Category: Envision Math

Envision Math 5th Grade Textbook Answer Key Topic 2 Test Prep

Test prep

Question 1.
The Chen family’s home has 1,515 square feet downstairs and 625 square feet upstairs. Which of the following is the best estimate of the total square footage in the home? (2-3)
A. 2,100
B. 2,200
C. 2,300
D. 2,500
Answer:

Question 2.
What is 2.934 rounded to the nearest hundredth? (2-2)
A. 2.90
B. 2.93
C. 2.94
D. 3.00
Answer:

Question 3.
Eduardo is training for a marathon. He ran his first mile in 12.567 minutes and his second mile in 12.977 minutes. What is his combined time for the first two miles? (2-5)
A. 24.434 minutes
B. 24.544 minutes
C. 25.444 minutes
D. 25.544 minutes
Answer:

Question 4.
To add 18 + 25 using mental math, Braxton did the following. What is the missing number that makes the statement true?

A. 43
B. 25
C. 20
D. 2
Answer:

Question 5.
Which two trails combined are less than 4 miles? Use estimation to decide. (2-3)

A. Red and Yellow
B. Blue and Green
C. Red and Green
D. Blue and Yellow
Answer:

Question 6.
The Thomas Jefferson Memorial is on 18.36 acres of land and the Franklin Delano Roosevelt Memorial is on 7.5 acres of land. How many more acres of land is the Jefferson Memorial on than the Roosevelt memorial? (2-6)
A. 9.86
B. 10.86
C. 11.31
D. 17.61
Answer:

Question 7.
The table shows the areas of two islands. How many more square miles is the area of Greenland than the area of New Guinea? (2-4)

A. 1,156,614
B. 1,145,504
C. 587,716
D. 523,384
Answer:

Question 8.
In 2005, there were 2,100,990 farms in the United States. Which of the following is 2,100,990 rounded to the nearest thousand? (2-2)
A. 2,101,100
B. 2,101,000
C. 2,100,900
D. 2,100,000
Answer:

Question 9.
Which picture represents the problem? Parson’s Sporting Goods ordered 56 T-shirts in sizes small, medium and large. If 23 T-shirts are medium and 12 T-shirts are large, how many are small? (2-7)

Answer:

Question 10.
A lecture hall has 479 desk chairs and 216 folding chairs. How many seats are there in all? Use mental math to solve. (2-1)
A. 615
B. 685
C. 695
D. 785
Answer:

Question 11.
Parker had a batting average of 0.287 and Keenan had an average of 0.301. How much higher was Keenan’s batting average than Parker’s? (2-6)
A. 0.256
B. 0.14
C. 0.023
D. 0.014
Answer:

Question 12.
April logged the miles she rode on her bicycle in the table shown. Which is the best estimate of the total miles April rode during the first two weeks? (2-3)

A. 19
B. 20
C. 26
D. 38
Answer:

Question 13.
What is 87.25 + 7.69? (2-5)
A. 79.56
B. 94.2569
C. 94.94
D. 95.94
Answer:

Question 14.
In the 2004 Presidential Election, 62,040,610 people voted for George W. Bush and 59,028,439 people voted for John F. Kerry. What was the total number of votes for the two men? (2-4)
A. 121,069,049
B. 121,068,049
C. 111,069,049
D. 121,169,049
Answer:

Envision Math 6th Grade Textbook Answer Key Topic 2.7 Using Expressions to Describe Patterns

Using Expressions to Describe Patterns

How can you write expressions to describe patterns?
Answer:
Delvin saves a part of everything he earns. The table at the right shows Delvin’s savings pattern.
The INPUT column shows the money he has earned.
The OUTPUT column shows the money he has saved.

Question.
Write an expression to describe the pattern.

Answer:

Guided Practice

Do you know HOW?
Use the input/output table for 1 and 2.

Question 1.
If the input number is 8, what is the output number?
Answer:
11
Explanation:

Question 2.
Write an algebraic expression that describes the output pattern.
Answer:
x + 3
Explanation:

Do you UNDERSTAND?
Question 3.
Suppose that Delvin earned $36 mowing lawns. What input and output entries would you add to his table?
Answer:
IN: $36; OUT: $18
Explanation:

Question 4.
Reasonableness Is it reasonable for an output to be greater than the input in the table above? Explain.
Answer:
See margin.
Explanation:

Question 5.
What is the algebraic expression that describes the output pattern for the table above if the input is x?
Answer:
\(\frac{1}{2}\)x.
Explanation:

Independent Practice

Use this table for 6 and 7.

Question 6.
What is the cost of 4 lb, 5 lb, and 10 lb of apples?
Answer:

Question 7.
Write an algebraic expression that describes the output pattern if the input is a variable a.
Answer:
2a
Explanation:

Use this table for 8 and 9.

Question 8.
Copy and complete the table.
Answer:

Question 9.
Write an algebraic expression that describes the relationship between the input and output values.
Answer:
x ÷ 3
Explanation:

An input/output table is a table of related values. Identify the pattern.
What is the relationship between the values?
\(\frac{1}{2}\) (84) = 42 → 42 is half of 84
\(\frac{1}{2}\) (66) = 33 → 33 is half of 66
\(\frac{1}{2}\) (50) = 25 → 25 is half of 50.

The pattern is: \(\frac{1}{2}\) (INPUT) = OUTPUT
Let x= INPUT.
So, the pattern is \(\frac{1}{2}\) x.
Use the pattern to find the missing values.

\(\frac{1}{2}\) (22) = 11
\(\frac{1}{2}\) (30) = 15

Problem Solving

Use the input/output table at right for 10 and 11.

Question 10.
Hazem keeps \(\frac{1}{3}\) of the tips he earns. Also, he gets $1 each night to reimburse his parking fee. This information is shown in the input/output table. Write an algebraic expression that describes the output pattern if the input is the variable k.
Answer:
(k ÷ 3) + 1 or \(\frac{1}{3}\) k + 1
Explanation:

Question 11.
How much money would Hazem keep in a night if he takes in $36 in tips?
Answer:
$13
Explanation:

Use the input/output table at right for 12 and 13.

Question 12.
Ms. Windsor’s classroom has a tile floor. The students are making stars to put in the center of 4-tile groups. This input/ output chart shows the pattern. Write an algebraic expression that describes the output pattern if the input is the variable t.
Answer:
t ÷ 4
Explanation:

Question 13.
Writing to Explain There are 30 rows with 24 tiles in each row on a floor. Explain how to find the number of stars needed to complete the pattern for the floor.
Answer:
See margin.
Explanation:

Use the table at right for 14.

Question 14.
Think About the Process Which algebraic expression shows the cost of a chosen number of books b?
A. b + $2.50
B. $2.50b
C. $b – $2.50
D. b + $2.50
Answer:
B. $2.50b

Envision Math 6th Grade Textbook Answer Key Topic 1.4 Decimal Place Value

Decimal Place Value

How can you read very small decimal numbers? One gallon equals 3.7854 liters. How do you read this number?
Answer:
A decimal is a number that uses a decimal point and has one or more digits to the right of the decimal point.

Another Example
What are different ways to write decimals?
Answer:
The atomic mass of the chemical chromium is 51.9961.
Use a place-value chart to write the decimal in different forms.

Standard form: 51.9961
Short-word form: 51 and 9,961 ten thousandths
Word form: fifty-one and nine thousand nine hundred sixty-one ten thousandths
Expanded form: (5 × 10) + (1 × 1) + (9 × 0.1) + (9 × 0.01) + (6 × 0.001) + (1 × 0.0001) = 50 + 1 + 0.9 + 0.09 + 0.006 + 0.0001

Explain It

Question 1.
What is the purpose of the decimal point in a decimal number?
Answer:
It separates the whole number portion of the number from the decimal portion of the number.
Explanation:

Question 2.
If the first digit to the right of the decimal were removed from the number above, how would you write it in different forms?
Answer:
51.0961; 51 and 961 ten thousandths; fifty-one and nine hundred sixty-one ten thousandths; (5 × 10) + (1 × 1) + (9 × 0.01) + (6 × 0.001) + (1 × 0.0001) = 50 + 1 + 0.09 + 0.006 + 0.0001
Explanation:

Use a place-value chart to help you read a decimal.

Short-word form: 3 and 7,854 ten thousandths
Standard form: 3.7854

Guided Practice

Do you know HOW?
In 1 through 4, write the place and value of the underlined digit.
Answer:
See margin.
Explanation:

Question 1.
17.001
Answer:

Question 2.
987.6542
Answer:

Question 3.
14.9284
Answer:

Question 4.
7.2916
Answer:

In 5 through 7, write the number in the form indicated.
Answer:
See margin.
Explanation:

Question 5.
1.5629 in word form
Answer:

Question 6.
568.0101 in short-word form
Answer:

Question 7.
27.6003 in expanded form
Answer:

Do you UNDERSTAND?
Question 8.
How do you use a decimal point to read and write very small numbers?
Answer:
See margin.
Explanation:

Question 9.
In the example at the top of the page, how do you know that 0.005 is the value of the digit 5?
Answer:
See margin.
Explanation:

Question 10.
What is the decimal portion of 63.029? What is the whole number portion?
Answer:
See margin.
Explanation:

Independent Practice

Tips: All digits to the left of the decimal point are whole numbers, and all digits to the right of the decimal point are decimals.

Write the place and value of the underlined digit.
Question 11.
1,957.01
Answer:
hundredths; 0.01
Explanation:

Question 12.
647.476
Answer:
thousandths; 0.006
Explanation:

Question 13.
84.48
Answer:
tenths; 0.4
Explanation:

Question 14.
327.0094
Answer:
hundredths; 0
Explanation:

Question 15.
0.0521
Answer:
thousandths; 0.002
Explanation

Question 16.
78.667
Answer:
tenths; 0.6
Explanation

Question 17.
3.016
Answer:
ones; 3
Explanation:

Question 18.
8.5914
Answer:
ten thousandths; 0.0004
Explanation:

Independent Practice

Use the place-value chart to answer 19 through 23.

Question 19.
What is the place value of the last digit?
Answer:
Ten thousandths
Explanation:

Question 20.
From left to right, what is the value Ten thousandths of the second 8 in the number?
Answer:
0.0008
Explanation:

Question 21.
How would you write the number in short-word form?
Answer:
22 and 9,808 ten thousandths
Explanation:

Question 22.
How would you write the number in word form?
Answer:
See margin.
Explanation:

Question 23.
How would you write the number in expanded form?
Answer:
(2 × 10) + (2 × 1) + (9 × 0.1) + (8 × 0.01) + (8 × 0.0001)

Problem Solving

Question 24.
Number Sense Write a decimal that has the digit 9 in the tenths place and happen if you removed the decimal the ten-thousandths place.
Answer:
Sample answer: 1.9009
Explanation:

Question 25.
Writing to Explain What would point from a number?
Answer:
The number would become a whole number, and its value would be greater.
Explanation:

Use this data table to answer items 26 through 29.

Question 26.
Number Sense Which place do you use to tell that the new record is faster?
A. tens
B. tenths
C. hundreds
D. thousandths
Answer:
B. tenths
Explanation:

Question 27.
Which is the word form of the new record?
A. one hundred fifty-four and one hundred sixty-five thousandths
B. one hundred fifty-four and twenty-five thousandths
C. one hundred fifty-four and twenty-five hundredths
D. one hundred fifty-four
Answer:
C. one hundred fifty-four and twenty-five hundredths
Explanation:

Question 28.
Think About the Process Which expression tells how to find how much faster the new record was?
A. 154.165 + 154.25
B. 154.25 – 154.165
C. 154.165 × 154.25
D. 154.25 ÷ 154.165
Answer:
B. 154.25 – 154.165
Explanation:

Question 29.
Writing to Explain Explain why writing the new record as 154.250 mph does not change its value.
Answer:
Sample answer: The 0 in the thousandths place has a value of 0.
Explanation:

Mixed Problem Solving

Use the table above to answer 1 through 3.
Question 1.
Write the height of an adult grizzly bear in short-word form.
Answer:
2 and 1 tenth
Explanation:

Question 2.
Write the length of an adult grizzly bear’s claw length in expanded form.
Answer:
(1 × 10) + (1 × 0.1) + (6 × 0.01)
Explanation:

Question 3.
If newborn grizzlies weigh about 0.45 kg, how many kilograms do grizzly bears gain from the time they are newborn until they are adults?
Answer:
681.37 kg
Explanation:

Question 4.
Answer:
If a bear ran at a speed of 54.078 km/h, then increased its speed two-hundredths of a kilometer per hour, how fast would it be running?
Answer:
54.098 km/h
Explanation:

Question 5.
The grizzly bear disappeared from the state of California in 1922. How many years before 2009 did the grizzly disappear?
Answer:
87 years
Explanation:

Question 6.
The female grizzly has one to four cubs every other year. If a female has four cubs every other year for 12 years, how many cubs would she have given birth to?
Answer:
24 cubs
Explanation:

Question 7.
If one cub weighed 0.45 kg and another cub weighed 1.23 kg, how much more would the heavier cub weigh than the lighter one?
Answer:
0.78 kg
Explanation:

Envision Math 6th Grade Textbook Answer Key Topic 1.1 Place Value

Review What You Know

Vocabulary
Choose the best term from the box,

Question 1.
A period placed in a number to separate whole number values from values less than one is called a ? .
Answer:
decimal point
Explanation:

Question 2.
The value of the position of any digit in a number is called its ? .
Answer:
place
Explanation:

Question 3.
The symbols used to write numbers 0, 1,2 3, 4, 5, 6, 7, 8, and 9 are ? .
Answer:
digits
Explanation:

Writing Numbers
Write each word form in standard form.
Question 4.
nineteen
Answer:
19
Explanation:

Question 5.
thirty-seven
Answer:
37
Explanation:

Question 7.
two thousand twelve
Answer:
2,012
Explanation:

Question 8.
forty thousand
Answer:
40,000
Explanation:

Question 9.
one hundred thousand
Answer:
100, 000
Explanation:

Write the word form of each number.
Answer:
See margin
Explanation:

Question 10.
49
Answer:

Question 11.
112
Answer:

Question 12.
10,465
Answer:

Decimals
Writing to Explain Write an answer for the question.

Question 13.
How would you locate 3.33 on the number line? Explain.
Answer:
See margin.
Explanation:

Place Value

How can you read very large numbers?
Answer:
In astronomy, a light-year is the distance that light can travel in one year. One light-year is equal to about 9,500,000,000,000 kilometers. Use a place-value chart to help you find the value of the digit 9 and read the number.

Another Example
What are different ways to write very large numbers?
Answer:
A place-value chart can help you write a very large number, such as 44,600,000,000, in different forms.

Standard form: 44,600,000,000
Word form: forty-four billion, six hundred million
Short word form: 44 billion, 600 million
Expanded form: 40,000,000,000 + 4,000,000,000 + 600,000,000 or
(4 × 10,000,000,000) + (4 × 1,000,000,000) + (6 × 100,000,000)

Explain It
Question 1.
What is the relationship between the commas in a number and the periods in a place-value chart?
Answer:
See margin.
Explanation:

Question 2.
In the example above, how do you know what the addends are for a number written in expanded form?
Answer:
See margin.
Explanation:

You can use the word form to read the number.
Word form: nine trillion, five hundred billion

Guided Practice

Do you know HOW?
In 1 through 4, write the place and value of the underlined digit.
Question 1.
1,234,567
Answer:
See margin.
Explanation:

Question 2.
9,870,563,142,000
Answer:

Question 3.
36,192,748
Answer:
See margin
Explanation:

Question 4.
82,765,432,109,497
Answer:

In 5 and 6, write each number in the form indicated.
Question 5.
57,000,000,009 in expanded form
Answer:
See margin.
Explanation:

Question 6.
321 trillion, 705 thousand in standard form
Answer:
See margin.
Explanation:

Do you UNDERSTAND?
Question 7.
How do you use periods to read and write very large numbers?
Answer:
See margin.
Explanation:

Question 8.
In the example at the top, how would you write the number in expanded form?
Answer:
See margin.
Explanation:

Question 9.
When writing 136,000,000 in expanded form, why would you skip the hundred thousands, ten thousands, thousands, hundreds, tens, and ones?
Answer:
Those places are occupied by zeros.
Explanation:

Independent Practice

In 10 through 12, write the place and value of the digit 3 in each number?
Answer:
See margin.
Explanation:
Question 10.
3,476
Answer:

Question 11.
384,400
Answer:

Question 12.
5,437,200,184,400
Answer:

In 13 through 15, write each number in short-word form.
Answer:
See margin.
Explantion:

Question 13.
18,429,000,050,000
Answer:

Question 14.
10,007,000,000,000
Answer:

Question 15.
8,507,004,041
Answer:

For 16 through 19, use the number 1,435,600,000,000.
Question 16.
What is the place and value of the digit 5? billions,
Answer:
5,000,000,000
Explanation:

Question 17.
What is the value of the digit 3?
Answer:
30,000,000,000
Explanation:

Question 18.
Write the number in word form.
Answer:
One trillion, four hundred thirty-five billion, six hundred million

Question 19.
Using both multiplication and addition, how would you write this number in expanded form?
Answer:
See margin.
Explanation:

Problem Solving

Question 20.
How do you write the number of stars in the Milky Way galaxy in standard form?
Answer:
200,000,000,000
Explanation:

Question 21.
Writing to Explain Describe how you would use the standard form of a number to write the short-word form.
Answer:
See margin.
Explanation:

In a recent year, the world used an estimated 15,850,000,000 kilowatt hours of electricity. Use this information to answer 22 through 24.

Question 22.
What is the value of each non-zero digit in the number
Answer:
10,000,000,000; 5,000,000,000; 800,000,000; 50,000,000
Explanation:

Question 23.
Number Sense From left to right, what is the place of the second 5 in this number?
A. trillions
B. hundred millions
C. ten millions
D. hundred thousands
Answer:
C. ten millions
Explanation:

Question 24.
Algebra At this rate, how many kilowatt hours of electricity might the world use over a 10-year period?
A. 160 million
B. 160 billion
C. 16 trillion
D. 160 trillion
Answer:
B. 160 billion
Explanation:

Question 25.
Which of these numbers represents seventy-six trillion, two hundred seven thousand?
A. 76,000,000,207,000
B. 76,000,000,007,200
C. 76,000,207,000,000
D. 76,000,207,000
Answer:
A. 76,000,000,207,000
Explanation:

Question 26.
Which of these numbers is ten million more than three billion, four hundred twenty-nine million?
A. 3,419,000,000,000
B. 3,439,000,000,000
C. 3,419,000,000
D. 3,439,000,000
Answer:
D. 3,439,000,000
Explanation:

Mixed Problem Solving

Ancient Civilizations in Today’s World

Use the estimated populations shown on the map above to answer 1 through 10.
Question 1.
Which countries have a population in the billions?
Answer:
India and China
Explanation:

Question 2.
Which value does the digit 1 have in Greece’s population?
Answer:
10 million
Explanation:

Question 3.
Which places does the digit 3 occupy in China’s population?
Answer:
Hundred millions, millions, thousands, and ones
Explanation:

Question 4.
Which country has a population close to 80 million?
Answer:
Egypt
Explanation:

Question 5.
Which countries have a population between ten million and one hundred million?
Answer:
Greece, Egypt, and Italy
Explanation:

Question 6.
Draw a place-value chart to show the place and value of each of the digits in I ndia’s population.
Answer:
Place-value chart should show 1,095,351,995.
Explanation:

Question 7.
Which country has the least population? 8. How much less is its population than the greatest population shown?
Answer:
Greece; 1,303,285,655
Explanation:

Question 8.
How many people would India need to gain for its population to equal that of China?
Answer:
218,621,718
Explanation:

Question 9.
In a recent year, the population of Italy’s 10. capital, Rome, was about 2,553,873. About how many times larger was Italy’s population than the population of Rome?
Answer:
About 20 times larger
Explanation:

Question 10.
It is projected that China’s population will increase approximately 20% by 2025. Approximately how many more people will China have?
A. 130,000,000
B. 89,000,000
C. 260,000,000
D. 3,190,000,000
Answer:
C. 260,000,000
Explanation:

Go through the enVision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 11 Represent and Interpret Data on Line Plots

Essential Questions:
How can you solve problems using data on a line plot? How can you make a line plot?

enVision STEM Project: Safety and Data
Do Research Use the Internet or other sources to find what causes an earthquake and how the power of an earthquake is measured. Tell how people can stay safe during earthquakes.
Journal: Write a Report Include what you found. Also in your report:

• The size, or magnitude, of an earthquake is measured with the Richter scale. Explain how the scale is used.
• Research the magnitudes of at least 6 earthquakes that have occurred in your lifetime. Make a table showing when they occurred and their magnitudes, and then show their magnitudes on a line plot.

Review What You Know
Vocabulary
Choose the best term from the box. Write it on the blank.

• compare
• data
• line plot
• scale

Question 1.
A _________ is a way to organize data on a number line.
Answer:
A __line plot_______ is a way to organize data on a number line.

Question 2.
Numbers that show the units used on a graph are called a __________
Answer:
Numbers that show the units used on a graph are called a __scale________.

 

Question 3.
_________ are pieces of information.
Answer:
___Data______ are pieces of information.

 

Comparing Fractions
Write >, <, or = in the .
Question 4.
\(\frac{7}{8}\) \(\frac{3}{4}\)
Answer:
\(\frac{7}{8}\) > \(\frac{3}{4}\).

Explanation:
\(\frac{7}{8}\) \(\frac{3}{4}\)
=> 0.875  __>__  0.75.

 

Question 5.
\(\frac{1}{2}\) \(\frac{5}{8}\)
Answer:
\(\frac{1}{2}\) < \(\frac{5}{8}\).

Explanation:
\(\frac{1}{2}\) \(\frac{5}{8}\)
=> 0.5   __<___  0.625.

 

Question 6.
\(\frac{1}{4}\) \(\frac{2}{8}\)
Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\)

Explanation:
\(\frac{1}{4}\) \(\frac{2}{8}\)
=> 0.25  __=___  0.25.

 

 

Fraction Subtraction

Find the difference.
Question 7.
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = _______
Answer:
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = 6\(\frac{1}{4}\).

Explanation:
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = ???
=> 6\(\frac{1}{4}\) .

 

Question 8.
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = _______
Answer:
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 1\(\frac{1}{2}\).

Explanation:
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = ???
=> 1\(\frac{1}{2}\).

 

 

Question 9.
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = __________
Answer:
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = 5.

Explanation:
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = ???
=> 5.

 

Interpreting Data
Use the data in the chart to answer each exercise.

Question 10.
What is the greatest snake length? What is the least snake length?
Answer:
The greatest snake length is 24 inches.
The least snake length is 12 \(\frac{1}{2}\) inches.

 

Question 11.
Which of the snake lengths are recorded more than once? Which length was recorded the most?
Answer:
The snake lengths are recorded more than once are 12 \(\frac{1}{2}\) inches, 16 inches and 17 inches.
Length that was recorded the most is 16 inches.

 

Question 12.
What is the difference between the greatest length and the shortest length recorded?
Answer:
The difference between the greatest length and the shortest length recorded is 11 \(\frac{1}{2}\) inches.

Explanation:
The difference between the greatest length and the shortest length recorded is:
The greatest snake length – The least snake length
= 24 inches – 12 \(\frac{1}{2}\) inches.
= 11 \(\frac{1}{2}\) inches.

 

 

Pick a Project
PROJECT 11A
What are fun ways to get up off the couch and move?
Project: Design a Park

Answer:

 

PROJECT 11B
What are the most commonly chosen state insects?
Project: Write a Poem and Make a Graph about a State Insect

Answer:

 

PROJECT 11C
Have you ever baked a pie?
Project: Make a Pamphlet of Pie Recipes

Answer:

 

3-ACT MATH PREVIEW
Math Modeling
It’s a Fine Line

I can… model with math to solve a problem that involves analyzing and interpreting data on line plots.

Lesson 11.1 Read Line Plots

Solve & Share
Emily went fishing. She plotted the lengths of 12 fish caught on the line plot shown below. What was the length of the longest fish caught? What was the length of the shortest fish caught?
I can … interpret data using line plots.

Look Back! What other observations can you make from the line plot about the lengths of fish caught?
Answer:
Other observations can be made from the line plot about the lengths of fish caught is that every quarterly he caught new fish added one more than it.

 

Essential Question
How Can You Read Data in a Line Plot?
Answer:
It is read easily because the line plot is clear stating its refers to lengths of different fishes caught and represented on the line its catching points of intervals, by this way I can read given Data in a Line Plot.

 

 

Visual Learning Bridge
A line plot shows data along a number line. Each dot above a point on the line represents one number in the data set.
The table below shows the distance Eli walked his dog each day for seven days.

Here is how the data look on a line plot.

The numbers along the bottom of the line plot are the scale of the graph.

Interpret the data on the line plot.
The most dots are above 1 on the line plot.
The most common distance walked is 1 mile.
The longest distance walked is 3 miles.
The shortest distance walked is \(\frac{1}{2}\) mile.

What is the difference between the longest distance and the shortest distance Eli walked his dog?
3 – \(\frac{1}{2}\) = \(\frac{6}{2}\) – \(\frac{1}{2}\)
= \(\frac{5}{2}\) or 2\(\frac{1}{2}\) miles

Convince Me! Model with Math Write and solve an equation to find how many miles m, Eli walked his dog in all for the 7 days.
Answer:
Total distance walked by Eli his dog in all for the 7 days = 9 \(\frac{1}{2}\) miles.

Explanation:
Distance walked by Eli on Monday = \(\frac{1}{2}\) mile.
Distance walked by Eli on Tuesday = 1 \(\frac{1}{2}\) miles.
Distance walked by Eli on Wednesday = 1 mile.
Distance walked by Eli on Thursday = 1 \(\frac{1}{2}\) miles.
Distance walked by Eli on Friday = 3 miles.
Distance walked by Eli on Saturday = 1mile.
Distance walked by Eli on Sunday = 1mile.
Total distance walked by Eli his dog in all for the 7 days = Distance walked by Eli on Monday + Distance walked by Eli on Tuesday + Distance walked by Eli on Wednesday + Distance walked by Eli on Thursday  + Distance walked by Eli on Friday  + Distance walked by Eli on Saturday + Distance walked by Eli on Sunday
= 1 + \(\frac{1}{2}\) + 1 \(\frac{1}{2}\) + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 1 \(\frac{1}{2}\)+ 1 \(\frac{1}{2}\) + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 3 + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 4 + 1 \(\frac{1}{2}\) + 3 + 1
= 5 \(\frac{1}{2}\) + 3 + 1
= 8 \(\frac{1}{2}\) + 1
= 9 \(\frac{1}{2}\) miles.

Guided Practice
Do You Understand?
Question 1.
How can you tell the longest distance Eli walked his dog from the line plot?
Answer:
It can be said the longest distance Eli walked his dog from the line plot by checking and comparing the numerical values given in the given data and finding out the highest among them in all.

 

Question 2.
If a line plot represented 10 pieces of data, how many dots would it have? Explain.
Answer:
If a line plot represented 10 pieces of data, dots would be of 10 because the data is of 10 pieces.

 

 

Do You Know How?
For 3-5, use the line plot below.

Question 3.
How many giraffes are 14 feet tall?
Answer:
Two or 2 giraffes are 14 feet tall.

 

Question 4.
What is the most common height?
Answer:
The most common height is 15 feet.

 

Question 5.
How tall is the tallest giraffe?
Answer:
16 feet is the tallest giraffe.

 

Independent Practice
For 6-10, use the line plot at the right.

Question 6.
How many people ran the 100-meter sprint?
Answer:
20 people ran the 100-meter sprint.

 

Question 7.
Which time was the most common?
Answer:
11 hours is the most common time.

 

Question 8.
What is the difference between the fastest sprint and the slowest sprint?
Answer:
The difference between the fastest sprint and the slowest sprint is 3 \(\frac{3}{4}\) seconds.

Explanation:
The fastest sprint = 10 \(\frac{1}{4}\).
The slowest sprint = 12 \(\frac{2}{4}\).
The difference between the fastest sprint and the slowest sprint:
= 12 \(\frac{2}{4}\) – 10 \(\frac{1}{4}\)
= 6 – 2 \(\frac{1}{4}\)
= 3 \(\frac{3}{4}\) seconds.

 

Question 9.
How many more people ran 100 meters in 11\(\frac{2}{4}\) seconds than in 10\(\frac{1}{4}\) seconds?
Answer:
2 more people ran 100 meters in 11\(\frac{2}{4}\) seconds than in 10\(\frac{1}{4}\) seconds.

Explanation:
More people ran 100 meters in 11 \(\frac{2}{4}\) seconds than in 10 \(\frac{1}{4}\) seconds
= 2.

 

Question 10.
Curtis said more than half the people ran 100 meters in less than 11 seconds. Do you agree? Explain.
Answer:
Yes, I agree with what Curtis said because its 17 people who ran 100 meters in less than 11 seconds.

 

 

Problem Solving
For 11-12, use the line plot at the right.

Question 11.
Reasoning Mr. Dixon recorded the times it took students in his class to complete a project. Which time was most often needed to complete the project?
Answer:
3 Hours was most often needed to complete the project.

 

Question 12.
How much longer was the greatest amount of time spent completing the project than the least amount of time?
Answer:
1 hour longer was the greatest amount of time spent completing the project than the least amount of time.

Explanation:
The greatest amount of time spent completing the project = 3 \(\frac{2}{4}\) hours.
The least amount of time spent completing the project = 2 \(\frac{2}{4}\) hours.
Difference:
The greatest amount of time spent completing the project – The least amount of time spent completing the project
= 3 \(\frac{2}{4}\) – 2 \(\frac{2}{4}\)
= 1 hour.

 

 

Question 13.
Number Sense Jorge collects sports cards. He displays his cards in an album. There are 72 pages in the album. Each page holds 9 cards. Explain how to decide whether or not the album holds more than 600 cards.
Answer:
Yes, the album holds more than 600 cards because by the calculation of total number of cards and result is 648.

Explanation:
Number of pages in the album = 72.
Number of cards in each page = 9.
Total number of cards the album holds = Number of pages in the album × Number of cards in each page
= 72 × 9
= 648.

 

 

Question 14.
Higher Order Thinking Bob and 2 friends each were able to juggle with bean bags for \(\frac{3}{4}\) minute. How long did they juggle altogether?
Answer:
Total time taken by them = \(\frac{9}{4}\) minutes.

Explanation:
Number of people were juggling with bean bags = 3.
Time taken for each to juggle with bean bags = \(\frac{3}{4}\) minute = 3/4 minute.
Total time taken by them = Number of people were juggling with bean bags × Time taken for each to juggle with bean bags
= 3 × \(\frac{3}{4}\) minute
= \(\frac{9}{4}\) minutes.

 

Assessment Practice
For 15-16, use the line plot at the right.

Question 15.
How much longer is the longest nail than the shortest nail?
A. 1\(\frac{1}{4}\) inches
B. 1\(\frac{2}{4}\) inches
C. 1\(\frac{3}{4}\) inches
D. 2\(\frac{1}{4}\) inches
Answer:
1\(\frac{2}{4}\) inches is the longest nail than the shortest nail.
B. 1\(\frac{2}{4}\)

Explanation:
The longest nail = 2 \(\frac{1}{4}\) inches.
The shortest nail = \(\frac{3}{4}\)  inches.
Difference:
The longest nail – The shortest nail
= 2 \(\frac{1}{4}\) – \(\frac{3}{4}\)
= 1\(\frac{2}{4}\) inches.

 

Question 16.
Ed measured the nails that were 2\(\frac{1}{4}\) inches long incorrectly. They were each actually \(\frac{3}{4}\) inch longer. What was the length of the nails?
A. \(\frac{3}{4}\) inch
B. 1\(\frac{2}{4}\) inches
C. 3 inches
D. 3\(\frac{1}{4}\) inches
Answer:
1\(\frac{2}{4}\) inches is the the length of the nails.
B. 1\(\frac{2}{4}\)

Explanation:
Wrong measurement of nails = 2\(\frac{1}{4}\) inches.
Correct measurement of nails = \(\frac{3}{4}\) inch.
the length of the nails = Wrong measurement of nails  – Correct measurement of nails
= 2\(\frac{1}{4}\) – \(\frac{3}{4}\)
= 1\(\frac{2}{4}\) inches.

 

 

 

Lesson 11.2 Make Line Plots

Solve & Share
The manager of a shoe store kept track of the lengths of the shoes sold in a day. Complete the line plot using the data from the shoe store. What length shoe was sold the most?
I can … make a line plot to represent data.

Look Back! Generalize How can you use a line plot to find the data that occur most often?
Answer:
We can use a line plot to find the data that occur most often by counting the number of times which occurred more in the given data.

Explanation:

Essential Question
How Can You Make Line Plots?
Answer:
We can make line plots by using the data given representing it on line. To create a line plot, ​first create a number line that includes all the values in the data set.

 

 

Visual Learning Bridge
Serena measured the lengths of her colored pencils. How can Serena make a line plot to show these lengths?

Making a Line Plot

Step 1
Draw a number line and choose a scale based on the lengths of Serena’s pencils. Mark halves, fourths, and eighths. The scale should show data values from the least to the greatest.

Step 2
Write a title for the line plot. Label the line plot to tell what the numbers represent.

Step 3
Draw a dot for each pencil length.

Convince Me! Model with Math Write and solve an equation to find the difference , in length between Serena’s two shortest colored pencils.
Answer:
Difference , in length between Serena’s two shortest colored pencils = \(\frac{1}{4}\) inches.

Explanation:
Length of First shortest colored pencil = 4 \(\frac{1}{2}\) inches.
Length of Second shortest colored pencil = 4 \(\frac{3}{4}\) inches.
Difference:
Length of Second shortest colored pencil – Length of First shortest colored pencil
= 4 \(\frac{3}{4}\) – 4 \(\frac{1}{2}\)
= \(\frac{1}{4}\) inches.

 

 

 

Guided Practice
Do You Understand?
Question 1.
The scale of the line plot, Lengths of Serena’s Pencils, goes from 4 to 5 by eighths. Why is this a good scale to use?
Answer:
This is a good scale to use because its easy to plot the measurements on the line and easy to understand the values.

Explanation:
The scale of the line plot, Lengths of Serena’s Pencils, goes from 4 to 5 by eighths. This is a good scale to use because its easy to plot and to understand too.

 

 

Question 2.
Use the table shown at the right to compare the lengths of Sandy’s pencils with the lengths of Serena’s pencils shown on the previous page. Who has more pencils that are the same length, Serena or Sandy? Which set of data was easier to compare? Why?
Answer:
Serena has more more pencils that are the same length of 4 \(\frac{3}{4}\) inches. Both set of data are easier to compare because the values are clear to understand.

Explanation:

 

 

 

Do You Know How?
Question 3.
Complete the line plot.

Answer:

Explanation:
Line plotting for the following data:

 

 

Independent Practice
Leveled Practice For 4-5, use the table at the right.

Question 4.
Use the data in the table to make a line plot.
Answer:

Explanation:
Line plotting of data:

 

 

Question 5.
What is the length of the longest bracelet? What is the shortest length? What is the difference?
Answer:
Difference = 2 inches.

Explanation:
Length of the longest bracelet =  8 \(\frac{1}{2}\) inches.
Length of the shortest bracelet = 6 \(\frac{1}{2}\) inches.
Difference:
Length of the longest bracelet – Length of the shortest bracelet
= 8 \(\frac{1}{2}\) – 6 \(\frac{1}{2}\)
= 2 inches.

 

 

Problem Solving
Question 6.
Nora weighed each of the 7 beefsteak tomatoes she picked from her garden. The total weight of the 7 tomatoes was 10\(\frac{3}{4}\) pounds. Her line plot shows only 6 dots. What was the weight of the missing tomato?

Answer:
Weight of the missing tomato = 1\(\frac{3}{4}\) pounds.

Explanation:
Total weight of the 7 tomatoes =10 \(\frac{3}{4}\) pounds.
Number of dots shown on line plot = 6.
Total weight of the 7 tomatoes = dots value plotted on line + Weight of the missing tomato
10 \(\frac{3}{4}\)  =  1 + 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\) + 2 + 2\(\frac{1}{4}\) + Weight of the missing tomato
=> 10 \(\frac{3}{4}\)  = 9 + Weight of the missing tomato
=> 10 \(\frac{3}{4}\) – 9 =  Weight of the missing tomato
=> 1\(\frac{3}{4}\) pounds = Weight of the missing tomato.

 

 

Question 7.
Make Sense and Persevere Alyssa made a pink-and-white-striped blanket for her bed. There are 7 pink stripes and 6 white stripes. Each stripe is 8 inches wide. How wide is Alyssa’s blanket? Explain.
Answer:
Total length of Alyssa’s blanket = 104 inches.

Explanation:
Number of blanket with pink stripes = 7.
Number of blanket with pink stripes = 6.
Length of each stripe = 8 inches.
Total length of Alyssa’s blanket = (Number of blanket with pink stripes + Number of blanket with pink stripes) × Length of each stripe
= (7 + 6) × 8
= 13 × 8
= 104 inches.

 

 

For 8-9, use the table at the right.

Question 8.
Trisha measured how far her snail moved each day for 5 days. Make a line plot of Trisha’s data.
Answer:

Explanation:

 

 

Question 9.
Higher Order Thinking Write a question that would require addition or subtraction to solve using Trisha’s data. What is the answer?
Answer:
Total distance Trisha’s snail moved in 5 days = 7 \(\frac{2}{8}\) inches.

Explanation:

Distance Trisha’s snail moved on Monday = 1\(\frac{4}{8}\)
Distance Trisha’s snail moved on Tuesday =1\(\frac{3}{8}\)
Distance Trisha’s snail moved on Wednesday =1\(\frac{1}{8}\)
Distance Trisha’s snail moved on Thursday = 2\(\frac{1}{8}\)
Distance Trisha’s snail moved on Friday = 1\(\frac{1}{8}\)
Total distance Trisha’s snail moved in 5 days = Distance Trisha’s snail moved on Monday +
Distance Trisha’s snail moved on Tuesday + Distance Trisha’s snail moved on Wednesday  + Distance Trisha’s snail moved on Thursday + Distance Trisha’s snail moved on Friday
= 1\(\frac{4}{8}\) + 1\(\frac{3}{8}\) + 1\(\frac{1}{8}\) + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 2 \(\frac{7}{8}\) + 1\(\frac{1}{8}\) + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 4 + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 6 \(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 7 \(\frac{2}{8}\) inches.

 

 

Assessment Practice
Question 10.
Brianna is making bracelets for her friends and family members. The bracelets have the following lengths in inches:
6, 6\(\frac{3}{4}\), 6\(\frac{1}{4}\), 5\(\frac{3}{4}\), 5, 6, 6\(\frac{2}{4}\), 6\(\frac{1}{4}\), 6, 5\(\frac{3}{4}\)
Use the data set to complete the line plot.

Answer:

Explanation:
The bracelets lengths in inches:
6, 6\(\frac{3}{4}\), 6\(\frac{1}{4}\), 5\(\frac{3}{4}\), 5, 6, 6\(\frac{2}{4}\), 6\(\frac{1}{4}\), 6, 5\(\frac{3}{4}\)

 

 

 

Lesson 11.3 Use Line Plots to Solve Problems

Solve & Share
Ms. Earl’s class measured the lengths of 10 caterpillars in the school garden. The caterpillars had the following lengths in inches:
\(\frac{3}{4}\), 1\(\frac{1}{4}\), 1\(\frac{3}{4}\), 1\(\frac{1}{2}\), 1, 1, \(\frac{3}{4}\), 1\(\frac{1}{4}\), 1\(\frac{3}{4}\), 1\(\frac{1}{2}\)
Plot the lengths on the line plot. Write and solve an equation to find the difference in length between the longest and shortest caterpillars.
I can … use line plots to solve problems involving fractions.

Look Back! How can a line plot be used to find the difference between the greatest and least values?
Answer:
A line plot can be used to find the difference between the greatest and least values by doing the subtraction function between the two numbers.

 

Essential Question
How Can You Use Line Plots to Solve Problems involving Fractions?
Answer:
We can use line plots to Solve Problems involving Fractions by dividing the fractions by fractions to find the required solution to the problem.

 

 

Visual Learning Bridge
Alma and Ben are filling water balloons. The line plots show the weights of their water balloons. Who filled more water balloons? How many more? How much heavier was Alma’s heaviest water balloon than Ben’s heaviest water balloon?

Who filled more water balloons? How many more?
Each dot in the line plots represents 1 water balloon.
Alma filled 20 water balloons.
Ben filled 15 water balloons.
20 – 15 = 5
Alma filled 5 more water balloons than Ben.

How much heavier was Alma’s heaviest water balloon than Ben’s heaviest water balloon?

The dot farthest to the right in each line plot represents the heaviest water balloon.
Alma’s heaviest water balloon was 2\(\frac{2}{8}\) pounds.
Ben’s heaviest water balloon was 2\(\frac{1}{8}\) pounds.
Subtract.
2\(\frac{2}{8}\) – 2\(\frac{1}{8}\) = \(\frac{1}{8}\)
Alma’s heaviest water balloon was pound heavier than Ben’s heaviest water balloon.

Convince Me! Make Sense and Persevere How much heavier was Alma’s heaviest water balloon than her lightest water balloon? How much heavier was Ben’s heaviest water balloon than his lightest water balloon? Write and solve equations.
Answer:
1\(\frac{1}{8}\) pounds heavier was Alma’s heaviest water balloon than her lightest water balloon.
\(\frac{6}{8}\) pounds heavier was Ben’s heaviest water balloon than her lightest water balloon.

Explanation:
Weight of Alma’s heaviest water balloon = 2\(\frac{2}{8}\) pounds
Weight of Alma’s lightest water balloon = 1\(\frac{1}{8}\) pounds
Difference:
Weight of Alma’s heaviest water balloon – Weight of Alma’s lightest water balloon
= 2\(\frac{2}{8}\) – 1\(\frac{1}{8}\)
= 1\(\frac{1}{8}\) pounds.

Weight of Ben’s heaviest water balloon = 2\(\frac{1}{8}\)pounds
Weight of Ben’s lightest water balloon = 1\(\frac{4}{8}\) pounds
Difference:
Weight of Ben’s heaviest water balloon – Weight of Ben’s lightest water balloon
= 2\(\frac{1}{8}\) – 1\(\frac{4}{8}\)
= \(\frac{6}{8}\) pounds.

Another Example!
Rowan’s class measured the snowfall for 5 days. The line plot shows the heights of snowfall they recorded. How many inches of snow were recorded? What amount of snowfall occurred most often?

Find the total number of inches of snowfall recorded.
\(\frac{1}{4}\) + \(\frac{2}{4}\) + \(\frac{2}{4}\) + \(\frac{2}{4}\) + \(\frac{3}{4}\) = 2\(\frac{2}{4}\) inches
The amount of snowfall that occurred most often was \(\frac{2}{4}\) inch.

Guided Practice
Do You Understand?
Question 1.
Use Structure How could you use the Commutative and Associative Properties of Addition to make the addition in the Another Example easier?
Answer:
We can use the Commutative and Associative Properties of Addition to make the addition in the Another Example easier by rewriting the values and doing addition because the result is same.

 

 

Do You Know How?
For 2-3, use the example on the previous page.
Question 2.
Who filled more water balloons over 2 pounds?
Answer:
Ben filled more water balloons over 2 pounds.

Explanation:
Ben’s heaviest water balloon was 2\(\frac{1}{8}\) pounds.

 

Question 3.
How much heavier were Alma’s two heaviest water balloons than Ben’s two heaviest?
Answer:
\(\frac{1}{8}\) pounds heavier were Alma’s two heaviest water balloons than Ben’s two heaviest.

Explanation:
Weight of Alma’s two heaviest water balloons = 2 × 2\(\frac{2}{8}\)
Weight of Ben’s two heaviest water balloon = 2 × 2\(\frac{1}{8}\) pounds.
Difference:
Weight of Alma’s two heaviest water balloons – Weight of Ben’s two heaviest water balloon
= 2 × 2\(\frac{2}{8}\) – 2 × 2\(\frac{1}{8}\)
= 4 \(\frac{2}{8}\)  – 4 \(\frac{1}{8}\)
= \(\frac{1}{8}\) pounds.

 

Independent Practice
For 4-5, use the line plot at the right.

Question 4.
What is the difference in height between the tallest and shortest patients?
Answer:
1 \(\frac{3}{4}\) feet is the difference in height between the tallest and shortest patients.

Explanation:
Height of the tallest patient = 6 feet.
Height of the shortest patient = 4\(\frac{1}{4}\) feet.
Difference:
Height of the tallest patient – Height of the shortest patient
= 6 – 4\(\frac{1}{4}\)
= 6 – 4.25
= 1 \(\frac{3}{4}\) feet.

 

Question 5.
Oscar says 5 feet is the most common height Dr. Chen measured. Do you agree? Explain.
Answer:
No, 5 feet is not the most common height Dr. Chen measured as Oscar says because 5 \(\frac{2}{4}\) feet is most common height Dr. Chen measured.

Explanation:
Most common height Dr. Chen measured = 5\(\frac{2}{4}\) feet in the given data.

 

Problem Solving
Question 6.
Make Sense and Persevere Marcia measured her dolls and showed the heights using a line plot. How much taller are Marcia’s two tallest dolls combined than her two shortest dolls? Explain.

Answer:
2\(\frac{3}{4}\) inches taller are Marcia’s two tallest dolls combined than her two shortest dolls.

Explanation:
Marcia’s two tallest dolls heights = 7 inches and 6\(\frac{3}{4}\) inches.
Marcia’s two tallest dolls combined = 7 inches + 6\(\frac{3}{4}\) inches.
= 13 \(\frac{3}{4}\)  inches.
Marcia’s two shortest dolls heights = 5\(\frac{1}{4}\) inches and 5 \(\frac{3}{4}\) inches.
Marcia’s two shortest dolls combined = 5\(\frac{1}{4}\) inches + 5 \(\frac{3}{4}\) inches.
= 5.25 + 5.75
= 11 inches.
Difference:
Marcia’s two tallest dolls combined – Marcia’s two tallest dolls combined
= 13 \(\frac{3}{4}\) inches – 11 inches
= 2\(\frac{3}{4}\) inches.

 

 

Question 7.
Higher Order Thinking Marlee is knitting a scarf. The line plot shows the length she knits each day. How many more inches does Marlee need to knit so the scarf is 30 inches long?

Answer:
2 inches more inches Marlee needs to knit so the scarf is 30 inches long.

Explanation:
The length she knits each day = 2, 2\(\frac{2}{8}\) inches, 2\(\frac{2}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{5}{8}\) inches, 2\(\frac{6}{8}\) inches, 2\(\frac{6}{8}\) inches,  2\(\frac{7}{8}\) inches, 3 inches.

Total of the lengths she knits all days = 2 + 2\(\frac{2}{8}\) + 2\(\frac{2}{8}\)  + 2\(\frac{4}{8}\) + 2\(\frac{4}{8}\) + 2\(\frac{4}{8}\) + 2\(\frac{5}{8}\) + 2\(\frac{6}{8}\) + 2\(\frac{6}{8}\)  + 2\(\frac{7}{8}\) + 3 inches
= 28 inches.

More inches Marlee needs to knit so the scarf is 30 inches long = 30 – Total of the lengths she knits all days
= 30 – 28 inches
= 2 inches.

 

Assessment Practice
For 8-9, use the line plot.

Question 8.
Which of the following statements are true? Select all that apply.
☐ Most of the players are 6 feet or taller.
☐ Five players are 6 feet tall.
☐ The combined height of two of the shortest players is 1\(\frac{1}{2}\) feet.
☐ The difference between the tallest and the shortest players is \(\frac{3}{4}\) foot.
☐ All of the players are taller than 5\(\frac{3}{4}\) feet.
Answer:
Statements which are true:
Most of the players are 6 feet or taller.
All of the players are taller than 5\(\frac{3}{4}\) feet.

Explanation:
Statements which are true:
☐ Most of the players are 6 feet or taller.
☐ Five players are 6 feet tall.
☐ The combined height of two of the shortest players is 1\(\frac{1}{2}\) feet.
Combined height of two of the shortest players =
5\(\frac{3}{4}\) + 5\(\frac{3}{4}\)
= 11\(\frac{2}{4}\).

☐ The difference between the tallest and the shortest players is \(\frac{3}{4}\) foot.
Tallest player height = 6\(\frac{3}{4}\) feet.
Shortest player height = 5\(\frac{3}{4}\) feet.
Difference:
Tallest player height – Shortest player height
= 6\(\frac{3}{4}\) – 5\(\frac{3}{4}\)
= 1 feet.

☐ All of the players are taller than 5\(\frac{3}{4}\) feet.

 

 

Question 9.
If one of the shortest players grew \(\frac{3}{4}\) foot before the next season started, how tall would the player be?
A. \(\frac{6}{4}\) feet
B. 5\(\frac{3}{4}\) feet
C. 6 feet
D. 6\(\frac{2}{4}\) feet

Answer:
6\(\frac{2}{4}\) feet taller the player would be.

Explanation:
Shortest player height = 5\(\frac{3}{4}\) feet.
If one of the shortest players grew \(\frac{3}{4}\) foot.
=> 5\(\frac{3}{4}\) + \(\frac{3}{4}\)
=> 6\(\frac{2}{4}\) feet.

 

 

Lesson 11.4 Problem Solving

Critique Reasoning
Solve & Share
A class made a line plot showing the amount of snowfall for 10 days. Nathan analyzed the line plot and said, “The difference between the greatest amount of snowfall recorded and the least amount of snowfall recorded is 3 because the first measurement has one dot and the last measurement has 4 dots.” How do you respond to Nathan’s reasoning?
I can … use what I know about line plots to critique the reasoning of others.

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

• What questions can ask to understand other people’s thinking?
• Are there mistakes in other people’s thinking?
• Can I improve other people’s thinking?

Look Back! Critique Reasoning Millie said that the total amount of snowfall for the 5 days above was 10 inches. Is Millie correct?
Answer:
No, Millie is incorrect because Total amount of snowfall for the 5 days is 5 \(\frac{2}{4}\) inches. not 10 inches.

Explanation:
Amount of snowfall for the 5 days = \(\frac{3}{4}\), 1, 1, 1\(\frac{1}{4}\), 1\(\frac{2}{4}\)
Total amount of snowfall for the 5 days = \(\frac{3}{4}\) + 1 + 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\)
= 5 \(\frac{2}{4}\) inches.

 

 

Essential Question
How Can You Critique the Reasoning of Others?
Answer:
We can Critique the Reasoning of Others by checking the process how the problem is solved and finally tallying their solution.

 

 

Visual Learning Bridge
The line plots show the amount of rainfall for two months.

Val said, “The total rainfall for February was greater than the total rainfall for January because \(\frac{7}{8}\) + \(\frac{7}{8}\) equals \(\frac{14}{8}\), and the highest rainfall in January was \(\frac{5}{8}\)“.

What is Val’s reasoning?
Val compared the two highest amounts of rainfall for each month.

How can I critique the reasoning of others?
I can

• ask questions for clarification.
• decide if the strategy used makes sense.
• look for flaws in estimates or calculations.

Here’s my thinking.
Val’s reasoning is not correct.
She compared the days with the greatest amount of rainfall for the two months. The days with the greatest amounts of rainfall are not the total for the months.

Val should have added the amounts for each month. Then she could compare the amounts.
January \(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{3}{8}+\frac{3}{8}+\frac{3}{8}+\frac{5}{8}=\frac{17}{8}\) inches
February: \(\frac{1}{8}+\frac{1}{8}+\frac{5}{8}+\frac{7}{8}+\frac{7}{8}=\frac{21}{8}\) inches
During February, there was \(\frac{21}{8}-\frac{17}{8}=\frac{4}{8}\) inch more rain than January

Convince Me! Critique Reasoning Bev thought January had more rainfall because it rained on 7 days and February only had rain on 5 days. How do you respond to Bev’s reasoning?
Answer:
Well, Bev’s reasoning is not correct because to find the more rainfall in between January and February months, you should calculate the rainfall not the number of days.

 

Guided Practice
Critique Reasoning At a dog show, a judge wrote down the heights of 12 dogs. Cole made a line plot of the heights, shown to the right. He concluded, “The height with the most dots is 1\(\frac{1}{4}\) feet, so that is the greatest height of the dogs at the dog show.”

Question 1.
What is Cole’s conclusion? How did he reach this conclusion?
Answer:
Cole concluded, “The height with the most dots is 1\(\frac{1}{4}\) feet, so that is the greatest height of the dogs at the dog show.” He reached this conclusion by marking most dots on 1\(\frac{1}{4}\) feet in the line plot chart.

 

 

Question 2.
Is Cole’s conclusion correct? Explain.
Answer:
No, Cole’s conclusion incorrect because what he marked as the highest height of dog is the most common height of dogs and highest height of dog is 3 feet not 1\(\frac{1}{4}\) feet.

 

 

Independent Practice
Critique Reasoning
Natasha keeps a log of the total amount of time her students practiced on their violins outside of their weekly lesson. She creates the line plot shown. Each dot represents one student who practices a specific amount of time in one week. Natasha says that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours because there are 5 dots above 1\(\frac{1}{4}\).

Question 3.
What is Natasha’s argument? How does she support it?
Answer:
Natasha’s argument is that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours. She supports it because there are 5 dots above 1\(\frac{1}{4}\).

 

Question 4.
Critique Natasha’s reasoning.
Answer:
Natasha’s reasoning says that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours because there are 5 dots above 1\(\frac{1}{4}\). She thinks its correct but she is saying about more common hours the students who practiced a specific amount of time in one week.

 

 

Problem Solving
Performance Task

Taking Inventory
Mr. Pally is building a desk using screws of different lengths. The instructions show how many screws of each length he will need to use. Mr. Pally concludes he will use more of the shortest screws than the longest screws.
Question 5.
Model with Math Draw a line plot to show the screw lengths Mr. Pally will use to build the desk.

Answer:

Explanation:

 

 

Question 6.
Reasoning How can you use the line plot to find which length of screw Mr. Pally will need the most?
Answer:
We use the line plot to find which length of screw Mr. Pally will needs the most by counting the dots potted on the line, which occurred many times.

 

 

Question 7.
Critique Reasoning is Mr. Pally’s conclusion correct? How did you decide? If not, what can you do to improve his reasoning?

Answer:
Yes, Mr. Pally conclusion he will use more of the shortest screws than the longest screws is correct because in the line plotted shows many dots on shorter screws than the longest screws.

Explanation:
Mr. Pally concludes he will use more of the shortest screws than the longest screws.

 

 

Topic 11 Fluency Practice Activity

Find a Match
Work with 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.
I can …add and subtract multi-digit whole numbers.

Clues
A. The sum is between 3,510 and 3,520.
B. The difference is exactly 3,515.
C. The sum is between 3,560 and 3,570.
D. The difference is between 3,530 and 3,540.
E. The sum is exactly 3,584.
F. The difference is between 3,590 and 3,600.
G. The sum is exactly 3,987.
H. The difference is between 1,000 and 2,000.

Answer:

Explanation:
Clues
A. The sum is between 3,510 and 3,520.
B. The difference is exactly 3,515.
C. The sum is between 3,560 and 3,570.
D. The difference is between 3,530 and 3,540.
E. The sum is exactly 3,584.
F. The difference is between 3,590 and 3,600.
G. The sum is exactly 3,987.
H. The difference is between 1,000 and 2,000.

 

 

 

 

Topic 11 Vocabulary Review

Understand Vocabulary
Word List

• data set
• graph
• line plot
• number line
• scale
• table

Write T for true and F for false.
Question 1.
________ Graphs are used to display and represent data.
Answer:
__True______ Graphs are used to display and represent data.

 

Question 2.
_________ A data set is a collection of pieces of information.
Answer:
____True_____ A data set is a collection of pieces of information.

 

Question 3.
__________ A table is never used to display data.
Answer:
___False_______ A table is never used to display data.

 

Question 4.
__________ A line plot shows data along a number line.
Answer:
___True_______ A line plot shows data along a number line.

 

Question 5.
_________ A line plot may have more points than there are numbers in the data set.
Answer:
___False______ A line plot may have more points than there are numbers in the data set.

 

Write always, sometimes, or never.
Question 6.
A line plot _________ displays data.
Answer:
A line plot ___always______ displays data.

 

Question 7.
The scale on a line plot is ________ numbered using fractions.
Answer:
The scale on a line plot is ___sometimes_____ numbered using fractions.

 

Question 8.
A number line is __________ numbered out of order.
Answer:
A number line is ___never_______ numbered out of order.

 

 

Use Vocabulary in Writing
Question 9.
Use at least 3 terms from the Word List to describe another way Patrick can display his data.

Answer:
Graph, Line plot and Number line are the 3 terms from the Word List to describe another way Patrick can display his data.

Explanation:
Word List given:

• data set
• graph
• line plot
• number line
• scale
• table

 

 

Topic 11 Reteaching

Set A pages 417-420

The line plot shows the number of hours Mrs. Mack was at the gym each day, during a two week period.

Remember each dot above the line plot represents one value in the data set.

Question 1.
How many days did Mrs. Mack go to the gym?
Answer:
Mrs. Mack went to the gym for 11 days.

Question 2.
What is the least amount of time Mrs. Mack spent at the gym?
Answer:
1\(\frac{1}{4}\) hours is the least amount of time Mrs. Mack spent at the gym.

Question 3.
How many hours was Mrs. Mack at the the gym during the two weeks?
Answer:
25\(\frac{3}{4}\) hours Mrs. Mack was at the the gym during the two weeks.

Explanation:

Number of hours Mrs. Mack was at the the gym during the two weeks:
1, 1\(\frac{1}{4}\) , 1\(\frac{2}{4}\) ,2 , 2 , 2\(\frac{1}{4}\) , 2 \(\frac{1}{4}\) , 2\(\frac{1}{4}\) ,2 \(\frac{2}{4}\) , 2\(\frac{3}{4}\) ,3 , 3.
Total number of hours Mrs. Mack was at the the gym during the two weeks = 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\) + 2 + 2 + 2\(\frac{1}{4}\) + 2 \(\frac{1}{4}\) + 2\(\frac{1}{4}\) + 2 \(\frac{2}{4}\) + 2\(\frac{3}{4}\) + 3 + 3
= 25\(\frac{3}{4}\) hours.

Set B pages 421-424

Lilly measured the lengths of the ribbons in her craft kit and drew a line plot.

The number line shows the lengths from least to greatest. The labels show what the dots represent.

Remember to choose a reasonable scale for your number line.

A zoo in Australia studied platypuses. Their masses are recorded below.

Question 1.
Draw a line plot for the data set.
Answer:

Explanation:

 

 

 

Question 2.
What is the difference in mass of the platypus with the greatest mass and the platypus with the least mass?
Answer:
1\(\frac{1}{8}\) kg is the difference in mass of the platypus with the greatest mass and the platypus with the least mass.

Explanation:
The greatest mass of the platypus = 2\(\frac{6}{8}\) kg.
The least mass of the platypus = 1\(\frac{5}{8}\) kg.
Difference:
The greatest mass of the platypus – The least mass of the platypus
= 2\(\frac{6}{8}\)  – 1\(\frac{5}{8}\)
= 1\(\frac{1}{8}\) kg.

 

Set C pages 425-428

Carly and Freddie pick up trash. The line plots show how much they picked up each day for 14 days. What is the difference between the greatest and least amounts Carly picked up?

The greatest amount of trash Carly picked up was 3 pounds. The least amount was \(\frac{1}{2}\) pound.
Subtract. 3 – \(\frac{1}{2}\) = 2\(\frac{1}{2}\) pounds

Remember you can use equations to help solve problems with data from line plots.

For 1-3, use the line plots at the left.
Question 1.
Explain how to find the total weight of the trash Freddie picked up.
Answer:
We can find the total weight of the trash Freddie picked up in 14 days by adding the every day trash he collected.

Explanation:

Question 2.
Write and solve an equation to find , the difference between the greatest amount Freddie collected and the least amount he collected.
Answer:
2 pounds is the difference between the greatest amount Freddie collected and the least amount he collected.

Explanation:
The greatest amount Freddie collected = 2\(\frac{1}{2}\) pounds.
The least amount he collected = \(\frac{1}{2}\) pounds.
Difference:
The greatest amount Freddie collected – The least amount he collected
= 2\(\frac{1}{2}\) pounds – \(\frac{1}{2}\) pounds
= 2 pounds.

Question 3.
What is the sum of Carly’s most frequent weight and Freddie’s most frequent weight? Explain.
Answer:
5 pounds is the sum of Carly’s most frequent weight and Freddie’s most frequent weight.

Explanation:
Carly’s most frequent weight = 2\(\frac{1}{2}\) pounds.
Freddie’s most frequent weight = 1\(\frac{1}{2}\) pounds.
Sum:
Carly’s most frequent weight + Freddie’s most frequent weight
= 2\(\frac{1}{2}\) pounds + 1\(\frac{1}{2}\) pounds
= 5 pounds.

 

 

Set D pages 429-432

Think about these questions to help you critique the reasoning of others.
Thinking Habits!

• What questions can ask to understand other people’s thinking?
• Are there mistakes in other people’s thinking?
• Can I improve other people’s thinking?
  

Remember you can use math to identify mistakes in people’s thinking.

Question 1.
Spencer says 2\(\frac{3}{8}\) miles is the most common delivery distance. Do you agree? Explain.
Answer:
No, I disagree with what Spencer says 2\(\frac{3}{8}\) miles is the most common delivery distance because the most common delivery distance is \(\frac{6}{8}[/Latex] miles.

 

 

 

Topic 11 Assessment Practice

Question 1.
What is the difference between the heaviest and lightest weights?

Answer:
1 pounds is the difference between the heaviest and lightest weights.

Explanation:
The heaviest weight = 3[latex]\frac{2}{4}\) pounds.
The lightest weight = 2\(\frac{2}{4}\) pounds.
Difference:
The heaviest weight – The lightest weight
= 3\(\frac{2}{4}\)  – 2\(\frac{2}{4}\)
= 1 pounds.

Question 2.
How many dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data?

A. 3 dots
B. 2 dots
C. 1 dot
D. 0 dots
Answer:
3 dots dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data.
A. 3 dots.

Explanation:

Dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data:
3 dots.

 

 

Question 3.
Which is the most common length of snail Fred has in his backyard?

Answer:
3 inches is the most common length of snail Fred has in his backyard.

Explanation:

3 inches is the most common length of snail Fred has in his backyard.

 

Question 4.
During a sleep study, the number of hours 15 people slept was recorded in the table below.

A. Use the data in the table to draw a line plot.
Answer:

Explanation:

B. How many more hours did the person who slept the greatest number of hours sleep than the person who slept the least number of hours? Explain.
Answer:
3\(\frac{1}{2}\) more hours the person who slept the greatest number of hours sleep than the person who slept the least number of hours.

Explanation:
The person who slept the greatest number of hours = 9 .
The person who slept the least number of hours = 5\(\frac{1}{2}\).
Difference:
The person who slept the greatest number of hours – The person who slept the least number of hours
= 9 – 5\(\frac{1}{2}\)
= 3\(\frac{1}{2}\).

Question 5.
Use the line plot below. Select all the true statements.

☐ The greatest height is 2\(\frac{1}{2}\) inches.
☐ More plants have a height of 2 inches than 1\(\frac{1}{2}\) inches.
☐ There are 3 plants with a height of 1 inch.
☐ There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches.
☐ The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant.
Answer:
All the true statements:
The greatest height is 2\(\frac{1}{2}\) inches.
There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches.
The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant.

Explanation:
Select all the true statements:
☐ The greatest height is 2\(\frac{1}{2}\) inches. (True)
☐ More plants have a height of 2 inches than 1\(\frac{1}{2}\) inches. (False)
☐ There are 3 plants with a height of 1 inch. (False)
No, There are 2 plants with a height of 1 inch.
☐ There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches. (True)
☐ The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant. (True)
=> Tallest plant height = 2\(\frac{1}{2}\) inches.
Shortest plant height = 1inches.
Difference:
Tallest plant height – Shortest plant height
= 2\(\frac{1}{2}\) – 1
= 1\(\frac{1}{2}\).

 

Question 6.
Mr. Tricorn’s class measured the lengths of crayons. How many crayons did they measure? Use the line plot.

Answer:
Total number of crayons they measured = 10.

Explanation:
Number of crayons of length 1\(\frac{1}{2}\) inches = 1.
Number of crayons of length 2\(\frac{1}{2}\) inches = 4.
Number of crayons of length 3\(\frac{1}{2}\) inches = 2.
Number of crayons of length 4\(\frac{1}{2}\) inches = 3.
Total number of crayons measured = Number of crayons of length 1\(\frac{1}{2}\) inches + Number of crayons of length 2\(\frac{1}{2}\) inches + Number of crayons of length 3\(\frac{1}{2}\) inches + Number of crayons of length 4\(\frac{1}{2}\) inches
= 1 + 4 + 2 + 3
= 10.

 

 

Question 7.
Use the line plot from Exercise 6. How many crayons were greater than 3 inches long?
A. 9
B. 5
C. 6
D. 3
Answer:
Number of crayons greater than 3 inches long = 5.
B. 5.

Explanation:
Number of crayons of length 1\(\frac{1}{2}\) inches = 1.
Number of crayons of length 2\(\frac{1}{2}\) inches = 4.
Number of crayons of length 3\(\frac{1}{2}\) inches = 2.
Number of crayons of length 4\(\frac{1}{2}\) inches = 3.
Number of crayons greater than 3 inches long = Number of crayons of length 3\(\frac{1}{2}\) inches + Number of crayons of length 4\(\frac{1}{2}\) inches
= 2 + 3
= 5.

 

Question 8.
Ms. Garcia measured the heights of her students.

A. Use the data in the table to draw a line plot.
Answer:

Explanation:

 

 

B. Use the data in Exercise 8. Select all of the statements that are true.
☐ The tallest student is 4 feet tall.
☐ The tallest student is 4\(\frac{2}{4}\) feet tall.
☐ The shortest student is 3\(\frac{3}{4}\) feet tall.
☐ The tallest student is 1 foot taller than the shortest student.
☐ The most common height of the students was 4 feet tall.
Answer:
All of the statements that are true:
The tallest student is 4\(\frac{2}{4}\) feet tall.
The tallest student is 1 foot taller than the shortest student.
The most common height of the students was 4 feet tall.

Explanation:
Select all of the statements that are true.
☐ The tallest student is 4 feet tall. (False)
☐ The tallest student is 4\(\frac{2}{4}\) feet tall. (True)
☐ The shortest student is 3\(\frac{3}{4}\) feet tall. (False)
☐ The tallest student is 1 foot taller than the shortest student. (True)
=> Tallest student = 4\(\frac{2}{4}\) feet.
Shortest student = 3\(\frac{2}{4}\) feet.
Difference:
Tallest student – Shortest student
= 4\(\frac{2}{4}\) feet  – 3\(\frac{2}{4}\) feet
= 1 feet.
☐ The most common height of the students was 4 feet tall. (True)

 

 

Topic 11 Performance Task

Measuring Pumpkins Mr. Chan’s class picked small pumpkins from the pumpkin patch and then weighed their pumpkins.
Question 1.
The class made the Pumpkin Weights line plot of the data.

Part A
What is the most common weight of the pumpkins?
Answer:
The most common weight of the pumpkins = 4\(\frac{1}{4}\) pounds.

Part B
Write and solve an equation to find, how much more the heaviest pumpkin weighs than the lightest pumpkin.
Answer:
1\(\frac{3}{4}\) pounds more the heaviest pumpkin weighs than the lightest pumpkin.

Explanation:
The heaviest pumpkin weight = 5pounds.
The lightest pumpkin weight = 3\(\frac{1}{4}\) pounds.
Difference:
The heaviest pumpkin weight – The lightest pumpkin weight
= 5 – 3\(\frac{1}{4}\)
= 1\(\frac{3}{4}\) pounds.

Part C
Ayana said 3 pumpkins weigh 4\(\frac{2}{4}\) pounds. Critique Ayana’s reasoning. Is she correct?
Answer:
Yes, she is correct because there are three pumpkins weigh 4\(\frac{2}{4}\) pounds.

 

Question 2.
The class also measures the distance around their pumpkins to the nearest half-inch. They recorded their data in the Pumpkin Size list. Pumpkin Size: 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 19\(\frac{1}{2}\), 20, 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 20, 21, 22, 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 21, 21, 21\(\frac{1}{2}\), 20\(\frac{1}{2}\)

Part A
Draw a line plot of Pumpkin Size data.
Answer:

Explanation:
Pumpkin Size:
19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 19\(\frac{1}{2}\), 20, 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 20, 21, 22, 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 21, 21, 21\(\frac{1}{2}\), 20\(\frac{1}{2}\)

 

 

Part B
Drew says 1 more pumpkin was 20\(\frac{1}{2}\) inches around than was 19\(\frac{1}{2}\) inches because 20\(\frac{1}{2}\) – 19\(\frac{1}{2}\) = 1. Critique Drew’s reasoning.
Answer:
No, he is incorrect because pumpkin size of 20\(\frac{1}{2}\) – pumpkin size of 19\(\frac{1}{2}\) = 1 is the difference between two different sized pumpkins but not 1 more pumpkins added to the count.

Explanation:
20\(\frac{1}{2}\) – 19\(\frac{1}{2}\) = 1. Difference between different pumpkins.

 

Part C
What is  the difference between the longest distance and the shortest distance ? Write and solve an equation.
Answer:
3 inches is the difference between the longest distance and the shortest distance

Explanation:
The longest pumpkin sized = 22 inches.
The shortest pumpkin sized = 19 inches.
Difference:
The longest pumpkin sized – The shortest pumpkin sized
= 22 – 19
= 3 inches.

Envision Math 5th Grade Textbook Answer Key Topic 2.7 Problem Solving

Problem Solving

Draw a Picture and Write an Equation

Three friends have music collections. How many more CDs does Susan have than Larry?

Another Example

Rori had some balloons and then gave 35 of them away. She now has 21 left. How many balloons did Rori have to begin with?

One Way
Think The total is unknown.
35 were given away and 21 are left.
Write an Equation
x – 35 = 21
21 + 35 = 56, so 56 is the total.
x = 56

Another Way
Think 35 were given away. Rori has 21 left.
The total is unknown.
Write an Equation
35 + 21 = x
35 + 21 = 56, so 56 is the total.
x = 56
Rori had 56 balloons to begin with.

Explain It

Question 1.
Why do both ways use addition to solve for x?
Answer:

Question 2.
How can you check if 56 is a reasonable answer?
Answer:

Read and Understand

What do I know?
Susan has 42 CDs and Larry has 26 CDs.
What am I asked to find?
The difference between the number of CDs from these two collections

Plan and Solve

Draw a Picture

Write an Equation
Let n = the number of
additional CDs Susan has.
42 – 26 = n

Susan has 16 more CDs in her collection than Larry

Guided Practice*

Do you know HOW?

Draw a picture and write an equation. Solve.

Question 1.
Alec prints digital photos at a camera store. The first order was for 24 prints. The second order was for 85 prints, and the third for 60 prints. How many fewer prints were in the first order than the third order?
Answer:

Question 2.
What phrase from the above example gives you a clue that you will use subtraction in your drawing to solve the problem?
Answer:

Question 3.
Write a Problem Write a real-world problem that uses subtraction and can be solved by drawing a picture and writing an equation.
Answer:

Independent Practice

In 4, copy and complete the picture. Then write an equation and solve.

Question 4.
Rose needs 22 tacos for a party. She has made 12 tacos so far. How many more tacos does Rose need to make?

In 5, draw a picture, write an equation in two different ways, then solve.

Question 5.
Aryanna is planning to spend a certain number of days on a trip to Florida. If she plans to spend 5 of the days in Orlando, she’ll have 16 more days for the rest of her vacation. How many days does Aryanna plan to spend in Florida?
Answer:

In 6, use the bar graph at the right.

Question 6.
Foster Middle School raised money to help care for some endangered animals. The bar graph shows the number of animals they will help with the money raised.
a. How many sea turtles and snow leopards can they help?
b. What is the difference between the greatest number of animals to be helped and the least number to be helped?
c. Show how you can use mental math to find the total number of animals helped.

Question 7.
Writing to Explain Don is adding 407 and 512. How do you know his sum will be less than 1,000?
Answer:

Question 8.
Writing to Explain Is 1,200 a good estimate for the difference of 4,725 – 2,689? Explain.
Answer:

Question 9.
A planetarium is 39 miles from Marco’s school. The class leaves for the field trip at 8:00 A.M. After driving for 17 minutes and traveling 15 miles, the driver of the bus got caught in traffic. How many more miles are left to travel to the planetarium? Write an equation to solve.

Answer:

Question 10.
Marlee is taking a class to improve her reading. She began reading a book on Monday and completed 3 pages. Tuesday she read 6 pages, Wednesday, 12 pages. If this pattern continues, how many pages will Marlee read on Friday?
Answer:

Think About the Process

Question 11.
Three fifth-grade classes took a survey and found that 35 students take the bus to school, 25 come by car, 15 walk, and 5 ride their bikes. Which shows how to find how many more students take the bus than walk?
A. Subtract 35 from 5
B. Subtract 15 from 35
C. Add 15 and 35
D. Add 35 and 5
Answer:

Question 12.
Darcy brought home 43 seashells from his vacation. Rich brought home x shells. Together they brought home 116 seashells. Which equation can you solve to find the number of shells Rich brought home?
A. 43 + x = 116
B. 116 + x = 43
C. 116 + 43 = x
D. x – 43 = 116
Answer:

Stop and Practice

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

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

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

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Question 14.
1.17 – 0.362
Answer:

Question 15.
4.9 – 1.003
Answer:

Question 16.
6.73 – 4.816
Answer:

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

Question 17.

Answer:

Question 18.

Answer:

Question 19.

Answer:

Question 20.

Answer:

Question 21.

Answer:

Number Sense

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

Question 22.
The sum of 56,141 and 3,052 is less than 59,000.
Answer:

Question 23.
The sum of 50.73 and 40.22 is greater than 90 but less than 92.
Answer:

Question 24.
The difference of 63,432 and 21,089 is greater than 41,000 and less than 43,000.
Answer:

Question 25.
The difference of 3,762 – 1,413 is 13 more than 2,362.
Answer:

Question 26.
The sum of 26.96 + 32.25 is 0.04 less than 59.25.
Answer:

Question 27.
The difference of 56.13 and 12.95 is closer to 44 than 43.
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 2.2 Rounding Whole Numbers and Decimals

How can you round whole numbers and decimals?
Rounding replaces one number with another number that tells about how many or how much. Round 634 to the nearest hundred.

Another Example

How do you round 2.36 to the nearest tenth? Is 2.36 closer to 2.3 or 2.4?
Think Is 2.36 closer to 2.3 or 2.4?

Step 1
Find the rounding place. Look at the digit to the right of the rounding place.
2.36

Step 2
If the digit is 5 or greater, add 1 to the rounding digit. If the digit is less than 5, leave the rounding digit alone.
Since 6 > 5,
add 1 to the 3.

Step 3
Drop the digits to the right of the rounding digit.
2.36 rounds to 2.4

Guided Practice*

Do you know HOW?

In 1 through 6, round each number to the place of the underlined digit.

Question 1.
16
Answer:

Question 2.
56.1
Answer:

Question 3.
1.32
Answer:

Question 4.
427,841
Answer:

Question 5.
1,652
Answer:

Question 6.
582,062
Answer:

Do you UNDERSTAND?

Question 7.
To round 7,458 to the nearest hundred, which digit do you look at? What is 7,458 rounded to the nearest hundred?
Answer:

Question 8.
A runner is running on a track with markers every 10 meters. If the runner has run 368 meters, is she closer to the 360-meter marker or
the 370-meter marker?
Answer:

Step 1
Find the digit in the rounding place. Underline this digit.
634

Step 2
Look at the digit to the right of the rounding place. If this digit is 5 or greater, add 1 to the rounding digit. If the digit is less than 5, leave the rounding digit alone.

Leave 6 the same

Step 3
Change all the digits to the right of the rounding digit to zeros.
634 rounds to 600.

Independent Practice

In 9 through 16, round each whole number to the place of the underlined digit.

Question 9.
677
Answer:

Question 10.
4,526
Answer:

Question 11.
12,064
Answer:

Question 12.
573
Answer:

Question 13.
34,739
Answer:

Question 14.
59,304
Answer:

Question 15.
930,998
Answer:

Question 16.
748,397
Answer:

In 17 through 24, round each number to the place of the underlined digit.

Question 17.
75.8
Answer:

Question 18.
0.758
Answer:

Question 19.
643.82
Answer:

Question 20.
0.472
Answer:

Question 21.
84.732
Answer:

Question 22.
738.29
Answer:

Question 23.
5.028
Answer:

Question 24.
23.009
Answer:

Problem Solving

Question 25.
The world’s largest aloha shirt is 4.26 meters around the chest. Round 4.26 to the nearest ones place and nearest tenths place.
Answer:

Question 26.
In the first 3 quarters of a basketball game, a team scored 17, 25, and 13 points. Their final score was 75. How many points did the team score in the fourth quarter?
Answer:

Question 27.
An African Watusi steer’s horn measures 95.25 cm around. What is 95.25 when rounded to the nearest tenth? Nearest whole number? Nearest ten?
Answer:

Question 28.
In a recent year, the population of Illinois was 12,653,544. What is that population when rounded to the nearest million?
A. 10,000,000
B. 12,000,000
C. 12,600,000
D. 13,000,000
Answer:

Question 29.
The world land speed record set on October 15, 1997, was 763.03 miles per hour. What is this speed rounded to the nearest ones place?
Answer:

Envision Math 4th Grade Textbook Answer Key Topic 1.3 Comparing and Ordering Whole Numbers

Comparing and Ordering Whole Numbers

How do you compare numbers?

Earth is not perfectly round. The North Pole is 6,356 kilometers from Earth’s center. The equator is 6,378 kilometers from the center. Which is closer to the Earth’s center: the North Pole or the equator?

Another Example

How do you order numbers?
The areas of 3 continents on Earth are shown in the table at the right. Which shows the areas in order from least to greatest?
A. 9,450,000; 4,010,000; 6,890,000
B. 4,010,000; 9,450,000; 6,890,000
C. 6,890,000; 9,450,000; 4,010,000
D. 4,010,000; 6,890,000; 9,450,000

Step 1
Plot the numbers on a number line.

Step 2
Order the numbers. On a number line, numbers to the right are greater.
Reading from left to right, 4,010,000; 6,890,000; 9,450,000.
The correct choice is D.

Explain It

Question 1.
Describe how you would order the continents’ areas using place value.
Answer:

Question 2.
Reasonableness How can you rule out choices A and C as the correct answer?
Answer:

Step 1

Use place value to compare numbers.
Write the numbers, lining up places. Begin at the left and compare.
6,356
6,378
The thousands digit is the same in both numbers.

Step 2

Look at the next digit.
6,356
6,378
The hundreds digit also is the same in both numbers.

Step 3

The first place where the digits are different is the tens place. Compare.

The symbol > means is greater than,
and the symbol < means is less than.
The North Pole is closer to Earth’s center than the equator.

Guided Practice*

Do you know HOW?

In 1 through 4, copy and complete by writing > or < for each .

Question 1.
2,643 2,801
Answer:

Question 2.
6,519 6,582
Answer:

Question 3.
785 731
Answer:

Question 4.
6,703 6,699
Answer:

In 5 and 6, order the numbers from least to greatest.

Question 5.
7,502 6,793 6,723
Answer:

Question 6.
80,371 15,048 80,137
Answer:

Question 7.
Writing to Explain Why would you look at the hundreds place to order these numbers? 32,463 32,482 32,947 Answer:

Question 8.
Compare the area of Europe and South America. Which is greater?
Answer:

Independent Pracice

In 9 through 16, copy and complete by writing > or < for each .

Question 9.
221,495 210,388
Answer:

Question 10.
52,744 56,704
Answer:

Question 11.
138,752 133,122
Answer:

Question 12.
4,937 4,939
Answer:

Question 13.
22,873 22,774
Answer:

Question 14.
1,912,706 1,913,898
Answer:

Question 15.
412,632 412,362
Answer:

Question 16.
999,999,999 9,990,999
Answer:

Independent Practice

Leveled Practice In 17 through 20, copy and complete the number lines. Then use the number lines to order the numbers from greatest to least.

Question 17.
27,505 26,905 26,950

Answer:

Question 18.
3,422,100 3,422,700 3,422,000

Answer:

Question 19.
7,502 7,622 7,523 7,852

Answer:

Question 20.
3,030 3,033 3,003

Answer:

In 21 through 28, write the numbers in order from least to greatest.

Question 21.
57,535 576,945 506,495
Answer:

Question 22.
18,764 18,761 13,490
Answer:

Question 23.
25,988 25,978 25,998
Answer:

Question 24.
87,837 37,838 878,393
Answer:

Question 25.
43,783 434,282 64,382
Answer:

Question 26.
723,433 72,324 72,432
Answer:

Question 27.
58,028 85,843 77,893
Answer:

Question 28.
274,849,551 283,940,039 23,485,903
Answer:

Problem Solving

Question 29.
Estimation Aaron added 57 and 20 and said the answer is greater than 100. Is Aaron correct?
Answer:

Question 30.
Number Sense Write three numbers that are greater than 780,000 but less than 781,000.
Answer:

Question 31.
Reasoning Could you use only the millions period to order 462,409,524, 463,409,524, and 463,562,391?
Answer:

Question 32.
Describe how to compare 7,463, 74,633, and 74,366 from least to greatest.
Answer:

Question 33.
The heaviest snake living in captivity is a Burmese Python named “Baby.” An average Anaconda snake weighs 330 pounds. Which snake weighs more?

Answer:

Question 34.
Which list of numbers is in order from least to greatest?
A. 1,534 1,576 1,563
B. 18,732 18,723 18,765
C. 234,564 234,568 234,323
D. 383,847 383,848 383,849
Answer:

Question 35.
Asia and Africa are the two largest continents on Earth. Which continent is larger?

Answer:

Question 36.
The chart below shows the number of game cards owned by the top collectors in one school. Which student had the most cards?
A. Shani
B. Lin
C. Ariel
D. Jorgé

Answer:

Question 37.
The Atlantic Ocean has an area of 33,420,000 square miles. This area is between which numbers?
A. 33,400,000 and 33,440,000
B. 33,000,000 and 33,040,000
C. 33,100,000 and 33,419,000
D. 33,430,000 and 33,500,000
Answer:

Envision Math 6th Grade Textbook Answer Key Topic 2.2 Properties of Operations

Properties of Operations

How can you use properties of operations to rewrite expressions?
Answer:
The Commutative Property of Addition states the order in which numbers are added does not change the sum of the numbers. The Commutative Property of Multiplication states the order in which numbers are multiplied does not change the product of the numbers.

Guided Practice

Do you know HOW?
Find each missing number.Tell what property is shown.
Question 1.
19 + (42 + 8) = (☐ + 42) + 8
Answer:
19; Associative Property of Addition
Explanation:

Question 2.
12 + 8 = ☐ +12
Answer:
8; Commutative Property of Addition
Explanation:

Question 3.
42 × 8 × 3 = 42 × 8 × ☐ × 3
Answer:
1; Identity Property of Multiplication
Explanation:

Question 4.
32 × 85 = 85 × ☐
Answer:
32; Commutative Property of Multiplication
Explanation:

Do you UNDERSTAND?
Question 5.
For the Identity Property, why does addition involve a zero and multiplication involve a one? Why don’t they both use one or both use zero?
Answer:
See margin.
Explanation:

Question 6.
Yuen Lee put 3 cartons of markers in the closet. Each carton contains 3 rows of 7 boxes. Use one of the Associative Properties to show two different ways of finding the number of marker boxes.
Answer:
(3 × 3) × 7; 3 × (3 × 7)
Explanation:

Independent Practice

Find each missing number. Tell what property or properties are shown.
Answer:
See margin.
Explanation:

Question 7.
☐ × (14 × 32) = (5 × 14) × 32
Answer:

Question 8.
5 + 23 + 4 = 23 + 4 + ☐
Answer:

Question 9.
25 + 0 + (3 + 16) = (25 + ☐) + 3
Answer:

Question 10.
(7 + 1 2) + 4 = (7 + ☐) + 12
Answer:

Question 11.
(5 × 7) (3 × 8) = (5 × 3) × (8 × ☐)
Answer:

Question 12.
(43 × 1) × 4 = ☐ × 43
Answer:

Question 13.
(6 + 3) + 4 = 6 + (3 + ☐)
Answer:

Question 14.
(8 × 9) × ☐ = 8 × (9 × 10)
Answer:

Question 15.
7 × ☐ = 6 × 7
Answer:

Question 16.
15 + 48 = ☐ + 15
Answer:

Question 17.
8 + ☐ = 4 + 8
Answer:

Question 18.
(1 × 2) × 3 = ☐ × (2 × 3)
Answer:

The Associative Property of Addition states that the way numbers are grouped does not affect the sum.
a + (b + c) = (a + b) + c
2 + (8 + 10) = (2 + 8) + 10
The Associative Property of Multiplication states that the way numbers are grouped does not affect the product.
a × (b × c) = (a × b) × c
2 × (4 × 5) = (2 × 4) × 5
The Identity Property of Addition states that adding zero to a number does not change the number.
a + 0 = a
24 + 0 = 24
The Identity Property of Multiplication states that the product of a number and one is that number.
a × 1 × a
36 × 1 × 36

Find each missing number. Tell what property or properties are shown.
Question 19.
(41 × 43) × (3 × 19) = (41 × ☐) × (19 × 43)
Answer:

Question 20.
(5 × 3) × ☐ = 5 × (8 × 3)
Answer:

Question 21.
328 × 1 = ☐
Answer:

Question 22.
(12 + 0) × (1 × 12) = ☐ × ☐
Answer:

Problem Solving
For 23 and 24, use the table to the right.

Question 23.
Donnie and Pete live in Coldwater. They rode their bikes to Blanco and then to Pulga. Then they rode back home, using the same route. Write a number sentence using the Commutative Property of Addition to show the distances they rode each way.
Answer:

Question 24.
Once they rode from Pulga to Littleville, from Littleville to Zion, and then rode back to Pulga. How many miles did they ride that time?
Answer:

Question 25.
Think About the Proces Stage 15 of the Tour de France bicycle race includes legs from Gap to Embrun, Embrun to Guillestre, and Guillestre to Arvieux. One way to express these legs is 33.5 + (20.5 + 21.5). Which expression below is another way to express these legs?
A. (23 + 33.5) + (20.5 – 21.5)
B. (33.5 + 20.5) + 21.5
C. 33.5 + (20.5 × 21.5)
D. (33.5 × 21.5) + 20.5
Answer:

Question 26.
Write the standard form for 6.45 billion.
Answer:

Question 27.
Writing to Explain Can you use the Associative Property with subtraction and division? Use (14 – 8) – 2 and 24 o (4 o 2) to explain.
Answer:

Envision Math 3rd Grade Textbook Answer Key Topic 1.3 Greater Numbers

Greater Numbers

How can you read and write greater numbers?
Answer:
Capitol Reef National Park in Utah covers 241,904 acres of land.

Guided Practice

Do you know HOW?
Write each number in standard form.
Question 1.
three hundred forty-two thousand, six hundred seven
Answer:

Question 2.
ninety-eight thousand, three hundred twenty
Answer:

Question 3.
500,000 + 40,000 + 600 + 90 + 3
Answer:

Question 4.
What is the value of the 9 in the number 379,050?
Answer:

Do you UNDERSTAND?
Question 5.
Number Sense Ramos says the value of the digit 7 in 765,450 is 70,000. Do you agree? Why or why not?
Answer:

Question 6.
Writing to Explain Describe how 130,434 and 434,130 are alike and how they are different.
Answer:

Independent Practice

Write each number in standard form.
Question 7.
twenty-seven thousand, five hundred fifty
Answer:

Question 8.
800,000 + 20,000 + 6,000 + 300 + 50
Answer:

Write each number in expanded form.
Question 9.
46,354
Answer:

Question 10.
395,980
Answer:

Write the place of the underlined digit. Then write its value.
Question 11.
404,705
Answer:

Question 12.
163,254
Answer:

Question 13.
45,391
Answer:

Question 14.
983,971
Answer:

Question 15.
657,240
Answer:

How can you show 241,904 in different ways?
place-value chart:

standard form: 241, 904
expanded form: 200,000 + 40,000 + 1,000 + 900 + 4
word form: two hundred forty-one thousand, nine hundred four

Algebra Find each missing number.
Question 16.
26,305 = 20,000 + ☐ + 300 + 5
Answer:

Question 17.
801,960 = 800,000 + 1,000 + ☐ + 60
Answer:

Question 18.
400,000 + ☐ + 30 + 2 = 470,032
Answer:

Question 20.
300,000 + ☐ + 600 + 3 = 304,603
Answer:

Question 19.
618,005 = ☐ + 10,000 + 8,000 + 5
Answer:

Question 21.
200,000 + 4,000 + 60 + 3 = ☐
Answer:

Problem Solving

For 22-24, use the table.

Question 22.
Write the population of each city in the table in expanded form.
Answer:

Question 23.
Write the population of Columbus, OH in word form.
Answer:

Question 24.
Which cities listed have fewer than eight hundred thousand people?
Answer:

Question 25.
A new world record was set when 303,628 dominos fell. Write 303,628 in expanded form.
Answer:

Question 26.
Which is the word form of 805,920?
A. eighty-five thousand, ninety-two
B. eight hundred five thousand, ninety-two
C. eight thousand, five hundred ninety-two
D. eight hundred five thousand, nine hundred twenty
Answer: