Category: Envision Math

Envision Math 6th Grade Textbook Answer Key Topic 2.4 The Distributive Property

The Distributive Property

How can you use the Distributive Property to evaluate expressions?
Answer:
The Distributive Property states that multiplying a sum (or difference) by a number gives the same result as multiplying each number in the sum
(or difference) by the number and adding (or subtracting) the products.

Guided Practice

Do you know HOW?
In 1 through 4, find each missing number.
Question 1.
8(7 + 23) = 8(7) + 8(☐)
Answer:
23
Explanation:

Question 2.
4(28) = 4(20) + 4 (☐)
Answer:
8
Explanation:

Question 3.
8(57) – 8(7) = 8(☐)
Answer:
50
Explanation:

Question 4.
5(26 – 3) = 5 (☐) – 5(3)
Answer:
26
Explanation:

Use mental math to evaluate 5 and 6.
Question 5.
6(32) = ☐
Answer:
192
Explanation:

Question 6.
20(5) – 20(2) = ☐
Answer:
60
Explanation:

Do you UNDERSTAND?
Question 7.
Why is it easier to evaluate 7 × 60 than to evaluate 7 × 55 + 7 × 5?
Answer:
See margin.
Explanation:

Question 8.
Tony read 22 pages in the morning and 28 pages in the afternoon for 5 days. Lois read 47 pages each day for 5 days. Explain howto use the Distributive Property to find how many pages each of them read.
Answer:
See margin.
Explanation:

Independent Practice

Leveled Practice In 9 through 16, find each missing number.
Question 9.
3(28) + (3)2 = ☐ (30)
Answer:
3
Explanation:

Question 10.
9(23) = 9(☐) + 9(3)
Answer:
20
Explanation:

Question 11.
6(46) – 6(6) = 6(☐)
Answer:
40
Explanation:

Question 12.
4(33) = 4(30) + 4(☐)
Answer:
3
Explanation:

Question 13.
30(22 – 10) = 30(22) – 30(☐)
Answer:
10
Explanation:

Question 14.
8(99) = 8(100) – 8(☐)
Answer:
1
Explanation:

Question 15.
20(33 – 5) = 20(☐)
Answer:
28
Explanation:

= 20(☐) + 20(8)
Answer:
20
Explanation:

Question 16.
5(42) + 5(5) = 5(☐)
Answer:
47
Explanation:

= 5(☐) + 5(7)
Answer:
40
Explanation:

Use the Distributive Property to break apart a number to find the product for 5 × 27.
5 × 27 ← Break 27 apart.

5(20) +5 (7) ← Multiply each addend.
100 + 35 ← Add.
135
5 × 27 = 135

Use the Distributive Property to join numbers together to find 8(32) – 8(2).
8(32) – 8(2)
8(32 — 2) ← Join factors.
8(30) ← Subtract.
240 ← Multiply.
8(32) – 8(2) = 240

Independent Practice

Use the Distributive Property and mental math to evaluate.
Tips: When doing mental math, choose to join or break apart based on which is easier.
Question 17.
7(29)
Answer:
203
Explanation:

Question 18.
6(21) + 6(31)
Answer:
312
Explanation:

Question 19.
5(22) + 5(8)
Answer:
150
Explanation:

Question 20.
8(47)
Answer:
376
Explanation:

Question 21.
6(41) + 6(9)
Answer:
300
Explanation:

Question 22.
30(3) + 30(5)
Answer:
240
Explanation:

Question 23.
3(21) – 3(11)
Answer:
30
Explanation:

Question 24.
5(25 – 3)
Answer:
110
Explanation:

Problem Solving

Question 25.
Writing to Explain The 6th graders ordered lunch from the Big Group Menu.They ordered 22 organic chilis and 8 veggie plates.Their order can be expressed as 6(22) + 6(8). Explain what mental math steps you would use to find the total cost of the order.

Answer:
See margin.

Question 26.
Using the Big Group Menu, write and solve a problem where you can use the Distributive Property.
Answer:
See margin.

Question 27.
Writing to Explain Jamal said that 9.45 is greater than 9.8 because 45 is greater than 8. Is he correct? Explain.
Answer:
No; sample answer: 0.8 = 0.80 and 80 > 45.
Explanation:

Question 28.
Hiroko put money in a savings account each week. After 9 weeks, there was $49.50 in the account. If Hiroko put the same amount in each week, how much did she save each week?

Answer:
$5.50
Explanation:

Question 29.
Think About the Process Which choice shows a problem with common factors that could be used for mental math?
A. 3(45) + 3(5)
B. 4(18) – 7(8)
C. 2(22) + 3(33)
D. 8(39) + 4(40)
Answer:
A. 3(45) + 3(5)

Envision Math 6th Grade Textbook Answer Key Topic 1 Test Prep

Test Prep

Question 1.
The table gives the number of members in some Native American tribes. Which lists the tribes from the least to the greatest membership? (1-2)

A. Ute, Ottawa, Yakama, Crow
B. Ottawa, Ute, Yakama, Crow
C. Yakama, Ottawa, Ute, Crow
D. Ute, Crow, Ottawa, Yakama
Answer:
A. Ute, Ottawa, Yakama, Crow
Explanation:

Question 2.
What is the value of the 7 in the number 3.0871? (1-4)
A. seven ten-thousandths
B. seven thousandths
C. seven hundredths
D. seven thousands
Answer:
B. seven thousandths
Explanation:

Question 3.
In the fall of 2004, the University of California had an undergraduate enrollment of 158,431 students. Which of the following is this number written in expanded form? (1-3)
A. (1 × 10⁶) + (5 × 10⁵) + (8 × 10⁴) + (4 × 10³) + (3 × 10²) + (1 × 10¹)
B. (1× 10⁴) + (5 × 10³) + (8 × 10²) + (4 × 10¹) + (3 × 10⁰) + 1
C. (1 × 10⁵) + (5 × 10⁴) + (8 × 10³) + (4 × 10²) + (3 × 10¹) + (1 × 10⁰)
D. (1 × 10⁶) + (5 × 10⁵) + (8 × 10³) + (4 × 10²) + (31 × 10¹)
Answer:
C. (1 × 10⁵) + (5 × 10⁴) + (8 × 10³) + (4 × 10²) + (3 × 10¹) + (1 × 10⁰)
Explanation:

Question 4.
What is the value of the 6 in 196,937,500? (1-1)
A. 6 billion
B. 6 million
C. 6 hundred million
D. 6 hundred thousand
Answer:
B. 6 million
Explanation:

Question 5.
Which of the following is equal to 5⁴? (1-3)
A. 4 × 4 × 4 × 4 × 4
B. 5 × 4
C. (4 × 5)4
D. 5 × 5 × 5 × 5
Answer:
D. 5 × 5 × 5 × 5
Explanation:

Question 6.
Which of the following is between 0.007 and 0.016? (1-5)
A. 0.0008
B. 0.070
C. 0.0015
D. 0.010
Answer:
D. 0.010
Explanation:

Question 7.
Which of the following is a way to write four and eight hundred two ten-thousandths? (1-4)
A. 4.802
B. 4.082
C. 4.0802
D. 4.0082
Answer:
C. 4.0802
Explanation:

Question 8.
Which of the following lists the decimals in order from greatest to least? (1-5)
A. 2.1027, 2.1127, 2.0127
B. 2.1027, 2.0127, 2.1127
C. 2.1127, 2.0127, 2.1027
D. 2.1127, 2.1027, 2.0127
Answer:
D. 2.1127, 2.1027, 2.0127
Explanation:

Question 9.
The record for the fastest car belongs to a British jet car which traveled at 763.035 miles per hour. What is this number written in expanded form? (1-4)
A. 700 + 60 + 3 + 0.03 + 0.05
B. 700 + 60 + 3 + 0.3 + 0.5
C. 700 + 60 + 3 + 0.3 + 0.05
D. 700 + 60 + 3 + 0.03 + 0.005
Answer:
D. 700 + 60 + 3 + 0.03 + 0.005

Question 10.
The maximum climbing speed of a three-toed sloth is 0.15 miles per hour. Which speed is less than 0.15 mph? (1-5)

A. 0.146 mph
B. 0.162 mph
C. 0.157 mph
D. 0.153 mph
Answer:
A. 0.146 mph
Explanation:

Question 11.
Which country listed in the table has a population greater than 188,078,227? (1-2)
Population

A. Bangladesh
B. Indonesia
C. Pakistan
D. Russia
Answer:
B. Indonesia
Explanation:

Question 12.
Pluto’s mean distance from the sun is about 5 billion 900 million kilometers. What is this number written in expanded form? (1-1)
A. 5,000,000,000 + 900,000,000
B. 5,000,000 + 900,000
C. 500,000,000 + 90,000,000
D. 5,000,000,000,000 + 900,000,000
Answer:
A. 5,000,000,000 + 900,000,000
Explanation:

Question 13.
Which is 10,000,000 written in exponential form? (1-3)
A. 7¹⁰
B. 10⁷
C. 10⁸
D. 8¹⁰
Answer:
B. 10⁷
Explanation:

Question 14.
In a recent year, the United States had about two trillion, two hundred two billion, six hundred million dollars in outstanding consumer credit. What is this number in standard form? (1-1)
A. $2,202,600,000
B. $2,000,202,600,000
C. $2,202,600,000,000
D. $200,202,600,000,000
Answer:
C. $2,202,600,000,000
Explanation:

Question 15.
Make an organized list to determine all the possible combinations of pennies, nickels, dimes and quarters that total 25 cents. How many combinations are possible? (1-6)
A. 13
B. 11
C. 9
D. 4
Answer:
A. 13

Envision Math 6th Grade Textbook Answer Key Topic 1.3 Exponents and Place Value

Exponents and Place Value

How can you write a number
using exponents?
Answer:
Each place in a place-value chart has a value that is 10 times as great as the place to its right. Use this pattern to write 1,000,000 as repeated multiplication.

Another Example
How do you write the expanded form of a number using exponents?
Answer:
Standard form: 562,384
Expanded form: (5 × 100,000) + (6 × 10,000) + (2 × 1,000) + (3 × 100) + (8 × 10) + 4
Expanded form
using exponents: (5 × 10⁵) + (6 × 10⁴) + (2 × 10³) + (3 × 10²) + (8 × 10¹ ) + (4 × 10⁰)
Any number raised to the first power always equals that number. 10¹ = 10.

Explain It

Question 1.
How many times is 9 used as a factor in the exponent 98?
Answer:
8 times
Explanation:

Question 2.
Why does 3 × 100 = 3?
Answer:
10⁰ = 1, so 3 × 10⁰ = 3

Other Examples
Write each in exponential form.
100,000 = 10⁵ 10 × 10 × 10 = 10³ 1 trillion = 10¹²
Evaluate numbers in exponential form.
5³ = 5 × 5 × 5 = 125 3⁴ = 3 × 3 × 3 × 3 = 81

You can write the repeated multiplication of a number in exponential form.

Each place in the place-value chart can be written using an exponent.

Guided Practice

Do you know HOW?
Question 1.
Write 10,000 as repeated multiplication.
Answer:
10,000 = 10 × 10 × 10 × 10
Explanation:

Question 2.
Write 7 × 7 × 7 × 7 in exponential form.
Answer:
7⁴
Explanation:

Question 3.
Write 37,169 in expanded form using exponents.
Answer:
(3 × 10⁴) + (7 × 10³) + (1 × 10²) + (6 × 10¹) + (9 × 10⁰)
Explanation:

Question 4.
Write 5³ in standard form.
Answer:
125
Explanation:

Do you UNDERSTAND?
Question 5.
In the example at the top, why was the number 10 used as the base to write 1,000,000 in exponential form?
Answer:
See margin.
Explanation:

Question 6.
Using the example, how many times would 10 be repeatedly multiplied to equal 100,000?
Answer:
5 times. 100,000 = 10 × 10 × 10 × 10 × 10 = 10
Explanation:

Question 7.
How many zeros are in 107 when it is written in standard form?
Answer:
7
Explanation:

Independent Practice

Leveled Practice What number is the base?
Question 8.
4⁹
Answer:
4
Explanation:

Question 9.
17⁹
Answer:
17
Explanation:

What number is the exponent?
Question 10.
31⁹
Answer:
9
Explanation:

Question 11.
2¹⁰⁰
Answer:
100
Explanation:

Write each in exponential form.
Question 12.
1,000
Answer:
10³
Explanation:

Question 13.
1,000,000,000
Answer:
10⁹
Explanation:

Question 14.
10 × 10 × 10 × 10 × 10
Answer:
10⁵
Explanation:

Write each number in expanded form using exponents.
Answer:
See margin
Explanation:

Question 15.
841
Answer:

Question 16.
5,832
Answer:

Question 17.
1,874,161
Answer:

Question 18.
22,600,000
Answer:

Evaluate 19 through 22.
Question 19.
6² = ☐
Answer:
36
Explanation:

Question 20.
10⁴ = ☐
Answer:
10,000
Explanation:

Question 21.
4³ = ☐
Answer:
64
Explanation:

Question 22.
2⁷ = ☐
Answer:
128
Explanation:

Problem Solving

Question 23.
The population of one U.S. state is approximately 33,871,648. What is this number in expanded form using exponents?
Answer:
See margin
Explanation:

Question 24.
Reasoning What number raised to both the first power and the second power equals 1?
Answer:
1; 1¹ = 1 and 1² = 1
Explanation:

Question 25.
Writing to Explain Explain how to compare 24 and 42.
Answer:
2⁴ = 2 × 2 × 2 × 2 = 16; 4² = 4 × 4 = 16; So 2⁴ = 4².
Explanation:

Question 26.
In Exercise 23, what is the place of the digit 7?
A. hundreds
B. thousands
C. ten thousands
D. millions
Answer:
C. ten thousands
Explanation:

Question 27.
Writing to Explain Kalesha was asked to write 80,808 in expanded form using exponents. Her response was (8 × 10²) + (8 × 10¹) + (8 × 10⁰). Explain where she made mistakes and write the correct response.
Answer:
See margin
Explanation:

Question 28.
Think About the Process You invest $1 in a mutual fund. Every 8 years, your money doubles. If you don’t add more money, which expression shows how much your investment is worth after 48 years?
A. 1 48
B. 1 × 2 × 2 × 2 × 2 × 2
C. 1 + 2 + 2 + 2 + 2 + 2 + 2
D. 1 × 2 × 2 × 2 × 2 × 2 × 2
Answer:
Explanation:
D. 1 × 2 × 2 × 2 × 2 × 2 × 2

Question 29.
Number Sense Using the map, write the population of the United States in expanded form using exponents.

Answer:
See margin
Explanation:

Question 30.
In 1900, there were 76,803,887 people in the United States. How many more people were there in the United States in a recent year than in 1900?
Answer:
See margin
Explanation:

Algebra Connections

Solution Pairs
An equation is a mathematical sentence that uses an equals sign to show that two expressions are equal. Any values that make an equation true are solutions to the equation.

An inequality is a mathematical sentence that contains <, >, ≤, or ≥. Any value that makes the inequality true is a solution. You can graph the solutions of an inequality on a number line.

Example: Find two values for each variable that make the equation,
y = x + 3, true.
If x = 1, then y = 1 + 3 = 4 is true.
If x = 5, then y = 5 + 3 = 8 is true.
(1, 4) and (5, 8) are solution pairs.

Example: Graph three values that make the inequality, x > 3, true.
x = 3.1, x = 4, x = 5
Draw a number line. Plot three points that are greater than 3

For 1 through 4, copy the table and find two values for each variable that make the equation true.
Question 1.
y = 4 + x
Answer:

Explanation:

Question 2.
b = a – 2
Answer:

Explanation:

Question 3.
t = 3w
Answer:

Explanation:

Question 4.
y = x ÷ 2
Answer:

Explanation:

Question 5.
Copy the number line and graph 3 values that make the inequality, d ≥ 9, true.

Answer:
Any 3 points right of 9; or 9
Explanation:

Question 6.
Copy the number line and graph 3 values that make the inequality,\(\frac{x}{3}\) < 4, true.

Answer:
Any 3 points to left of 12
Explanation:

Envision Math 6th Grade Textbook Answer Key Topic 1.2 Comparing and Ordering Whole Numbers

Comparing and Ordering Whole Numbers

How can you compare numbers?
Answer:
Use the data in the table to compare the heights of the buildings. Which is taller, the Petronas Towers or the Sears Tower?

Another Example

How do you compare and order more than two numbers?
Answer:
Order the heights of the buildings in the above table from least to greatest.
Step 1:
Write the numbers, lining up the places. Compare the digits.

Step 2:
Write the remaining numbers, lining up the places. Compare.

Step 3:
Order the numbers and the heights of the buildings from least to greatest.
1,380; 1,450; 1,483; 1,670
Jin Mao Tower, Sears Tower, Petronas Towers, Taipei 101

Guided Practice

Do you know HOW?
In 1 and 2, use < or > to compare.
Question 1.
27,318 _____ 28,001
Answer:
27,318 28,001
Explanation:

Question 2.
1,000,001 _____ 1,000,010
Answer:
1,000,001 1,000,010
Explanation:

In 3, order the numbers from least to greatest.
Question 3.
3,964 4,160 3,395 4,000
Answer:
3,395; 3,964; 4,000; 4,160
Explanation:

Do you UNDERSTAND?
Question 4.
In the example at the top, where do you begin comparing digits?
Answer:
Thousands place
Explanation:

Question 5.
Two International Finance Centre is 1,362 feet tall. Use the table above to find which is taller,Two International Finance Centre or the Jin Mao Tower?
Answer:
Jin Mao Tower
Explanation:

Step 1:
Write the numbers in a column to line up the places.
1,483
1,450
Compare the digits from left to right.

Step 2:
Find the first place where
the digits are different.
1,483
1,450
Use > or < to compare. 8 > 5
So, 1,483 > 1,450

Step 3:
Write your answer.
1,483 > 1,450
or
1,450 < 1,483
The Petronas Towers are taller than the Sears Tower

Independent Practice

For 6 through 8, use < or > to compare.
Question 6.
8,867 ____ 8,896
Answer:
8,867 8,896
Explanation:

Question 7.
102,086 _______ 100,266
Answer:
102,086 100,266

Question 8.
5,743,834 _____ 5,745,618
Answer:
5,743,834 5,745,618
Explanation:

For 9 and 10, order the numbers from least to greatest.
Tips: Compare each place from left to right.
Question 9.
85,634; 86,364; 86,446; 68,989
Answer:
68,989; 85,634; 86,364; 86,446
Explanation:

Question 10.
4,088,777; 4,221,000; 4,202,006
Answer:
4,088,777; 4,202,006; 4,221,000
Explanation:

For 11 and 12, order the numbers from greatest to least.
Question 11.
400 billion; 857 thousand; 3 trillion
Answer:
3 trillion; 400 billion; 857 thousand
Explanation:

Question 12.
5,743,834; 5,754,618; 5,900,962
Answer:
5,900,962; 5,754,618; 5,743,834
Explanation:

Problem Solving

Question 13.
Writing to Explain The SR-71 spy plane can fly at an altitude of 85,000 feet. Explain how you would compare this altitude with the altitude of the Helios shown below. Tell which plane could fly higher.

Answer:
See margin.
Explanation:

Question 14.
Number Sense When comparing 1,290 km and 1,130 km, which place do you use to determine which number is greater?
Answer:
Hundreds place
Explanation:

Question 15.
Geometry Which measurement of this rectangular vegetable garden has the greatest value?

A. length
B. width
C. perimeter
D. length + width
Answer:
C. perimeter
Explanation:

Envision Math 3rd Grade Textbook Answer Key Topic 2 Reteaching

Reteaching

Set A, pages 24-25

What is the number halfway between 800 and 900?

Use a number line.
Find the number that is the same distance from the beginning number and the ending number.

The number that is halfway between 800 and 900 is 850.

Remember to check that your number is the same distance from the beginning number and the ending number on a number line.

Find the number halfway between each pair of numbers.
Question 1.
60 and 70

Answer:

Question 2.
2,000 and 3,000

Answer:

Question 3.
900 and 1,000
Answer:

Question 4.
3,300 and 3,400
Answer:

Question 5.
860 and 870
Answer:

Set B, pages 26-28

Round 867 to the nearest hundred.

On the number line, 867 is closer to 900 than to 800.
You can also use place value.

Since 6 > 5, increase the digit in the hundreds place by one. Then change all the digits to the right to zero.
To the nearest hundred, 867 rounds to 900.

Remember to think of the halfway number when rounding.

Round to the nearest ten.
Question 1.
65
Answer:

Question 2.
813
Answer:

Question 3.
489
Answer:

Question 4.
24
Answer:

Question 5.
78
Answer:

Question 6.
942
Answer:

Round to the nearest hundred.
Question 7.
229
Answer:

Question 8.
349
Answer:

Question 9.
651
Answer:

Question 10.
856
Answer:

Question 11.
109
Answer:

Question 12.
783
Answer:

Set C, pages 30-31

Round 2,613 to the nearest thousand. You can use place value.

• Find the digit in the rounding place. That digit is 2.
• If the next digit to the right is 5 or greater, increase the digit in the rounding place by 1. If the next digit is less than 5, keep the digit in the counding place as it is. Since 6 > 5, increase the 2 to 3.
• Change all the digits to the right of the rounding place to zero.
  To the nearest thousand, 2,613 rounds to 3,000.

Remember to compare the correct digit to 5 to find if the digit in the rounding place should change.

Round to the nearest thousand.
Question 1.
3,817
Answer:

Question 2.
6,495
Answer:

Question 3.
8,562
Answer:

Question 4.
1,709
Answer:

Question 5.
2,500
Answer:

Question 6.
7,248
Answer:

Question 7.
5,692
Answer:

Question 8.
3,178
Answer:

Question 9.
9,714
Answer:

Round to the nearest hundred.
Question 10.
2,136
Answer:

Question 11.
5,624
Answer:

Question 12.
4,449
Answer:

Question 13.
7,751
Answer:

Question 14.
6,275
Answer:

Question 15.
8,941
Answer:

Question 16.
4,307
Answer:

Question 17.
9,768
Answer:

Question 18.
3,549
Answer:

Set D, pages 32-33

Follow these steps for using Try, Check, and Revise to solve problems.
Step 1: Think to make a reasonable first try.
Step 2: Check using information from the problem.
Step 3: Revise. Use your first try to make a reasonable second try. Check.
Step 4: Continue trying and checking until you find the correct answer.

Remember to check each try.

Use Try, Check, and Revise to solve.
Question 1.
Mark and Tony have 32 markers. Mark has 2 more markers than Tony. How many markers does each boy have?
Answer:

Question 2.
There are 28 players in the soccer club. There are 4 more girls than boys. How many boys are in the soccer club?
Answer:

Question 3.
Jason and Dave have 45 baseball cards together. Jason collected 7 fewer cards than Dave. How many baseball cards does Dave have?
Answer:

Envision Math 3rd Grade Textbook Answer Key Topic 2 Test Prep

Test Prep

Question 1.
What number is halfway between 1,000 and 2,000? (2-1)

A. 500
B. 1,050
C. 1,500
D. 1,600
Answer:

Question 2.
To the nearest ten pounds, Riley weighs 90 pounds. Which could be her weight? (2-2)
A. 84
B. 86
C. 95
D. 98
Answer:

Question 3.
Each of the 26 students in Carrie’s class chose either drums or horns to play during music. If 4 more students chose drums than horns, how many chose each? (2-4)
A. 16 chose drums and 10 chose horns
B. 15 chose drums and 11 chose horns
C. 14 chose drums and 12 chose horns
D. 14 chose drums and 10 chose horns
Answer:

Question 4.
The Nile River in Africa is the world’s longest river. It is 4,160 miles long. What is 4,160 to the nearest hundred? (2-3)
A. 4,000
B. 4,100
C. 4,200
D. 5,000
Answer:

Question 5.
Interstate 40 runs from Barstow, California, to Wilmington, North Carolina. It is 2,554 miles long.
What is 2,554 to the nearest thousand? (2-3)

A. 2,000
B. 2,500
C. 2,600
D. 3,000
Answer:

Question 6.
Zoe saw a 268 pound ostrich at the zoo. What is 268 rounded to the nearest ten? (2-2)
A. 200
B. 260
C. 270
D. 300
Answer:

Question 7.
Mr. Kipper’s class collected $453 for the local animal shelter. What is $453 to the nearest hundred? (2-2)
A. $500
B. $460
C. $450
D. $400
Answer:

Question 8.
The number 950 is halfway between which pair of numbers? (2-1)
A. 900 and 1,000
B. 900 and 910
C. 940 and 950
D. 800 and 900
Answer:

Question 9.
Deception Island in Antarctica is still considered an active volcano. It is 1,890 feet tall. What is 1,890 to the nearest thousand? (2-3)
A. 1,000
B. 1,800
C. 1,900
D. 2,000
Answer:

Question 10.
Party favors come in packages of 10, 20, or 25. Cristina bought 50 favors in 3 packages. Which sizes of packages could she have bought? (2-4)
A. 20, 10, and 10
B. 20, 20, and 10
C. 25 and 25
D. 25 and 20
Answer:

Question 11.
The trees below are found in Sequoia and Kings Canyon National Parks. (2-2)

Which tree is 260 feet tall to the nearest ten?
A. General Grant
B. General Sherman
C. Lincoln
D. Boole
Answer:

Question 12.
Callahan Tunnel is an underwater tunnel for cars and trucks in Boston, Massachusetts. The tunnel is 5,070 feet long. What is 5,070 to the nearest thousand? (2-3)
A. 6,000
B. 5,200
C. 5,100
D. 5,000
Answer:

Question 13.
What is 7,248 to the nearest ten? (2-3)
A. 7,000
B. 7,200
C. 7,240
D. 7,250
Answer:

Envision Math 3rd Grade Textbook Answer Key Topic 1 Test Prep

Test Prep

Question 1.
The place-value blocks show how many square miles are in Alpine County, California. How many square miles are in Alpine County? (i-i)

A. 7,039
B. 739
C. 730
D. 729
Answer:

Question 2.
On Friday, 1,593 people watched the play Cinderella. On Saturday, 1,595 people watched, and on Sunday, 1,586 people watched. Which lists these numbers in order from least to greatest? (1-5)
A. 1,586 1,593 1,595
B. 1,586 1,595 1,593
C. 1,593 1,595 1,586
D. 1,595 1,593 1,586
Answer:

Question 3.
In 295,463 what is the value of the 9? (1-3)
A. 90
B. 9,000
C. 90,000
D. 900,000
Answer:

Question 4.
The place-value chart shows how many miles of shoreline California has. Which is another way to write the number in the place-value chart? (1-2)

A. 300 + 400 + 20 + 7
B. 3,000 + 40 + 20 + 9
C. 3,000 + 400 + 7
D. 3,000 + 400 + 20 + 7
Answer:

Question 5.
Which of the following is the word form of 6,450? (1-2)
A. Six thousand, forty-five
B. Six thousand, four hundred fifty
C. Six, four fifty
D. Six thousand, four hundred five
Answer:

Question 6.
Mike’s school had 4,324 people attend the school carnival. Tiffany said her school had a greater attendance. Which of these numbers is greater than 4,324? (1-4)
A. 4,342
B. 4,314
C. 4,322
D. 3,424
Answer:

Question 7.
One of the games at the Test Your Estimation Olympics was to estimate how many beans were in a large glass jar. Keira guessed 34,003 beans. Which is another way to write 34,003? (1-3)
A. Three thousand four hundred three
B. Thirty-four hundred, three
C. Thirty-four thousand, three
D. Thirty-four and three
Answer:

Question 8.
Which number is between 3,674 and 5,628? (1-5)

A. 5,629
B. 3,673
C. 3,629
D. 5,575
Answer:

Question 9.
Which of the following has a 7 in the thousands place and a 3 in the ones place? (1-2)
A. 7,403
B. 6,937
C. 5,743
D. 5,271
Answer:

Question 10.
Which equals 700 + 8? (1-1)
A. 78
B. 708
C. 780
D. 7,008
Answer:

Question 11.
The school sold 2,346 concert tickets for Thursday’s performance, 2,356 for Friday’s, and 2,364 for Saturday’s. Which statement is true? (1-4)
A. 2,346 > 2,356
B. 2,346 = 2,364
C. 2,356 < 2,346 D. 2,356 > 2,346
Answer:

Question 12.
Alex, Eric, Josh, and Tony are playing tennis. How many different groups of 2 can they make? (1-6)
A. 12
B. 8
C. 6
D. 2
Answer:

Question 13.
The table shows the number of people who went to the fair each night.

More than 347 but fewer than 352 people went to the fair on which night? (1-4)
A. Wednesday
B. Thursday
C. Friday
D. Saturday
Answer:

Envision Math 3rd Grade Textbook Answer Key Topic 1.6 Problem Solving

Problem Solving

Make an Organized List
Randy is playing a game called Guess the Number. What are all the possible numbers that fit the clues shown at the right?

Question.
You can make an organized list to find all the possible numbers.
Clues

• It is a 3-digit even number.
• The digit in the hundreds place is greater than 8.
• The digit in the tens place is less than 2.

Answer:

Guided Practice

Do you know HOW?
Make an organized list to solve.
Question 1.
Rachel has a quarter, a dime, a nickel, and a penny. She told her brother he could take two coins. List all the different pairs of coins her brother can take.
Answer:

Do you UNDERSTAND?
Question 2.
Writing to Explain How did making an organized list help you solve Problem 1 ?
Answer:

Question 3.
Write a Problem Write and solve a real-world problem by making an organized list.
Answer:

Independent Practice

For 4 and 5, make an organized list to solve.
Question 4.
List all the 4-digit numbers that fit these clues.

• The thousands digit is less than 2.
• The hundreds digit is greater than 5.
• The tens digit and ones digit both equal 10 – 5.

Answer:

Question 5.
Jen, Meg, and Emily are standing in line at the movies. How many different ways can they line up? List the ways.
Answer:

Plan
What the clues tell us:

Solve
Make an organized list to find all the possible numbers.
900      910
902      912
904      914
906      916
908      918

For 6-8, use the table.

Question 6.
How many different kinds of sandwiches can you choose if you want white bread?
Answer:

Question 7.
How many different kinds of sandwiches can you choose if you don’t want turkey?
Answer:

Question 8.
Suppose wheat bread was added as a bread choice. How many different kinds of sandwiches could you choose then?
Answer:

Question 9.
Jeremy has tan pants and black pants. He also has three shirts: blue, green, and red. List all the different outfits that Jeremy can wear.
Answer:

Question 10.
Dennis bought a 3-pound bag of apples for $3. He also bought some grapes for $4. How much did Dennis spend?
Answer:

Question 11.
How many different ways can you make 15 cents using dimes, nickels, or pennies?
A. 15 ways
B. 9 ways
C. 6 ways
D. 3 ways
Answer:

Question 12.
Carla bought 4 sheets of poster board. Each sheet cost $2. She paid with a $10 bill. Carla cut each sheet into 2 pieces. How many pieces does Carla have?
Answer:

Question 13.
Reasoning What is this 3-digit number?

• The hundreds digit is 3 less than 5.
• The tens digit is greater than 8.
• The ones digit is 1 less than the tens digit.

Answer:

Envision Math 3rd Grade Textbook Answer Key Topic 1.5 Ordering Numbers

Ordering Numbers

How can you order numbers?
Answer:
When you order numbers, you write them from greatest to least or from least to greatest.

Question.
Three rivers are shown on the map. Write their lengths in order from greatest to least.

Answer:

Guided Practice

Do you know HOW?
For 1 and 2, order the numbers from least to greatest.
Question 1.
769 679 697
Answer:

Question 2.
359 368 45
Answer:

For 3 and 4, order the numbers from greatest to least.
Question 3.
4,334 809 4,350
Answer:

Question 4.
1,137 1,573 1,457
Answer:

Do you UNDERSTAND?
Question 5.
Writing to Explain The length of another river has a 2 in the hundreds place. Can this river be longer than the Colorado? Why or why not?
Answer:

Question 6.
Draw a place-value chart showing hundreds, tens, and ones. Write the numbers 315, 305, and 319 in the place-value chart. Use the place- value chart to write the numbers in order from greatest to least.
Answer:

Independent Practice

Order the numbers from least to greatest.
Question 7.
6,743 6,930 6,395
Answer:

Question 8.
995 1,932 1,293
Answer:

Question 9.
8,754 8,700 8,792
Answer:

Order the numbers from greatest to least.
Question 10.
2,601 967 2,365
Answer:

Question 11.
3,554 3,454 3,459
Answer:

Question 12.
5,304 5,430 5,403
Answer:

You can use a place-value chart to help you.

The lengths of the rivers in order from greatest to least are:
Mississippi: 2,348 miles;
Missouri: 2,315 miles;
Colorado: 1,450 miles.

Problem Solving

Use the pictures for 13-16.

Question 13.
Which animal weighs 100 pounds more than a moose?
Answer:

Question 14.
Number Sense A ton is equal to 2,000 pounds. Which animals weigh less than 1 ton?
Answer:

Question 15.
Write the names of the animals in the order of their weights from least to greatest.16. Reasonableness Margo says the camel weighs about fifteen hundred pounds. Do you agree or disagree?
Answer:

Question 16.
Reasonableness Margo says the camel weighs about fifteen hundred pounds. Do you agree or disagree?
Answer:

Question 17.
Writing to Explain Describe how you would write the numbers below from least to greatest.
3,456 3,654 2,375
Answer:

Question 18.
The grooves around the outside of some coins are called reeds. List the coins in the table in order from least to greatest number of reeds.

Answer:

Question 19.
Which number is between 5,695 and 6,725?

A. 5,659
B. 6,735
C. 6,632
D. 6,728
Answer:

Envision Math 1st Grade Textbook Answer Key Topic 2 Test

Test

Oral Directions Say: Mark the correct answer. 1. Look at the cube towers. Which sentence compares them? 2. Which shows the numbers in order from least to greatest? Use cubes to help. 3. Which shows the numbers in order from greatest to least?
Use cubes to help.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Oral Directions Say: Mark the correct answer. 4. Use the number line. Which number comes next? 5. Use the number line. Luke has some fish. The number he has is between 4 and 7. How many fish does Luke have? 6. Use cubes to act out the story. Annie planted 5 seeds. Javy planted 8 seeds. Raina planted 7 seeds. Which shows the number of seeds from the least to the greatest? 7. Use cubes to act out the story. Randy has 10 ribbons. Nate has 8 ribbons. Olivia has 11 ribbons. Which shows the names in order from who has the greatest to who has the least?

Question 4.
9, 10, _____

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer: