Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers

Envision Math 4th Grade Textbook Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers

Estimating Sums and Differences of Whole Numbers

How can you estimate sums and differences of whole numbers?

The Empire State Building was completed in 1931. From ground to tip, it measures 1,250 feet. At the top of the building is a lightning rod which measures 204 feet. Estimate the total height of the structure.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 1

Guided Practice*

Do you know HOW?

In 1 through 6, estimate each sum or difference.

Question 1.
Envision Math 4th Grade Textbook Answers Topic 2.4 Estimating Sums and Differences of Whole Numbers 432
Answer:

Question 2.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 3
Answer:

Question 3.
645 + 253
Answer:

Question 4.
262 – 132
Answer:

Question 5.
952 – 402
Answer:

Question 6.
398 + 121
Answer:

Do You understand?

Question 7.
Writing to Explain In the first example above, why can’t you round both numbers to the nearest thousand?
Answer:

Estimating Sums and Differences of Whole Numbers 1

Question 8.
The Statue of Liberty was completed in 1886. About how many years later was the Empire State Building completed than the Statue of Liberty?

Independent practice

In 9 through 16, estimate by rounding to the nearest ten.

Question 9.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 30
Answer:

Question 10.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 31
Answer:

Question 11.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 32
Answer:

Question 12.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 33
Answer:

Question 13.
738 + 741
Answer:

Question 14.
895 – 305
Answer:

Question 15.
755 – 344
Answer:

Question 16.
586 + 278
Answer:

In 17 through 24, estimate by rounding to the nearest hundred.

Question 17.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 34
Answer:

Question 18.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 35
Answer:

Question 19.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 36
Answer:

Question 20.
Envision Math Grade 4 Answer Key Topic 2.4 Estimating Sums and Differences of Whole Numbers 37
Answer:

Question 21.
423 + 196
Answer:

Question 22.
891 + 223
Answer:

Question 23.
1,724 – 731
Answer:

Question 24.
551 – 249
Answer:

Round each number to the nearest hundred.
Envision Math 4th Grade Textbook Answers Topic 2.4 Estimating Sums and Differences of Whole Numbers 40
The total height is about 1,500 feet.
The answer is reasonable because the total height is greater than the height of the Empire State Building.

The Washington Monument was completed in 1884. About how many years after was the Empire State
Building completed?
Envision Math 4th Grade Textbook Answers Topic 2.4 Estimating Sums and Differences of Whole Numbers 42
The Empire State Building was completed about 50 years later.

Problem Solving

Question 25.
The time line below shows the years that the Big Basin Redwoods State Park and the Mount Diablo State Park opened to the public. Use the time line to estimate the difference in years between the time they opened.
Envision Math 4th Grade Textbook Answers Topic 2.4 Estimating Sums and Differences of Whole Numbers 43
Answer:

Question 26.
This year, 35,658 people ran in a marathon. Last year, 8,683 fewer people ran. About how many people
ran last year?
Answer:

Question 27.
During swimming practice, Juan swam 15 laps and Ted swam 9 laps. How many more laps did Juan swim
than Ted?
Answer:

Estimating Sums and Differences of Whole Numbers 2

Question 28.
The table below shows the number of students per grade. Estimate the total number of students in Grades 3, 4, and 5. About how many students are in Grades 4 and 5?
Answer:

Question 29.
Alex sold 86 tickets to a school talent show on Thursday and 103 tickets on Friday. About how many tickets to the talent show did Alex sell altogether?
A. About 100
B. About 200
C. About 300
D. About 400
Answer:

Envision Math Grade 4 Answer Key Topic 2.3 Using Mental Math to Add and Subtract

Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract

Using Mental Math to Add and Subtract

How can you use mental math to add and subtract?
Properties can sometimes help you add using mental math. How many years have Ms. Walston and Mr. Randall been teaching? What is the total number of years all of the teachers in the chart have been teaching?
Envision Math 4th Grade Answer Key Topic 2.3 Using Mental Math to Add and Subtract 1

Other Examples

Add using mental math.

Find 135 + 48.
Envision Math 4th Grade Answer Key Topic 2.3 Using Mental Math to Add and Subtract 2

Use breaking apart to find a ten.
Adding 5 to 135 is easy. Break apart 48.
Envision Math 4th Grade Answer Key Topic 2.3 Using Mental Math to Add and Subtract 3
135 + 5 = 140
140 + 43 = 183
So, 135 + 48 = 183.

Use compensation.
135 + 48
135 + 50 = 185
Think I added 2 too many,
so I will subtract 2.
185 – 2 = 183
So, 135 + 48 = 183.

Subtract using mental math.
Find 400 – 165.
Use counting on.
Envision Math 4th Grade Answer Key Topic 2.3 Using Mental Math to Add and Subtract 4
165 + 5 = 170
170 + 30 = 200
200 + 200 = 400
5 + 30 + 200 = 235
So, 400 -165 = 235.
Use compensation.

Find 260 – 17.
It is easy to subtract 20.
260 – 20 = 240
Think I subtracted 3 too many,
so I will add 3.
240 + 3 = 243
So, 260 – 17 = 243.

Commutative Property of Addition
You can add two numbers in any order.
Envision Math 4th Grade Answer Key Topic 2.3 Using Mental Math to Add and Subtract 8

Ms. Walston and Mr. Randall have been teaching a combined total of 42 years.

Associative Property of Addition

You can change the grouping of addends.
Envision Math Grade 4 Answer Key Topic 2.3 Using Mental Math to Add and Subtract 9
The total number of years the three teachers have been teaching is 47 years.

Identity Property of Addition

Adding zero does not change the number.
12 + 0 = 12

Guided Practice*

Do You Know how?

In 1 through 6, use mental math to add or subtract.

Question 1.
86 + 25
Answer:

Question 2.
497 + 0
Answer:

Question 3.
566 – 359
Answer:

Question 4.
169 – 48
Answer:

Question 5.
239 + 509
Answer:

Question 6.
(40 + 5) + 8
Answer:

Do You Understand?

Question 7.
How could you use compensation to find 391 – 26?
Answer:

Question 8.
Writing to Explain Explain how you used mental math to find the answer to Exercise 4.

Independent Practice

Leveled Practice In 9 through 18, use mental math to complete the calculation.

Question 9.
400 – 227
Envision Math Grade 4 Answer Key Topic 2.3 Using Mental Math to Add and Subtract 10
Answer:

Question 10.
500 – 89
Envision Math Grade 4 Answer Key Topic 2.3 Using Mental Math to Add and Subtract 11
Answer:

Question 11.
906 – 289
Envision Math Grade 4 Answer Key Topic 2.3 Using Mental Math to Add and Subtract 12
Answer:

Question 12.
7,000 + 2,130
Envision Math Grade 4 Answer Key Topic 2.3 Using Mental Math to Add and Subtract 13
Answer:

Question 13.
583 + 317
Envision Math 4th Grade Textbook Answers Topic 2.3 Using Mental Math to Add and Subtract 14
Answer:

Question 14.
125 + 28
Envision Math 4th Grade Textbook Answers Topic 2.3 Using Mental Math to Add and Subtract 15
Answer:

Question 15.
1,700 – 315
Answer:

Question 16.
2,000 + 4,996
Answer:

Question 17.
438 – 129
Answer:

Question 18.
0 + 284
Answer:

Problem Solving

Envision Math 4th Grade Textbook Answers Topic 2.3 Using Mental Math to Add and Subtract 15.1

For 19 through 21 , use the table to the right.

Question 19.
Which state has the greatest land area in square miles?
Answer:

Question 20.
Which two states shown in the table have the smallest difference in land area?
Answer:

Question 21.
Which two states shown in the table have the greatest difference in land area?
Answer:

Question 22.
Colin had 148 CDs in his collection. He traded 32 of them for 23 that he really wanted. How many CDs does Colin now have in his collection? Use mental math.
A. 106 CDs
B. 108 CDs
C. 116 CDs
D. 139 CDs
Answer:

Question 23.
Ms. Gomez’s class collected pencils for the community school supplies drive. Ethan’s group brought in 143 pencils and Marcelina’s group added 78 more. How many pencils did the groups contribute altogether?
A. 184 pencils
B. 204 pencils
C. 221 pencils
D. 245 pencils
Answer:

Question 24.
Number Sense Is 881 – 262 more or less than 500? Explain how you can tell using mental math.
Answer:

Question 25.
Writing to Explain How can you use mental math to subtract 158 – 29?
Answer:

Question 26.
An adult human body has a total of 206 bones. There are 300 bones in a child’s body because some of a child’s bones fuse together as a child grows. How many more bones are in a child’s body than in an adult’s body?
Envision Math 4th Grade Textbook Answers Topic 2.3 Using Mental Math to Add and Subtract 50
Envision Math 4th Grade Textbook Answers Topic 2.3 Using Mental Math to Add and Subtract 51
Answer:

Question 27.
Number Sense Write two numbers that have a 6 in the ones place and an 8 in the hundreds place.
Answer:

Algebra Connections

Solving Number Sentences with Addition and Subtraction

A number sentence uses the equal sign (=) to show that two expressions have the same value. Fill in the box in each number sentence with the whole number that makes the number sentence true. Check your answers.

Example:
Envision Math 4th Grade Textbook Answers Topic 2.3 Using Mental Math to Add and Subtract 56

Think What number plus 8 equals 35?
When solving an addition number sentence, use subtraction to identify the missing number.
Think What is 35 minus 8?
Subtract 8 from 35.
35 – 8 = 27
Now, add 8 and 27.
8 + 27 = 35

Copy and complete each number sentence.

Question 1.
7 + Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 31
Answer:

Question 2.
Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 + 6 = 21
Answer:

Question 3.
26 – Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 25
Answer:

Question 4.
56 – Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 38
Answer:

Question 5.
Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 – 47 = 12
Answer:

Question 6.
66 + Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 85
Answer:

Question 7.
Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 – 98 = 1
Answer:

Question 8.
103 – Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 72
Answer:

Question 9.
10 + Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 13
Answer:

Question 10.
Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 – 8 = 12
Answer:

Question 11.
1 + Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 7
Answer:

Question 12.
744 – Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 327
Answer:

For 13 through 16, copy and complete the number sentence below each problem. Use it to help explain your answer.

Question 13.
Cheryl made 8 free-throw shots. She shot a total of 10 free-throw shots. How many free-throw shots did she miss?
8 + Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 10

Question 14.
7 rabbits less than a certain number of rabbits is 13 rabbits. What is the value of the variable?
Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 – 7 = 13
Answer:

Question 15.
George delivered 118 newspapers in two days. He delivered 57 newspapers the first day. How many newspapers did George deliver the second day?
57 + Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 118
Answer:

Question 16.
The cost of an apple is 39¢. Robert had 25¢ in his pocket. How much more money did Robert need to purchase the apple?
25 + Envision Math 4th Grade Textbook Answer Key Topic 2.3 Using Mental Math to Add and Subtract 60 = 39
Answer:

Envision Math Grade 4 Answer Key Topic 1 Reteaching

Envision Math 4th Grade Textbook Answer Key Topic 1 Reteaching

Set A, pages 4-6,8-9

Use a place-value chart to write the expanded Remember that periods can help form and word form of 26,500.

Expanded form: 20,000 + 6,000 + 500

Word form: twenty-six thousand, five hundred
Envision Math Grade 4 Answer Key Topic 1 Reteaching 1
Remember that periods can help you read large numbers. Use place-value charts to write each number in expanded form and word form.

Question 1.
7,549
Answer:

Question 2.
27,961
Answer:

Question 3.
321,209
Answer:

Question 4.
3,454
Answer:

Question 5.
6,792,365
Answer:

Question 6.
15,164,612
Answer:

Question 7.
413,109,657
Answer:

Question 8.
83,251
Answer:

Question 9.
4,806
Answer:

Question 10.
6,138,405
Answer:

Set B, pages 10–13

Write > or < for each Envision Math Grade 4 Answer Key Topic 1 Reteaching 10.

45,423 Envision Math Grade 4 Answer Key Topic 1 Reteaching 10 44,897

Step 1
Use place value to compare.

Step 2
Start comparing from the left.

Step 3
Look for the first digit that is different.
45,423
44,897
5 > 4
So, 45,423 > 44,897.

Remember that a number line can be used to compare numbers. Write > or < for each Envision Math Grade 4 Answer Key Topic 1 Reteaching 30.

Question 1.
11,961 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 12,961
Answer:

Question 2.
23,901 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 23,899
Answer:

Question 3.
42,661,907 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 42,659,824
Answer:

Question 4.
735,291,000 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 735,291,001
Answer:

Question 5.
6,103,582 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 6,130,449
Answer:

Question 6.
462,918 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 461,349
Answer:

Question 7.
8,457 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 8,451
Answer:

Question 8.
163,492,708 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 163,492,807
Answer:

Question 9.
38,605 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 38,650
Answer:

Question 10.
871,943 Envision Math Grade 4 Answer Key Topic 1 Reteaching 30 871,934
Answer:

Set C, pages 14-15

Use expanded form to compare and order numbers. Which is greater, 3,500 or 3,005? 3,500 = 3,000 + 500 3,005 = 3,000 + 5 500 > 5
So, 3,500 > 3,005.
Write the numbers from greatest to least.
3,050       3,005         3,500
Write the numbers in expanded form.
3,050 = 3,000 + 50
3,005 = 3,000 + 5
3,500 = 3,000 + 500
500 > 50 > 5
So, 3,500 > 3,050 > 3,005.

Remember to use a place-value chart to help compare and order numbers.
Write each number in expanded form. Then, copy and complete by writing > or < for each Envision Math Grade 4 Answer Key Topic 1 Reteaching 75.

Question 1.
8,500 Envision Math Grade 4 Answer Key Topic 1 Reteaching 75 8,005
Answer:

Question 2.
2,002 Envision Math Grade 4 Answer Key Topic 1 Reteaching 75 2,020
Answer:

Question 3.
3,600 Envision Math Grade 4 Answer Key Topic 1 Reteaching 75 3,006
Answer:

Question 4.
7,004 Envision Math Grade 4 Answer Key Topic 1 Reteaching 75 7,040
Answer:

Order the numbers from greatest to least.

Question 5.
1,009 1,900 1,090
Answer:

Question 6.
6,008 6,800 6,080
Answer:

Set D, pages 16-17

Using only hundreds and tens blocks, how many ways can you make 440?

Envision Math Grade 4 Answer Key Topic 1 Reteaching 80

Record the combinations using an organized list.
Envision Math Grade 4 Answer Key Topic 1 Reteaching 81

Remember that the way you organize a list can help you find all the possibilities in a problem.
Solve. Make an organized list to help you.

Question 1.
A game has yellow, red, black, and green counters. How many 2-color combinations can you make?
Answer:

Question 2.
Troy collects plastic banks. He has three different plastic banks: a pig, a cow, and a frog. How many ways can he arrange his banks on a shelf?
Answer:

Envision Math Grade 4 Answer Key Topic 1.5 Problem Solving

Envision Math 4th Grade Textbook Answer Key Topic 1.5 Problem Solving

Problem Solving

Make an Organized List

Arthur is tiling a bathroom wall. He has 520 wall tiles. He wants to arrange them in patterns of hundreds and tens. Using only hundreds and tens blocks, how many ways can he make 520?
Envision Math Grade 4 Answer Key Topic 1.5 Problem Solving 1

Guided Practice*

Do you know HOW?

Solve. Make an organized list to help you.

Question 1.
It costs Celia 50¢ admission to enter the aquarium. How many different ways can Celia pay the admission using only quarters, dimes, and nickels?
Answer:

Do you UNDERSTAND?

Question 2.
What were the titles for the columns of your list in Problem 1?
Answer:

Question 3.
Write a Problem Write a problem that you can solve using an organized list.
Answer:

Independent Practice

Solve.

Question 4.
Using only hundreds blocks and tens blocks, list the ways to show 340.
Answer:

Question 5.
Simon asked Margaret to guess a number. He gave these hints.

  • The number has 3 digits.
  • The digit in the 100s place is less than 2.
  • The digit in the 10s place is greater than 8.
  • The number is even.

What are the possible numbers?

Question 6.
Make a list showing the ways you can make a dollar using only quarters, dimes, and nickels using no more than one nickel and no more than 9 dimes.

Read & Understand Plan

Envision Math Grade 4 Answer Key Topic 1.5 Problem Solving 20

Plan
Record the combinations using an organized list.
Envision Math Grade 4 Answer Key Topic 1.5 Problem Solving 21
There are 6 ways to make 520.

Question 7.
Lou’s sandwiches are made with either wheat or white bread and have only one type of cheese—
Swiss, Cheddar, American, or Mozzarella. How many different kinds of sandwiches can Lou make?
Answer:

Question 8.
A magazine has a total of 24 articles and ads. There are 9 articles. How many ads are there?
Envision Math Grade 4 Answer Key Topic 1.5 Problem Solving 70
Answer:

Question 9.
Janie is making a bracelet. She has 1 red bead, 1 blue bead, and 1 white bead. How many possible ways can Janie arrange the beads?
Answer:

Question 10.
Reasoning What two numbers have a sum of 12 and a difference of 4?
Answer:

Question 11.
Alan has a cat, a goldfish, and a dog. He feeds them in a different order each day. How many different ways can he feed his pets?
Answer:

Question 12.
Heather is writing a 3-digit number. She uses the digits 1, 5, and 9. What are the possible numbers she can write?
Answer:

Question 13.
At the driving range, James wants to buy 200 golf balls. The golf balls are sold in buckets of 100, 50, and 10 golf balls. How many different ways can James buy 200 golf balls?
Envision Math Grade 4 Answer Key Topic 1.5 Problem Solving 71
Answer:

Envision Math Grade 4 Answer Key Topic 1.4 Understanding Zeros in Place Value

Envision Math 4th Grade Textbook Answer Key Topic 1.4 Understanding Zeros in Place Value

Understanding Zeros in Place Value

How do you compare and order numbers with zeros?
Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 1
Lena wrote three book reports. Which report used the most disk space on her computer? Use expanded form to compare and order numbers.

Guided Practice*

Do you know HOW?

In 1 and 2, write each number in expanded form. Then write > or < for each Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 2.

Question 1.
6,400 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 2 6,004
Answer:

Question 2.
1,002 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 2 1,020
Answer:

In 3 and 4, order the numbers from greatest to least.

Question 3.
7,002 7,200 7,020
Answer:

Question 4.
8,006 8,600 8,060
Answer:

Do You Understand?

Question 5.
Number Sense Write a 5-digit number with 0 in the hundreds place and 0 in the ones place. Then, write your number in expanded form.
Answer:

Question 6.
Looking at the chart above, which book report used the least amount of disk space on Lena’s computer? How much disk space did it use?

Independent Practice

Leveled Practice In 7 through 17, compare. Write < or > for each Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50.

Question 7.
1,040 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 1,000 + 40
1,004 = 1,000 + 4
1,040 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 1,004
Answer:

Question 8.
18,020 = 10,000 + 8,000 + 20
18,200 = 10,000 + 8,000 + 200
18,020 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 18,200
Answer:

Question 9.
2,070 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 2,700
Answer:

Question 10.
13,200 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 13,020
Answer:

Question 11.
5,406 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 5,460
Answer:

Question 12.
4,130 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 4,103
Answer:

Question 13.
31,002 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 30,102
Answer:

Question 14.
26,008 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 26,800
Answer:

Question 15.
10,250 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 10,205
Answer:

Question 16.
60,802 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 68,002
Answer:

Question 17.
42,910 Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 50 42,901
Answer:

Compare the first two numbers. Which is greater, 9,050 or 9,005?
9,050 = 9,000 + 50
9,005 = 9,000 + 5
50 > 5
So, 9,050 > 9,005.

Write the numbers from greatest to least.
9,050 9,005 9,500
Write the numbers in expanded form.
9,050 = 9,000 + 50
9,005 = 9,000 + 5
9,500 = 9,000 + 500
500 > 50 > 5
So, 9,500 > 9,050 > 9,005.
Grandfather’s Journey took up the most disk space on Lena’s computer.

In 18 through 21 , order the numbers from greatest to least.

Question 18.
3,007 3,070 3,700
Answer:

Question 19.
9,800 9,008 9,080
Answer:

Question 20.
30,200 30,002 32,000 30,020
Answer:

Question 21.
40,060 40,006 40,600 46,000
Answer:

For 22 and 23, pick four numbers between 143,000 and 144,000. Include exactly two zeros in each number.

Question 22.
Order the numbers you chose from least to greatest.
Answer:

Question 23.
What do the numbers have in common?
Answer:

For 24 and 25, use the chart at the right.

Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 60

Question 24.
Which month were the most carnival tickets sold?
Answer:

Question 25.
Writing to Explain Explain why this statement is NOT correct: More tickets were sold in June than August because 40 > 20.
Answer:

Question 26.
The chart at the right shows the results of this year’s reading contest. Which could NOT be the missing number?
Envision Math 4th Grade Answer Key Topic 1.4 Understanding Zeros in Place Value 62
A. 32,006
B. 33,006
C. 33,060
D. 34,006
Answer:

Envision Math Grade 4 Answer Key Topic 1.2 Millions

Envision Math 4th Grade Textbook Answer Key Topic 1.2 Millions

Millions

What are some ways to represent numbers in the millions?

From 2001 through 2005, 356,039,763 fans attended professional baseball games. Write the expanded form and word form for 356,039,763.
Use a place-value chart to help.
Envision Math Grade 4 Answer Key Topic 1.2 Millions 1

Guided Practice*

Do you know HOW?

In 1 and 2, write the number in word form. Then, tell the value of the red digit in each number.

Question 1.
75,600,295
Answer:

Question 2.
249,104,330
Answer:

In 3 through 6, write the number in expanded form.

Question 3.
6,173,253
Answer:

Question 4.
75,001,432
Answer:

Question 5.
16,107,320
Answer:

Question 6.
430,290,100
Answer:

Question 7.
What is the value of 5 in 356,039,763?
Answer:

Question 8.
What is the value of 9 in 356,039,763?
Answer:

Question 9.
Between 1996 and 2000
335,365,504 fans attended games. Which digit is in the millions place in 335,365,504?
Answer:

Independent Practice

In 10 through 12, write each number in standard form.

Question 10.
300,000,000 + 40,000,000 + 7,000,000 + 300,000 + 10,000 + 6,000 + 20 + 9
Answer:

Question 11.
900,000,000 + 20,000,000 + 6,000,000 + 20,000 + 4,000 + 10
Answer:

Question 12.
80,000,000 + 1,000,000 + 600,000 + 20,000 + 900 + 40 + 8
Answer:

In 13 through 16, write the number in word form. Then, tell the value of the red digit in each number.

Question 13.
7,915,878
Answer:

Question 14.
23,341,552
Answer:

Question 15.
21 4,278,216

Question 16.
334,290,652
Answer:

Use a place-value chart to show 356,039,763.
Envision Math Grade 4 Answer Key Topic 1.2 Millions 2

There is a 3 in the hundred millions place. Its value is 300,000,000.
Envision Math Grade 4 Answer Key Topic 1.2 Millions 16

In 17 through 20, write the number in expanded form. Then, tell the value of the red digit in each number.

Question 17.
7,330,968
Answer:

Question 18.
30,290,447
Answer:

Question 19.
1 33,958,840
Answer:

Question 20.
309,603,114
Answer:

Problem Solving

Question 21.
Writing to Explain Which number will take less time to write in expanded form, 800,000,000 or 267,423?

Question 22.
Write the expanded form of 123,456,789 and 987,654,321. Which digit has the same value in both numbers?
Answer:

Question 23.
In 2005, seventy-four million, nine hundred fifteen thousand, two hundred sixty-eight fans attended baseball games. Which choice shows this number in standard form?
A. 74,015,268
B. 74,900,268
C. 74,905,268
D. 74,915,268
Answer:

Question 24.
Write the standard form of a 9-digit number with a 5 in the millions place and a 9 in the tens place.
a. Write a number that is ten million more than the number you chose.
b Write a number that is one million less than the number you chose.
Answer:

Question 25.
Number Sense Fort Knox holds 147,300,000 ounces of gold. Write the number that is one million more
Envision Math Grade 4 Answer Key Topic 1.2 Millions 50
Answer:

Envision Math Grade 4 Answer Key Topic 1.1 Thousands

Envision Math 4th Grade Textbook Answer Key Topic 1.1 Thousands

Review What You Know

Question 1.
“Baby,” the snake, weighs 403 pounds. Is it the heaviest snake that is living in captivity? You will find out in Lesson 1-3.
Envision Math Grade 4 Answers Topic 1.1 Thousands 1
Answer:

Question 2.
How many towns and cities were there in California in 2004? You will find out in Lesson 1-1.
Envision Math Grade 4 Answers Topic 1.1 Thousands 2
Answer:

Review What You Know!

Vocabulary

Choose the best term from the box
Envision Math Grade 4 Answers Topic 1.1 Thousands 1.1

Question 1.
A group of three digits in a number separated by a comma is a __.
Answer:

Question 2.
A __ is a line that shows numbers in order using a scale.
Answer:

Question 3.
The number 8 is an ? number.
Answer:

Question 4.
The number 5 is an __ number.
Answer:

Comparing Numbers
Compare. Use >, <, or = for each Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2.

Question 5.
13 Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2 10
Answer:

Question 6.
7 Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2 7
Answer:

Question 7.
28 Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2 29
Answer:

Question 8.
14 Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2 5
Answer:

Question 9.
43 Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2 34
Answer:

Question 10.
0 Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2 1
Answer:

Question 11.
52 Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2 52
Answer:

Question 12.
13 Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2 65

Question 13.
22 Envision Math Grade 4 Answers Topic 1.1 Thousands 1.2 33

Place Value

Tell if the underlined digit is in the ones, tens, or hundreds place.

Question 14.
346
Answer:

Question 15.
17
Answer:

Question 16.
921
Answer:

Question 17.
106
Answer:

Question 18.
33
Answer:

Question 19.
47
Answer:

Question 20.
217
Answer:

Question 21.
320

Question 22.
810
Answer:

Question 23.
1,006
Answer:

Question 24.
999
Answer:

Question 25.
1,405
Answer:

Question 26.
Writing to Explain How does using commas to separate periods help you read large numbers?

Thousands

What are some ways to represent numbers in the thousands?
An altimeter measures height above sea level. Jill’s altimeter shows she is 3,241 feet above sea level. There are different ways to represent 3,241.
Envision Math Grade 4 Answers Topic 1.1 Thousands 5

Another Example

How do you read and write numbers in the thousands?

Another bicycle racer’s altimeter shows he is 5,260 feet above sea level. Write 5,260 in standard form, expanded form, and word form.
When writing a number in standard form,
Envision Math Grade 4 Answers Topic 1.1 Thousands 6.3
write only the digits: 5,260.

Each group of 3 digits starting from the right forms a period.
A number in expanded form is written as the sum of the value of the digits: 5,000 + 200 + 60 + 0.
Use periods in the place-value chart to write
5,260 in word form: five thousand, two hundred sixty.

Explain It

Question 1.
Explain why the value of 5 in 5,264 is 5,000.
Answer:

Question 2.
Is the expanded form for 5,260 the same as for 5,206?
Answer:

You can represent numbers using place-value blocks.
Envision Math Grade 4 Answers Topic 1.1 Thousands 6.4

You can represent numbers on a number line.
Envision Math Grade 4 Answers Topic 1.1 Thousands 7

Guided Practice*

Do you know HOW?

In 1 through 4, write the word form, and tell the value of the red digit in each number.

Question 1.
15,324
Answer:

Question 2.
1 35,467
Answer:

Question 3.
921,382
Answer:

Question 4.
275,206
Answer:

In 5 and 6, write the expanded form.

Question 5.
42,158
Answer:

Question 6.
63,308
Answer:

Do you UNDERSTAND?

Question 7.
If Jill climbed 100 feet more, what would her altimeter read?
Answer:

Question 8.
What is the value of the 2 in 3,261? the 3? the 1?
Answer:

Question 9.
Write one hundred one thousand, eleven in standard form.
Answer:

Independent Practice

Leveled Practice In 10 through 13, write each number in standard form

Question 10.
Envision Math Grade 4 Answers Topic 1.1 Thousands 10
Answer;

Question 11.
Envision Math 4th Grade Answer Key Topic 1.1 Thousands 11
Answer:

Question 12.
Envision Math 4th Grade Answer Key Topic 1.1 Thousands 12
Answer:

Question 13.
Envision Math 4th Grade Answer Key Topic 1.1 Thousands 13
Answer:

Independent Practice

In 14 and 15, write each number in standard form.

Question 14.
Eighty-three thousand, nine hundred two
Answer:

Question 15.
Three hundred twenty-one thousand, two hundred nine
Answer:

In 16 and 17, write each number in expanded form.

Question 16.
Four hundred ninety-seven thousand, three hundred thirty-two
Answer:

Question 17.
Twenty-one thousand, eight hundred seven
Answer:

In 18 and 19, write each number in word form.

Question 18.
300,000 + 8,000 + 20 + 9
Answer:

Question 19.
Envision Math 4th Grade Answer Key Topic 1.1 Thousands 16

Problem Solving

Question 20.
Reasoning The pedometer below counts the number of steps you walk. It can show 5 digits. What is the greatest number it can show?
Envision Math 4th Grade Answer Key Topic 1.1 Thousands 17
Answer:

Question 21.
A town library has 124,763 books and 3,142 DVDs. This year, they bought 1,000 books and 2,000 DVDs. How many books does the library have now?
A. 5,142 books
B. 23,142 books
C. 125,763 books
D. 134,763 books
Answer:

Question 22.
Number Sense Which digit is in the same place in all three numbers below? Name the place-value position.
574,632 24,376 204,581

Question 23.
Reasoning What is the greatest 4-digit number you can write? What is the least 4-digit number?
Answer:

Question 24.
In 2004, California had 1,080 towns and cities. Use place-value blocks to represent 1,080. If this number increases by 300 in ten years, how many towns and cities will there be in ten years?
Answer:

Mixed Problem Solving

Envision Math Grade 4 Answer Key Topic 1.1 Thousands 50

Question 1.
How many more Kemp Ridley’s Sea Turtles were there in 1947 than in 1968?
Answer:

Question 2.
Did the population of Kemp Ridley’s Sea Turtles increase or decrease between 1991 and 2000?
Answer:

Question 3.
How many fewer Kemp Ridley’s Sea Turtles were found nesting in 1991 than in 1968?
Answer:

Envision Math Grade 4 Answer Key Topic 1.1 Thousands 55

Question 4.
Which is taller: the California jewel-flower or the Calistoga popcorn flower?
Answer:

Question 5.
Which is shorter: the Calistoga popcorn flower or the Slenderhorned spineflower?
Answer:

Question 6.
Order the California jewel-flower, the Sacramento Orcutt grass, and the Slender-horned spineflower from tallest to shortest using
their heights.

For 7 and 8, use the information below.

Question 7.
Which digit in the number 155,959 is in the thousands place? What does the 1 mean in this number?
Answer:

Question 8.
Strategy Focus Solve the problem using the strategy Write an Equation. How many square miles of California’s total area is covered by water?
Answer:

Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles

enVision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles

Go through the enVision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 15 Equal Shares of Circles and Rectangles

Essential Question:
What are some different names for equal shares?
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 1

Find Out Talk to friends and relatives about different objects that have wheels. Ask them how they use wheels in their everyday lives.
Journal: Make a Book Show what you found out. In your book, also:

  • Draw pictures of different objects that have wheels. Describe the shapes you see. How could you divide the shapes into equal shares?
  • Tell how wheels are used to move people or things.

Review What You Know

Vocabulary
Question 1.
Put an X on the circle.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 2
Answer:

Question 2.
Draw a rectangle.
Answer:

Explanation:
Draw a rectangle using a scale and pencil.

Question 3.
Draw the hands on the clock to show a time to the half hour.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 3
Answer:

Different kinds of Rectangles
Question 4.
Color all the rectangles.
Then draw an X on the rectangle that is a square.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 4
Answer:

Explanation:
Color all the rectangles
Then put X on the rectangle that is square

Question 5.
How many rectangles do you see?
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 5
____________ rectangles
Answer:
2 rectangles
Explanation:
A rectangle has four sides
The envelope has 4 sides
The unicorn puzzle has 4 sides
So there are 2 rectangles

What’s the Time?
Question 6.
Cody gets home at 4:30. Draw the hour and minute hands on the clock to show at what time Cody gets home.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 6
Answer:

Explanation:
Draw the minutes hand at 6 [30 minutes]
Draw the hours hand between 4 and 5

Pick a Project

PROJECT 15A
What games do you play at recess? Project: Design and Play a Game

Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 76
PROJECT 15A
Answer:

PROJECT 15B
Do you have a favorite dance? Project: Create Your Own Square Dance
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 77
Answer:

PROJECT 15C
Is every game fair? Project: Make a Pair of Spinners
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 78

3-ACT MATH PREVIEW

Math Modeling Pieced Out
Before watching the video, think: What shapes can you use to make a square? Can you find another way to use shapes to make a square? What kind of designs can you make?
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 7
I can … model with math to solve a problem that involves making a design with 2-D shapes
Answer:

Explanation:
We can create a square using equal shares of triangles and one fourths of a square
the first 2 squares are patterns using triangles
the last square are patterns using rectangles and squares

Lesson 15.1 Make Equal Shares

Solve & Share
Draw a line inside the blue circle to show 2 parts that are the same size.

Draw a line inside the yellow circle to show 2 parts that are NOT the same size.

How do you know the 2 parts you made in the blue circle are the same size?
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 8
I can … determine if shapes are divided into equal shares.
Answer:

Explanation:
In the blue circle the line is drawn exactly in the middle dividing the circle into 2 equal shares.

Visual Learning Bridge
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 9

Convince Me! Is this shape divided into equal shares? Explain how you know.
Answer:
In the second picture the rectangle is divided into 2 equal shares
In the third picture the rectangle is divided into 4 equal share.

Guided Practice

Decide if each picture shows equal shares. Then circle Yes or No.
Question 1.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 10

Question 2.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 11
Answer:

Question 3.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 12
Answer:

Question 4.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 13
Answer:

Question 5.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 14
Answer:

Question 6.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 15
Answer:

Independent Practice

Write the number of equal shares in each shape. Practice If the shares are NOT equal, write 0.
Question 7.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 16
__________ equal shares
Answer:
0 equal shares
Explanation:
The shares are not equal.

Question 8.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 17
________ equal shares
Answer:
2 equal shares
Explanation:
The shares are equal.

Question 9.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 18
________ equal shares
Answer:
2 equal shares
Explanation:
The shares are equal.

Question 10.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 19
_________ equal shares
Answer:
4 equal shares
Explanation:
The shares are equal.

Question 11.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 20
________ equal shares
Answer:
4 equal shares
Explanation:
The shares are equal.

Question 12.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 21
_________ equal shares
Answer:
2 equal shares
Explanation:
The shares are equal.

Question 13.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 22
_________ equal shares
Answer:
0 equal shares
Explanation:
The shares are not equal.

Question 14.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 23
_________ equal shares
Answer:
4 equal shares
Explanation:
The shares are equal.

Question 15.
Higher Order Thinking
Draw a square, a circle, or a rectangle. Divide your shape into equal shares. Then write the number of equal shares in your shape.
_________ equal shares
Answer:
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 19
4 equal shares.

Problem Solving

Solve each problem below.
Question 16.
Be Precise Matt makes a flag with 4 equal shares. Which flag did he make? Circle the correct flag.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 24
Answer:

Explanation:
The red flag has equal shares

Question 17.
Be Precise Ruth picks a flag with equal shares. Which flag did she pick? Circle the correct flag.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 25
Answer:

Explanation:
The yellow flag has equal shares

Question 18.
Higher Order Thinking Mr. Kelly made 2 pizzas. He sliced each one into 4 slices. Each slice is the same size piece. How many slices are there? Draw a picture. Then write an equation.
Answer:

Explanation:
8 slices
1 pizza is divided into 4 slices
4 + 4 = 8 slices

Question 19.
Assessment Practice Which square does NOT show 4 equal shares?
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 26
Answer:
D
Explanation:
In all the options the square is divided into 4 equal shares, But in option D the square is divided into 3 shares.

Lesson 15.2 Make Halves and Fourths of Rectangles and Circles

Solve & Share
Draw a line inside the circle to show 2 equal shares. Color 1 of the shares. Then write numbers to tell how many shares you colored.

Draw lines inside the rectangle to show 4 equal shares. Color 2 of the shares. Then write numbers to tell how many shares you colored.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 27
I can … divide shapes into 2 and 4 equal shares and use words to describe those shares.
Answer:

I colored 2 out of 4 equal shares.

Visual Learning Bridge
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 28

Convince Me! What share of the rectangle is green?
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 29
Answer:
The 3rd share of the rectangle is Green.

Guided Practice

Circle the correct shapes for each problem.
Question 1.
One quarter blue
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 30
Explanation:
one quarter blue means we have to color one fourth blue.

Question 2.
One half yellow
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 31
Answer:

Independent Practice

Color the shapes for each problem.
Question 3.
One half red
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 32
Answer:

Explanation:
We have to color one half of the figure red.

Question 4.
One fourth orange
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 33
Answer:

Explanation:
one fourth means we have to color one of the Orange.

Question 5.
One quarter green
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 34
Answer:

Explanation:
one fourth means we have to color one of the Green.

Question 6.
One half blue
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 35
Answer:

Explanation:
one half blue means we have to color one of the halves blue.

Question 7.
Higher Order Thinking
Alex has one half of an oatmeal bar. Jen has one quarter of a different oatmeal bar. Jen’s piece is bigger. How could Jen’s piece be bigger? Use words or pictures to solve.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 36
Answer:
Alex has one half of an oatmeal bar. Jen has one quarter of a different oatmeal bar. Both oatmeal bars are of different size, as shown in the picture, hence Jen’s piece is bigger

Jens oat meal bar is bigger.

Question 8.
Explain Sam says the rectangle is divided into halves. Is he correct? Circle Yes or No. Then explain how you know.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 37
Answer:
Yes
Explanation:
The rectangle is divided in to two equal parts or two halves by the diagonal.

Question 9.
Explain Mia says the circle is divided into fourths. Lucy says it is divided into quarters. Who is correct? Explain how you know.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 38
Answer:
Lucy is correct
Explanation:
The difference between Fourth and Quarter. When used as nouns, fourth means the person or thing in the fourth position, whereas quarter meaning in math is 1/4 . When used as adjectives, fourth means the ordinal form of the number four, whereas quarter means pertaining to an aspect of a quarter.

Question 10.
Higher Order Thinking Dana draws a rectangle divided into fourths. She colors one half of the rectangle blue and one quarter of the rectangle green. Draw a rectangle to match the one Dana drew.
Answer:

Question 11.
Assessment Practice Yao colors a circle. One half of the circle is blue. The other half is NOT blue. Which shows the shape Yao could have colored? Choose two that apply.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 39
Answer:

Lesson 15.3 Understand Halves and Fourths

Which is larger: one half or one fourth of the same sandwich?
Divide the sandwiches. Then circle the sandwich that has larger equal shares.

I can … tell that more equal shares of the same whole creates smaller shares.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 40
Answer:

Visual Learning Bridge
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 41

Convince Me! David has a sandwich. Is half of the sandwich more or less food than one fourth of the sandwich? Explain.
Answer:
The half sandwich is more than the one fourth of the sandwich
Explanation:
One fourths means the sandwich is divided into 4 parts
whereas the half of sandwich means the sandwich is divided into 2 parts
half = 1 fourth + 1 fourth
so half of sandwich is more than one fourth of a sandwich

Guided Practice

Circle the shape that has more equal shares. Put an X on the shape that has larger equal shares.

Question 1.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 42

Question 2.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 43
Answer:

Question 3.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 44
Answer:

Question 4.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 45
Answer:

Independent Practice

Solve each Problem
Question 5.
Draw a line to divide this shape in half.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 46
Answer:

Explanation:
If we draw a line exactly in the middle of the rectangle the rectangle will be divided into 2 equal halves

Question 6.
Shade one quarter of this shape.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 47
Answer:

Explanation:
Shade 1 quarter of the circle.

Question 7.
Draw lines in the orange square to make smaller equal shares than are in the blue square.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 48
Answer:

Explanation:
Draw a line dividing the orange square into 2 equal shares like in the blue squares

Question 8.
Higher Order Thinking Joan cuts a rectangle into 2 equal shares. Then she cuts each share in half. How many equal shares are there now? What are these shares called? Use words or pictures to explain.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 49
Answer:
The rectangle is divided into 2 equal shares
The 2 equal shares are then divided into 2 equal share. which means
1 rectangle into 2 parts 2 parts into 2 parts each = 4 shares
These shares are called one fourth or quarters

Problem Solving

Solve each problem.
Question 9.
Reasoning Steve cuts one pan of cornbread into halves. He cuts another pan of cornbread into fourths. Each pan is the same size.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 50
How many pieces did Steve cut in all? Which pieces are larger, the halves or the fourths? Use the picture to help you solve.
_______ pieces in all
The _______ are larger.
Answer:
6 pieces in all
The halves are larger.
Explanation:
1st pan is cut into 2 shares
And the 2nd pan is cut into 4 shares
2 + 4 = 6 pieces in all.
So the half pieces are larger.

Question 10.
Higher Order Thinking Burke and Alisha each have a sheet of paper. Both sheets are the same size. Burke uses one half of his sheet. Alisha uses two fourths of her sheet. Alisha says that they used equal amounts of paper.
Is she correct? Explain your answer. You can draw a picture to help.
Answer:
Yes. Alisha is correct
Explanation:
Bruke uses one half of the sheet
Alisha uses 2 fourths of the sheet


1 half = 1 fourth + 1 fourth
1 half = 2 fourth
So Alisha is correct
They used equal amounts of paper.

Question 11.
Assessment Practice Joey has two circles of the same size. He cuts one into halves and the other into fourths. Which words describe how the halves compare to the fourths?
A. smaller, more
B. smaller, fewer
C. larger, more
D. larger, fewer
Answer:
D
Explanation:
The halves are larger and fewer than the fourths.

Lesson 15.4 Problem Solving

Model with Math

Mary’s blanket is divided into 2 equal shares. One share of the blanket is yellow and the other is orange. How can you describe the share of the blanket that is yellow? Draw and color the blanket to show your work.
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 51

I can … make a drawing or diagram to show a problem about equal shares.
Answer:

Thinking Habits Can I use a drawing, diagram, table, graph, or objects to show the problem?
Envision Math Common Core 1st Grade Answer Key Topic 15 Equal Shares of Circles and Rectangles 52

Visual Learning Bridge
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 53

Convince Me! Amy buys a green and blue rug. It is divided into 4 equal shares. Half of the rug is green. The rest is blue. How many shares are blue? How do you know?
Answer:
Amy buys a green and blue rug
She divides the rug into 4 equal shares

half of the rug is green = 2 fourths
that means the other half is colored blue = 2 fourths
that means 2 shares are blue

Guided Practice

Draw a picture to solve the problem. Then complete the sentence.
Question 1.
Pete makes a purple and yellow flag. The flag is divided into fourths. 2 shares are yellow. The rest of the flag is purple. How many of the shares are purple?
2 out of 1 equal shares are purple.
Answer:

2 out of 1 equal shares are purple.
2 out of 1 equal shares are yellow
there are 2 purple shares

Independent Practice

Draw a picture to solve each problem. Then complete the sentence.
Question 2.
Tracy’s pizza is cut into halves. She eats 1 of the shares. How many shares of the pizza does she eat?
Tracy eats _________ out of _________ equal shares.
Answer:
Tracy eats 1 out of 2 equal shares.
Explanation:
The pizza is cut into 2 equal shares
She eats 1 of the shares
2 halves – 1 halves = 1half
she eats 1 share of the pizza

Question 3.
Mia cut her sandwich into quarters. 2 of the shares have cheese. What share of the sandwich does NOT have cheese?
_________ out of _________ shares do NOT have cheese.
Answer:
2 out of 4 shares do NOT have cheese.

Question 4.
Algebra Color the correct number of shares to continue the pattern.
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 54
Answer:

Problem Solving

Performance Task
Question 5.
Pizza Shares
Kim cuts a pizza into 4 equal shares. She gives half of the pizza to Stephen.
Model Draw a picture to show the shares of the pizza that Stephen has.
Answer:

Question 6.
Reasoning How many shares of the pizza are left after Kim gives half to Stephen? Write the missing numbers.
_________ out of _________ shares are left.
Answer:
2 out of 4 shares are left.

Question 7.
Explain What if kim gives Stephen only I share of the pizza?
Explain how you can find the number of shares that Kim has left.
Answer:
Kim gave Stephen 1 share
no of shares Kim has now : 4 – 1 = 3 shares

Topic 15 Fluency Practice Activity

Find a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box next to the match. Find a match for every clue.
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 55
I can … add and subtract within 10.

Clues
A. 4 + 2 + 1
B. 4 – 1
C. 5 – 3
D. 2 + 2 + 2
E. 5 – 1
F. 1 + 3 + 1
G. 4 + 4
H. 1 + 3 + 6
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 56

Vocabulary Review
Understand Vocabulary

Word List
• Equal shares
• Fourths
• Halves
• Quarters

Question 1.
Fill in the blank.
I can cut my sandwich into two equal parts called _______.
Answer:
Halves
Explanation:
I can cut my sandwich into two equal parts called halves.

Question 2.
Fill in the blank.
When you share a sandwich equally with three other people, you cut it into _______.
Answer:
Equal shares
Explanation:
When you share a sandwich equally with three other people, you cut it into equal shares.

Question 3.
Fill in the blank.
If you want everyone to get the same amount of a sandwich, you need to cut it into _______.
Answer:
Quarters
If you want everyone to get the same amount of a sandwich, you need to cut it into quarters.

Question 4.
Fill in the blank.
Four people share one whole carton of juice and each person gets the same amount. The whole carton is divided into _______.
Answer:
Fourths
Explanation:
Four people share one whole carton of juice and each person gets the same amount. The whole carton is divided into fourths.

Use Vocabulary in Writing
Question 5.
Explain one way you could share a snack with one or more friends. Use at least one term from the Word List.
Answer:
I could share a snack with one or more friend by dividing it into equal shares among the friends.

Topic 15 Reteaching

Set A
You can divide a whole into shares.
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 57
4 equal shares

Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 58
0 equal shares

Write the number of equal shares in each shape. If the shares are NOT equal, write 0.
Question 1.
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 59
_______ equal shares
Answer:
2 equal shares

Question 2.
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 60
_______ equal shares
Answer:
0 equal shares

Set B

You can divide shapes into equal shares. You can describe the shares using the words half or fourth.
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 61

Divide and color the shapes for each problem.
Question 3.
one half green
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 62
Answer:

Explanation:
Divide the circle into halves and color one half of the circle green.

Question 4.
One fourth orange
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 63
Answer:

Explanation:
Divide the square into one fourths and color one fourth of the square orange

Set C

You can compare shares of the same shape that are different sizes.
These circles are the same size, but they are divided differently.
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 64
The red circle has larger equal shares.
The yellow circle has more equal shares.

Divide the shapes. Then circle the words that complete the sentences.
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 65
Answer picture:

Question 5.
The blue square has smaller / larger equal shares than the green square.
Answer:
Smaller
Explanation:
The blue square has smaller equal shares than the green square.

Question 6.
The green square has more / fewer equal shares than the blue square.
Answer:
Fewer
Explanation:
The green square has fewer equal shares than the blue square.

Set D

Thinking Habits
Model with Math
How can I use math words I know to help solve the problem?
Can I use a drawing, diagram, table, graph, or objects to show the problem?
Envision Math Common Core 1st Grade Answers Topic 15 Equal Shares of Circles and Rectangles 66

Draw a picture to solve the problem.
Question 7.
Maya’s scarf is divided into 4 equal shares. 1 share is green. 2 shares are yellow. The rest is blue. What share of the scarf is blue?
_______ out of _______ equal shares is blue.
Answer:
1 out of 4 equal shares is blue.

Topic 15 Assessment Practice

Question 1.
A. Which shape shows 2 equal shares?
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 67
Answer:
C

B. Describe the shares in your answer to A.
Answer:
C
Explanation:
If we cut the circle along the line the two pieces overlap each other,
that means the 2 halves are equal

Question 2.
A. Which shape does NOT show one fourth colored blue?
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 68
Answer:
D

B. How do you know your answer to A is correct?
Answer:
The answer to A is correct as D is not divided into 4 equal parts so it does not have one fourth of the figure colored blue.

Question 3.
Divide the rectangle into halves. Then color half of the rectangle.
Explain how you know that you colored the right amount.
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 69
Answer:

Explanation:
First draw a line to divide the rectangle into 2 equal shares
Color 1 half of the rectangle

Question 4.
Compare the two shapes. Circle two ways to describe the equal shares in each.
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 70
Answer:

Question 5.
Ron draws a flag divided into 4 equal shares. 2 shares are purple and the rest are blue. How many shares of the flag are blue?
Draw a picture to solve the problem. Then complete the sentence.
_______ out of _______ equal shares are blue.
Answer:
2 out of 4 equal shares are blue.
Explanation:
Total shares : 4
Purple shares : 2
Blue share :4 – 2 = 2 shares

Topic 15 Performance Task

Kerry’s Kitchen Kerry loves to cook! She makes many different foods.
Question 1.
Kerry bakes a loaf of bread. She cuts it into equal shares. How many equal shares are there?
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 71
Answer:
4 equal shares.
Explanation:
Count the number of shares of the bread

There are 4 equal shares.

Question 2.
Kerry makes a pizza.
She cuts it so that she and her sister each get an equal share. What are the shares called? _______
Show two ways that Kerry could divide the pizza.
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 72
Answer:
One fourths

Explanation:
Kerry divided the pizza into 4 equal shares
So she and her sister gets equal amount of shares

Question 3.
Kerry makes a sandwich. She eats one half of it. Color to show how much she ate.
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 73
How many halves make the whole sandwich?
_______ halves
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 74
Answer:
2 halves

Explanation:
Half means 2 equal shares
If we divide the sandwich into 2 equal shares
There will be 2 halves
Kerry eats 1 half
so there is 1 more half of the sandwich left
Draw a line in the middle of the sandwich
Color one of the halves of the sandwich like in the picture below

Question 4.
Kerry makes a pan of oatmeal bars. She cuts up the bars.
Kerry says that she divided the bars into fourths.
Envision Math Common Core Grade 1 Answer Key Topic 15 Equal Shares of Circles and Rectangles 75
Is she correct? Circle Yes or No.
Explain your answer.
Answer:

Explanation:
Dividing into fourths means every bar is the same size
Kerry divided incorrectly
Kerry must divide it like in the picture below:

Question 5.
Kerry makes a salad.
She cuts a tomato into four equal shares. She puts I equal share of the tomato in the salad.
Part A
Draw a picture to show the share of the tomato that is in the salad.

Part B
The equal shares that Kerry cut are called fourths.
What is another name for these shares?
Answer:
Quarters

Part C
How many fourths are in the whole tomato?
There are _______ fourths in the whole tomato.
Answer:
There are 4 fourths in the whole tomato.

Envision Math Grade 2 Answer Key Topic 2 Reteaching

Envision Math 2nd Grade Textbook Answer Key Topic 2 Reteaching

Set A

You can change the order of the addends. The sum will stay the same.

Envision Math Grade 2 Answer Key Topic 2 Reteaching 1

Write the sum. Then change the order of the addends and complete the problem.

Question 1.
9 + 3 = __
__ + __ = ___

Question 2.
6 + 4 = __
__ + __ = ___
Answer:

Set B

You can add any two numbers first.
Envision Math Grade 2 Answer Key Topic 2 Reteaching 3
I can add 6 and 4 first. 6 + 4 = 10. Then I can add the 3.10 + 3 = 13

Circle the numbers you add first. Write their sum in the box to the right. Then complete the problem

Question 3.
Envision Math Grade 2 Answer Key Topic 2 Reteaching 5
Answer:

Question 4.
Envision Math Grade 2 Answer Key Topic 2 Reteaching 6
Answer:

Set C

You can use a doubles fact to help you add a near double.
Envision Math Grade 2 Answer Key Topic 2 Reteaching 7
4 + 4 = 8
3 + 4 is 1 less than 4 + 4.
So, 3 + 4 = 7.

Complete the doubles facts. Use the doubles facts to solve the near doubles.

Question 5.
Envision Math Grade 2 Answer Key Topic 2 Reteaching 8
Answer:

Question 6.
Envision Math Grade 2 Answer Key Topic 2 Reteaching 9
Answer:

Set D

You can make 10 to help you add 8
Envision Math Grade 2 Answer Key Topic 2 Reteaching 10

Make 10 to add 8.

Question 7.
8 + 4 = ?
Envision Math Grade 2 Answer Key Topic 2 Reteaching 11
Answer:

Question 8.
5 + 8 = ?
Envision Math Grade 2 Answer Key Topic 2 Reteaching 12
Answer:

Envision Math Grade 2 Answer Key Topic 2.8 Problem Solving

Envision Math 2nd Grade Textbook Answer Key Topic 2.8 Problem Solving

Problem Solving
Draw a Picture and Write Draw a Picture and Write a Number Sentence

Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 1

Question 1.
__ + __ = ___
Answer:

Question 2.
__ + __ = __
Answer:

Question 3.
__ + __ = __
Answer:

Home Connection Your child drew pictures and wrote number sentences to solve math story problems.
Home Activity Place up to 10 small items in 3 piles and ask your child how many there are in all. He or she should place the items on the mat on this page and write a number sentence on a separate sheet of paper
to solve the problem. Repeat with different numbers of items.
AF 1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences. Also AF 1.2, MR 1.2, MR 2.1.

Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 2

Guided Practice

Use the table above. Draw counters and write number sentences to solve.

Question 1.
How many points did Benita score in all?
Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 3
Answer:

Question 2.
How many points did Billy score altogether?
Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 11
__ + __ + __ = __ points
Answer:

Do you understand? Sam scored 12 points in all. Write a number sentence for Sam’s points.

__ + __ + __ = 12 points

Independent Practice

Tomaz and Amy planted flowers. The table shows how many flowers they planted. Draw counters and write number sentences to solve.
Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 12
Answer:

Question 3.
How many flowers did Tomaz plant in all?
Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 12
__ + __ + __ = __ flowers
Answer:

Question 4.
How many flowers did Amy plant altogether?
Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 13
__ + __ + ___ = __ flowers
Answer:

Problem Solving

Solve the problems below.

Question 5.
Kathy and Julio collect shells. The table shows how many shells each collected. How many shells did Julio collect altogether? Draw counters and write number sentences to solve.
Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 14
Answer:

Question 6.
Which number sentence tells how many shells Kathy had collected after Weeks 1 and 2?
Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 15
Answer:

Question 7.
Journal Explain what addition strategy you used to check your answer to exercise 5.
Envision Math 2nd Grade Answer Key Topic 2.8 Problem Solving 17
Answer: