answer:
The rails of the track are parallel. The ties are perpendicular to the rails.

Construct a line perpendicular to \(\overleftrightarrow{L N}\) and a line parallel to \(\overleftrightarrow{L N}\).

Answer:

Another Example
How do you construct a line segment congruent to a given line segment?
Without measuring with a ruler, draw \(\overleftrightarrow{J K}\) congruent to \(\overleftrightarrow{S T}\).

Step 1: Draw a ray. Label the endpoint J.

Step 2 : On \(\overleftrightarrow{S T}\), with point S as the center, open the compass so that it lines
up with point T.
Then place the compass on the ray with point J as the center.
Without changing the compass setting, draw an arc that intersects the ray. Label the point of intersection K. \(\overleftrightarrow{J K}\) is congruent to \(\overleftrightarrow{S T}\).

Explain it
Question 1.
How is constructing a figure different from drawing a figure?
Answer:

Question 2.
In Step 2, could the ray be any length?
Answer:

Question 3.
Does a line segment need to be horizontal in order to construct another segment congruent to it?
Answer:

Draw a line with points L and N. With L as center, draw two arcs that intersect \(\overleftrightarrow{L N}\). Label the points W and X.

Set the compass wider. Using W and X as centers, draw arcs that intersect. Label the point Y. Draw \(\overleftrightarrow{L Y}\)

Repeat Steps 1 and 2 at Y to find point Z.

\(\overleftrightarrow{L Y}\) ⊥ \(\overleftrightarrow{L N}\) and \(\overleftrightarrow{L N}\) || \(\overleftrightarrow{Y Z}\)

Guided Practice

Do you know HOW?
Question 1.
Draw a line perpendicular to line CD. Copy \(\overleftrightarrow{C D}\) on a separate sheet of paper and construct \(\overleftrightarrow{T C}\) so that it is perpendicular to \(\overleftrightarrow{C D}\).

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Question 2.
Draw as egment congruent to \(\overline{E F}\). Copy \(\overline{E F}\) on a separate sheet of paper. Then draw a ray labele d \(\overleftrightarrow{M N}\). On that ray, construct \(\overline{M P}\) so that \(\overline{M P}\) is congruent to \(\overline{E F}\).

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Do you UNDERSTAND?
Question 3.
Writing to Explain In Step 2 of the example above, why is it necessary to set the compass wider than the length of segment WL?
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Question 4.
Look at the line TC you constructed in Problem 1 that is perpendicular to line CD. Use point Tand construct a line perpendicular to line TC. How is that line related to line CD?
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Independent Practice

In 5 through 7, copy the figures on a separate sheet of paper and follow the directions.
Question 5.
Construct a line perpendicular to line XY.

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Question 6.
Construct a line perpendicular to line MN. Then construct a line through it that is parallel to line MN.

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Question 7.
Draw a line segment that is congruent to CD .

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Problem Solving

Engineers are making plans to lay new railroad tracks between cities. In 8 and 9, use the information in the table.

Question 8.
If it costs $155 per mile to construct railroad tracks, how much would it cost to build tracks from San Francisco to Los Angeles?
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Question 9.
Estimation Railroad ties are set about 2 feet apart. About how many railroad ties are there between Eureka and Sacramento?
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Question 10.
If you are comparing two negative integers on a number line, how can you tell which one is greater?
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Question 11.
Four friends played golf. Their scores were +3, -1, *4, and ~4 in relation to par. The least score wins. Arrange the scores from best to worst.
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Question 12.
Algebra Ted has 15 trophies. This is 5 times as many as Harold has. How many trophies does Harold have? Write and solve an equation to answer the question.
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Question 13.
Writing to Explain Explain how perpendicular lines are similar to intersecting lines.
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Question 14.
Use the figure to tell whether the statements are true or false

a. \(\overline{P Q}\) is parallel to \(\overline{U V}\)
b. \(\overline{P Q}\) intersects \(\overline{U V}\)
c. \(\overline{P Q}\) is perpendicular to \(\overline{U V}\)
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Question 15.
Estimation The gas tank in Shondra’s car can hold 18 gallons. Her car gets about 22 miles per gallon of gas. On a recent trip, Shondra used about 12 gallons of gas. Which is the best estimate of the distance Shondra drove?
A. 120 miles
B. 200 miles
C. 400 miles
D. 1,200 miles
Answer:

Stop and Practice

Find each difference. Simplify if possible.
Question 1.

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Question 2.

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Find each difference. Simplify if possible.
Question 9.

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Question 11.

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Question 12.

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Question 18.

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Error Search Find each answer that is not correct. Write it correctly and explain the error.
Question 19.

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Question 21.

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Question 23.

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Number Sense
Estimating and Reasoning Write whether each statement is true or false. Explain your reasoning.
Question 24.
The quotient of 1,546 ÷ 5 is less than 300.
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Question 25.
The product of 9.32 and 4.7 is less than 36.
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Question 26.
The difference of 6,631 and 3,021 is greater than 2,000 and less than 4,000.
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Question 27.
The sum of 43.04 + 21.56 is 0.04 more than 64.56.
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Question 28.
When x = -9, the expression x + +5 equals -14.
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Question 29.
The expression (4\(\frac{5}{6}\) + 3\(\frac{1}{2}\) – × \(\frac{3}{4}\)) × 0 equals 0.
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Envision Math 5th Grade Textbook Answer Key Topic 20.1 Constructing Angles

Review What You Know

Vocabulary
Choose the best term from the box.

Question 1.
A ? extends in two directions infinitely.
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Question 2.
A ? has one endpoint and extends in one direction, while a ? has two endpoints.
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Question 3.
? lines intersect at one point and create four right angles.
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Identifying Angles
Classify each angle as acute, obtuse, straight or right.
Question 4.

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Question 5.

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Question 6.

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Question 7.

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Patterns
Find the next two numbers in each pattern.
Question 8.
1.5, 1.7, 1.9, 2.1,2.3, ☐, ☐
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Question 9.
26, 21,16, 11, ☐, ☐
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Shapes
Writing to Explain Write an answer for each question.
Question 10.
Can a triangle have two obtuse angles?
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Question 11.
Is a square always a rectangle?
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Constructing Angles

How can you construct an angle congruent to another angle?
Answer:
A geometric construction is the drawing of a figure using only a compass and a straightedge. A ruler and a protractor are not used in making a construction.

Question.
How would you construct ∠B congruent to ∠M?

Answer:

Guided Practice

Do you know HOW?
In 1 and 2, trace each angle on a sheet of paper. Then construct an angle congruent to each given angle.
Question 1.

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Question 2.

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Do you UNDERSTAND?
Question 3.
Writing to Explain Why is it important to keep the same compass setting in Step 1?
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Question 4.
How can you tell if a constructed angle is congruent to the original angle?
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Independent Practice

In 5 through 7, trace each angle on a sheet of paper. Then construct an angle congruent to each given angle
Question 5.

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Question 6.

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Question 7.

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Problem Solving
Question 8.
The Leaning Tower of Pisa is located in Italy. It leans to the south at the angle shown in the picture below. Construct an angle congruent to ∠A.

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Question 9.
Mario has saved a number of quarters, nickels, dimes, and pennies. He will use $3.93 to buy a new toy for his dog. Using the fewest coins, what combination of coins will equal $3.93?
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Question 10.
Justin climbed 15 steps to the second floor of a building. Each step is 8 inches high. How many feet higher is the second floor than the first?
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Question 11.
Diamond cutters must cut angles precisely so that the greatest amount of light is reflected from the facets. Refer to the photo of the diamond below. Construct an angle congruent to ∠W.

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Question 12.
The high temperatures in a city for 7 days were 87°, 87°, 90°, 90°, 90°, 92°, and 87°. What was the mean temperature for the 7 days?
A. 87°
B. 89°
C. 90°
D. 91°
Answer: