Category: Envision Math

Envision Math 5th Grade Textbook Answer Key Topic 19.2 Histograms

Histograms

How do you make and interpret a histogram?
Answer:
A radio station recorded the ages of 25 callers in a phone survey.
This data can be shown by a histogram, a bar graph that groups data into equal intervals shown on the horizontal axis. There is no space between the bars.

Question.
Make a histogram to show the frequency of data in each age interval.

Answer:

Guided Practice

Do you know HOW?
Question 1.
The table shows the number of minutes 25 students spent on homework each night. How would the lengths of the bars compare if you made a histogram to show the data?

Answer:

Do you UNDERSTAND?
Question 2.
According to the histogram in Exercise 1, what fraction of the students surveyed spent 30-59 minutes on homework each night?
Answer:

Question 3.
In the example above, how can you tell that \(\frac{1}{5}\) of the people surveyed were in the 40-59 age group?
Answer:

Independent Practice
Question 4.
The table shows the results of a class survey about the amount of time students spend on their cell phones each day. Copy and complete the histogram shown at the right.

Answer:

Step 1: List the age intervals along the horizontal axis.
Step 2: Along the vertical axis mark the scale. List the greatest and least numbers in the survey results Choose an interval. Label the axes.
Step 3: Graph the data by drawing bars of the correct height. Title the graph.

Step 4: Interpret the graph. Twice as many people were in the 20-39 age group as in the 0-19 age group. Most people were in the 20-39 age group.
The group with the least number was the 60-79 age group.

Problem Solving

One class took a survey of the amount of money they spent on CDs over 3 months and made a histogram of the results. The histogram is shown at the right.

Question 5.
a. How many students were surveyed?
Answer:

b. What fraction of students spent between 0 and $9.99 on CDs?
Answer:

c. In which range of money spent did twice as many students buy CDs than in the $20-$29.99 range?
Answer:

Question 6.
Reasoning Selma says that a histogram shows that 4 times as many people in the 21-25 age group answered the survey than in the 36-40 age group. How does she know this from looking at the histogram?
Answer:

Question 7.
On a coordinate grid, Sue drew a path starting at (6, 2). She moved 2 spaces to the right and 3 units up. What is the ordered pair for the point where she stopped?
Answer:

Question 8.
On a class trip, Harry spent $28. Nate spent $6 less than Harry. Which expression could you use to find how much both boys spent?
A. 28 + 28 + 6
B. 28 + (28 – 6)
C. 28 – (28 + 6)
D. 28 – 28 – 6
Answer:

Question 9.
At 6 A.M., the temperature was -5°F. By noon, the temperature had increased by 12°F. What was the temperature at noon?
A. 17°F
B. 7°F
C. -7°F
D. -12°F
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 19.1 Bar Graphs and Picture Graphs

Review What You Know

Vocabulary

Choose the best term from the box,

Question 1.
A(n) ? is either of two perpendicular lines in a graph.
Answer:

Question 2.
A(n) ? is an exact location in space,
Answer:

Question 3.
A pair of numbers used to locate a point on a graph is called a(n) ? .
Answer:

Number Lines

Use the number line to answer 4 through 6

Question 4.
Which point is halfway between 1 and 2?
Answer:

Question 5.
Which point is closest to 1 than to 2?
Answer:

Question 6.
Which point is closest to 2 than to 1?
Answer:

Writing Fractions
Question 7.
If 3 out of 6 marbles are red, what fraction, in simplest form, names the red marbles?
Answer:

Question 8.
If 1 out of 5 apples is green, what fraction names the part of the apples that are NOT green?
Answer:

Division Patterns
Writing to Explain Write an answer to the question.
Question 9.
How is the number of zeros in the quotient of 45,000 ^ 9 related to the number of zeros in the dividend?
Answer:

Bar Graphs and Picture Graphs

How do you display data collected from a count or measure?
Answer:
Students were surveyed about what they do after school. The results were displayed in a bar graph.

A bar graph uses rectangles (bars) to show and compare data that tells how many or how much.
Answer:

Another Example
How can you make and interpret picture graphs?
Answer:
Sonya gathered data about the number of ducks in some of the 2006 rubber duck derbies. Sonya listed the data in a frequency table.
Then she made a picture graph to display the data.

A picture graph uses pictures or symbols to represent data. Each picture represents a certain amount in the data.

Explain It
Question 1.
Which is easier to interpret, a picture graph or a frequency table? Explain.
Answer:

Step 1: List the survey answers along one axis.
Step 2: Choose an interval, the difference between adjoining numbers on an axis. Label both axes. Along the other axis mark the scale, the series of numbers at equal distances. Begin with 0 and include the least and greatest numbers in the survey results.
Step 3: Graph the data by drawing bars of the correct length or height.
Step 4: Title the graph.
Interpret the Graph
Most students play sports. The fewest number of students do chores.

Guided Practice

Do you know HOW?
In 1 and 2, decide if a bar graph or picture graph would better present the data.
Question 1.
The number of cats, dogs, and pet birds in a neighborhood
Answer:

Question 2.
The number of cattle on three ranches
Answer:

Do you UNDERSTAND?
Question 3.
Could the data in the example of the bar graph above be presented in a picture graph? Explain.
Answer:

Question 4.
How are bar graphs and picture graphs similar? How are they different?
Answer:

Independent Practice

In 5 through 8, answer the questions about the picture graph shown to the right.

Question 5.
How many people are represented by each picture?
Answer:

Question 6.
What is the difference in populations between the second most populated city and the least populated city?
Answer:

Question 7.
About how many people live in the two most populated cities?
Answer:

Question 8.
Can this data be presented in a bar graph? Explain.
Answer:

Problem Solving

In 9 through 12, use the bar graph.

Question 9.
What interval was used for the scale?
Answer:

Question 10.
About how many more eagle pairs were there in 1994 than in 1990?
Answer:

Question 11.
Writing to Explain Based on the graph, do you think the number of pairs of eagles will increase or decrease? Explain.
Answer:

Question 12.
Between which 2 years did the number of pairs of eagles increase the most?
Answer:

In 13 through 15, use the frequency table.

Question 13.
If you were to draw a bar graph for this frequency table, what scale would you use?
Answer:

Question 14.
How many more U.S. residents visited France than Italy in 2004?
Answer:

Question 15.
Writing to Explain
Why do you think more residents went to Mexico and Canada than the other destinations?
Answer:

16. Think About the Process
juli0 bought 3 dozen eggs. He had 13 eggs left after making egg salad for the picnic. Which shows how to find how many eggs Julio used?
A. (13 – 12) × 3
B. (12 – 3) – 13
C. (13 × 12) – 3
D. (3 × 12) – 13
Answer:

Question 17.
Think About the Process
12 soccer teams with 10 students on each team. The school wants to have only 8 soccer teams. Which shows how to find the number of students that would be on each team if there were only 8 teams?
A. Multiply 10 by 8.
B. Divide 120 by 8.
C. Divide 8 by 120.
D. Multiply 12 by 8.
Answer:

Question 18.
Point A represents which mixed number on this number

Answer:

Stop and Practice

Find each difference.
Question 1.
-5 ____ +6
Answer:

Question 2.
+7 _____ +3
Answer:

Question 3.
-3 _____ +4
Answer:

Question 4.
+8 ___ +9
Answer:

Question 5.
-10 ____ +2
Answer:

Question 6.
-1 ____ +1
Answer:

Find each product. Simplify if possible.
Question 7.
\(\frac{1}{2}\) × \(\frac{6}{10}\)
Answer:

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

Question 9.
\(\frac{1}{6}\) × \(\frac{3}{4}\)
Answer:

Question 10.
8 × \(\frac{5}{8}\)
Answer:

Question 11.
\(\frac{1}{4}\) × \(\frac{1}{5}\)
Answer:

Question 12.
\(\frac{3}{8}\) × \(\frac{1}{4}\)
Answer:

Question 13.
\(\frac{9}{10}\) × \(\frac{1}{10}\)
Answer:

Question 14.
\(\frac{3}{4}\) × \(\frac{1}{3}\)
Answer:

Question 15.
\(\frac{5}{6}\) × \(\frac{1}{10}\)
Answer:

Find each quotient. Simplify if possible.
Question 16.
3\(\frac{2}{3}\) ÷ 1\(\frac{5}{6}\)
Answer:

Question 17.
1\(\frac{1}{2}\) ÷ 1\(\frac{1}{3}\)
Answer:

Question 18.
6 ÷ \(\frac{7}{8}\)
Answer:

Question 19.
1\(\frac{5}{12}\) ÷ 1\(\frac{5}{12}\)
Answer:

Error Search Find each answer that is not correct. Write it correctly and explain the error.
Question 20.

Answer:

Question 21.

Answer:

Question 22.

Answer:

Question 23.

Answer:

Question 24.

Answer:

Number Sense

Estimating and Reasoning Write whether each statement is true or false. Explain your reasoning.
Question 25.
If a < 0 and b > 0, then a – b is negative.
Answer:

Question 26.
The product of 25 and 2,002 is 50 less than 50,000.
Answer:

Question 27.
The expression (64 ÷ 8) + 2 × (25 ÷ 5) is 50.
Answer:

Question 28.
The sum of 22,256 and 43,008 is less than 65,000.
Answer:

Question 29.
The product of 6\(\frac{3}{5}\) and 7\(\frac{1}{9}\) is greater than 42.
Answer:

Question 30.
The quotient of 13.8 ÷ 2.1 is greater than 4 and less than 7.
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 20 Reteaching

Reteaching

Set A, pages 452-453

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

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

Angle E is congruent to angle A.

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

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

Answer:

Question 2.

Answer:

Set B, pages 454-456

Construct a line perpendicular to another line.
Answer:

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

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

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

Answer:

Set C, pages 458-460

Construct a triangle congruent to triangle DEF.

Answer:

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

Construct a rectangle ABCD.
Answer:

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

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

Answer:

Question 2.
Construct a rectangle KLMN.
Answer:

Set D, pages 462-463

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

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

Answer:

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

Test Prep

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

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

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

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

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

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

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

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

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

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

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

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

Answer:

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

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

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

Problem Solving

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

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

Guided Practice

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

Answer:

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

Answer:

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

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

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

Answer:

Question 6.

Answer:

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

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

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

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

Here are 3 possible solutions.

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

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

Answer:

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

Answer:

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

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

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

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

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

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

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

Constructing Shapes

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

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

Answer:

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

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

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

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

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

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

Step 1
Construct ∠P congruent to ∠X.

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

Step 3
Draw segment QR. ∆PQR ≅ ∆XYZ

Guided Practice

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

Answer:

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

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

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

Independent Practice

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

Answer:

Question 6.

Answer:

Question 7.

Answer:

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

Answer:

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

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

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

Answer:

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

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

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

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

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

Answer:

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

Mixed Problem Solving

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

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

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

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

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

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

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

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

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

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

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

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

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

Answer:

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

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

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

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

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

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

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

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

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

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

Guided Practice

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

Answer:

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

Answer:

Do you UNDERSTAND?
Question 3.
Writing to Explain In Step 2 of the example above, why is it necessary to set the compass wider than the length of segment WL?
Answer:

Question 4.
Look at the line TC you constructed in Problem 1 that is perpendicular to line CD. Use point Tand construct a line perpendicular to line TC. How is that line related to line CD?
Answer:

Independent Practice

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

Answer:

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

Answer:

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

Answer:

Problem Solving

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

Question 8.
If it costs $155 per mile to construct railroad tracks, how much would it cost to build tracks from San Francisco to Los Angeles?
Answer:

Question 9.
Estimation Railroad ties are set about 2 feet apart. About how many railroad ties are there between Eureka and Sacramento?
Answer:

Question 10.
If you are comparing two negative integers on a number line, how can you tell which one is greater?
Answer:

Question 11.
Four friends played golf. Their scores were +3, -1, *4, and ~4 in relation to par. The least score wins. Arrange the scores from best to worst.
Answer:

Question 12.
Algebra Ted has 15 trophies. This is 5 times as many as Harold has. How many trophies does Harold have? Write and solve an equation to answer the question.
Answer:

Question 13.
Writing to Explain Explain how perpendicular lines are similar to intersecting lines.
Answer:

Question 14.
Use the figure to tell whether the statements are true or false

a. \(\overline{P Q}\) is parallel to \(\overline{U V}\)
b. \(\overline{P Q}\) intersects \(\overline{U V}\)
c. \(\overline{P Q}\) is perpendicular to \(\overline{U V}\)
Answer:

Question 15.
Estimation The gas tank in Shondra’s car can hold 18 gallons. Her car gets about 22 miles per gallon of gas. On a recent trip, Shondra used about 12 gallons of gas. Which is the best estimate of the distance Shondra drove?
A. 120 miles
B. 200 miles
C. 400 miles
D. 1,200 miles
Answer:

Stop and Practice

Find each difference. Simplify if possible.
Question 1.

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. Simplify if possible.
Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Question 14.

Answer:

Question 15.

Answer:

Question 16.

Answer:

Question 17.

Answer:

Question 18.

Answer:

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

Answer:

Question 20.

Answer:

Question 21.

Answer:

Question 22.

Answer:

Question 23.

Answer:

Number Sense
Estimating and Reasoning Write whether each statement is true or false. Explain your reasoning.
Question 24.
The quotient of 1,546 ÷ 5 is less than 300.
Answer:

Question 25.
The product of 9.32 and 4.7 is less than 36.
Answer:

Question 26.
The difference of 6,631 and 3,021 is greater than 2,000 and less than 4,000.
Answer:

Question 27.
The sum of 43.04 + 21.56 is 0.04 more than 64.56.
Answer:

Question 28.
When x = -9, the expression x + +5 equals -14.
Answer:

Question 29.
The expression (4\(\frac{5}{6}\) + 3\(\frac{1}{2}\) – × \(\frac{3}{4}\)) × 0 equals 0.
Answer:

Envision Math 5th Grade Textbook Answer Key Topic 20.1 Constructing Angles

Review What You Know

Vocabulary
Choose the best term from the box.

Question 1.
A ? extends in two directions infinitely.
Answer:

Question 2.
A ? has one endpoint and extends in one direction, while a ? has two endpoints.
Answer:

Question 3.
? lines intersect at one point and create four right angles.
Answer:

Identifying Angles
Classify each angle as acute, obtuse, straight or right.
Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Patterns
Find the next two numbers in each pattern.
Question 8.
1.5, 1.7, 1.9, 2.1,2.3, ☐, ☐
Answer:

Question 9.
26, 21,16, 11, ☐, ☐
Answer:

Shapes
Writing to Explain Write an answer for each question.
Question 10.
Can a triangle have two obtuse angles?
Answer:

Question 11.
Is a square always a rectangle?
Answer:

Constructing Angles

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

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

Answer:

Guided Practice

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

Answer:

Question 2.

Answer:

Do you UNDERSTAND?
Question 3.
Writing to Explain Why is it important to keep the same compass setting in Step 1?
Answer:

Question 4.
How can you tell if a constructed angle is congruent to the original angle?
Answer:

Independent Practice

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

Answer:

Question 6.

Answer:

Question 7.

Answer:

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

Answer:

Question 9.
Mario has saved a number of quarters, nickels, dimes, and pennies. He will use $3.93 to buy a new toy for his dog. Using the fewest coins, what combination of coins will equal $3.93?
Answer:

Question 10.
Justin climbed 15 steps to the second floor of a building. Each step is 8 inches high. How many feet higher is the second floor than the first?
Answer:

Question 11.
Diamond cutters must cut angles precisely so that the greatest amount of light is reflected from the facets. Refer to the photo of the diamond below. Construct an angle congruent to ∠W.

Answer:

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

Envision Math 6th Grade Textbook Answer Key Topic 2 Reteaching

Reteaching

Set A, pages 28-29

Variables stand for unknown values.
The number sentence 24 + n means “the sum of 24 and a number.” The unknown number is a variable that is expressed by a letter, n.
Answer Terms
Addition → Sum
Subtraction → Difference
Multiplication → Product
Division → Quotient

Remember that you can use any letter as a variable that stands for an unknown value.

Write the phrases as algebraic expressions.
Question 1.
22 less forks than a number, f
Answer:

Question 2.
48 times a number of game markers, g
Answer:

Question 3.
a number of eggs, e, divided by 12
Answer:

Question 4.
3 times the number of milk cartons, m, used by the 6th grade class
Answer:

Set B, pages 30-31

The properties of operations help you evaluate expressions.

Evaluate the expression: 4 + 8 + 3 + 2
Following properties of operations:
4 + 8 + 3 + 2 = 4 + 3 + 8 + 2 = 7 + 10 = 17

Remember that when the properties of operations are not followed, numerical expressions are computed incorrectly.

Tell what properties are shown
Question 1.
3(4 × 32) = (3 × 4)32
Answer:

Question 2.
21 × 10 = 10 × 21
Answer:

Question 3.
9 + 8 + 4 = 8 + 4 + 9
Answer:

Question 4.
9 + 0 = 9
Answer:

Question 5.
6 × 8 = 8 × 6
Answer:

Question 6.
5 + 4 = 4 + 5
Answer:

Question 7.
6 × (4 × 3) = (6 × 4) × 3
Answer:

Question 8.
8 + (2 + 4) = (8 + 2) + 4
Answer:

Question 9.
9 + 6 = 6 + 9
Answer:

Question 10.
12 + 0 = 12
Answer:

Question 11.
425 × 1 = 425
Answer:

Question 12.
(8 × 5) × 4 = 4 × (5 × 8)
Answer:

Set C, pages 32–34

The order of operations helps you get the correct answer. The order of operations rules are:
Step 1: Compute inside parentheses.
Step 2: Evaluate terms with exponents.
Step 3: Multiply and divide from left to right.
Step 4: Add and subtract from left to right.

Evaluate 8 + 6 × 9 – 4 ÷ 2.
First, multiply and divide. 8 + 54 – 2
Then, add and subtract. 60

Remember that when the order of operations rules are followed, it helps you get the correct answer.

Use parentheses to make each sentence true.
Question 1.
9 + 8 – 2 × 7 + 1 = 1
Answer:

Question 2.
40 – 4 × 4² ÷ 2 = 8
Answer:

Question 3.
5 × 5 – 3 – 2 = 0
Answer:

Question 4.
8 + 12 ÷ 4 + 6 = 11
Answer:

Question 5.
9 + 8 ÷ 2 × 4 + 3² = 19
Answer:

Question 6.
6 × 2 – 1 + 5² = 31
Answer:

Question 7.
8 × 3 + 8 – 2² = 84
Answer:

Question 8.
50 – 3 × 6 + 2 + 4² = 42
Answer:

Set D, pages 36-37

Use the Distributive Property to evaluate mentally.
8(42)
Break the numbers apart to find numbers that
are easier to multiply mentally.
8(40 + 2)
Apply the Distributive Property.
8(40) + 8(2)
Multiply the separate sections. Add the products.
320 + 16 = 336

Remember that the Distributive Property says that multiplying a sum by a number is the same as multiplying each addend by the number and adding the products.

Use the Distributive Property to evaluate mentally.
Question 1.
5(41) + 5(9)
Answer:

Question 2.
3(45)
Answer:

Question 3.
4(23)
Answer:

Question 4.
9(32) + 9(8)
Answer:

Question 5.
3(27)
Answer:

Question 6.
6(7) + 6(23)
Answer:

Set E, pages 38-40

Find 4 × 18 × 25 using compatible numbers to compute mentally.
Look for compatible 4 × 18 × 25
numbers that are easy
to compute. 4 × 25 × 18
Then, do the remaining calculation. 100 × 18 = 1,800
So, 4 × 18 × 25 = 1,800.

Remember to find compatible numbers to make your mental math easier.

Compute mentally.
Question 1.
15 + 67 + 25
Answer:
107
Explanation:

Question 2.
463 – 333
Answer:
130
Explanation:

Question 3.
6 × 23 × 5
Answer:
690
Explanation:

Question 4.
250 × 6 × 4
Answer:
6,000
Explanation:

Question 5.
921 + 529
Answer:
1,450
Explanation:

Question 6.
297 – 100
Answer:
197
Explanation:

Question 7.
2 × 8 × 5
Answer:
80
Explanation:

Question 8.
20 × 16 × 5
Answer:
1,600
Explanation:

Set F, pages 42-43

Evaluate this expression for x = 2 and y = 3.
Question 1.
7x – 3y
Answer:
7(2) – 3(3) ← Use substitution.
14 – 9 = 5 ← Compute.

Question 2.
4x + 2y
Answer:
4(2) + 2(3) ← Use substitution.
8 + 6 = 14 ← Compute.

Question 3.
9x ÷ 3y
Answer:
9(2) ÷ 3(3) ← Use substitution.
18 ÷ 9 = 2 ← Compute.

Remember that using substitution means to replace the variables with the chosen values.

Evaluate each expression for x = 4 and y = 6.
Question 1.
12x – 7y
Answer:
6
Explanation:

Question 2.
3x + 18
Answer:
30
Explanation:

Question 3.
11 x + 4
Answer:
48
Explanation:

Question 4.
8x + 2y
Answer:
44
Explanation:

Question 5.
6x ÷ 2y
Answer:
2
Explanation:

Question 6.
8x – 5y
Answer:
2
Explanation:

Question 7.
7x – 4y
Answer:
4
Explanation:

Question 8.
4y – 9
Answer:
15
Explanation:

Question 9.
22y – 6
Answer:
126
Explanation:

Question 10.
9x – 3y
Answer:
18
Explanation:

Question 11.
4x ÷ (y – 2)
Answer:
4
Explanation:

Question 12.
10y – 8x
Answer:
28
Explanation:

Set G, pages 44–45

You can write an algebraic expression that explains an input/output relationship. If x is 4, how can you express 9?

Try: 2x + 1 = 9
See if that works for the other input values.
2 × 8 + 1 = 17
2 × 11 + 1 = 23
Yes, it works!

Remember that input/ output tables can help you see patterns in expressions.

Use this input/ output table for 1 and 2.

Question 1.
Students earn prize points for selling fundraising items. Write an algebraic expression that explains the relationship between input and output values for a student who sells between $41 and $60.
Answer:
3x
Explanation:

Question 2.
How many prize points would a student earn for selling $115 worth of items?
Answer:
4 × 115 = 460
Explanation:

Set H, pages 46-48

Making a table to organize your data helps to identify patterns and quickly find solutions. When making a table, include labels for the variable and the expression. Enter the values of x you want to find. Then solve the expression for each value.
Ginny is paid $12 a week for doing chores. She puts the money in her savings account. If she started out with $112, find out how much money she has in her account after x weeks.
Step 1: Identify the expression.
$112 + $12x
Step 2: Make a table.

Remember to choose labels based on the information to be found.

Write an equation for each problem. Then make a table to solve it.
Question 1.
Anna walks her dog 2 miles a day, 5 days a week. Find out how far Anna and her dog walked after x weeks.
Answer:
(2 × 5)x
Explanation:

Question 2.
Todd earns $500 a week, plus $50 every time he sells a computer. Find out how much money Todd earns per week when he sells x computers.
Answer:
500 + 50x
Explanation:

Envision Math 6th Grade Textbook Answer Key Topic 2.8 Problem Solving

Problem Solving

Make a Table
The Douglas family had $700 in their road-trip fund. They spent $75 each day on their trip. If x equals the number of days, write an expression that describes the amount of money left in the fund after x days.

Question.
Make a table to show the values of the expression for x = 3 days, x = 5 days, and x = 9 days.
Answer:

Guided Practice

Do you know HOW?
Question 1.
The sixth-grade chess club is washing cars for a fund-raiser. They started with $150 in their fund and are charging $5 per car. Use the expression 150 + 5x to copy and complete the table, to find how much money the chess club will have after washing 25, 31, and 54 cars.

Answer:

Do you UNDERSTAND?
Question 2.
How do you know what labels to use in a table?
Answer:

Question 3.
Write a Problem Use the table to write a word problem that could be solved using the table below.

Answer:

Independent Practice

Question 4.
For every A Josh earns on his report card, he is given 2 movie passes. He still has 2 movie passes left from his last report card. If x equals the number of A’s Josh earns, use the expression 2x + 2 to copy and complete the table to find how many movie passes Josh will have for 1,2, or 3 A’s.

Answer:

Plan and Solve
Write an expression that describes the amount of money left in the fund after x days.

Total in fund – $75(number of days)
700 – 75x

Plan and Solve
Make a table to solve for different values of x. Include labels for the variable and the expression.
Enter the values of x you want to find. Then solve the expression for each value.

Question 5.
Kat is playing a game called “500.” Each player starts with 500 points and loses 10 points for each question answered correctly. The first player to reach 0 points wins. Which expression represents how many points Kat will have if she answers x questions correctly?
A. 500x
B. 500 – 10x
C. 500 + 10x
D. 10x – 500
Answer:
B. 500 – 10x
Explanation:

Question 6.
Copy and complete the table for Exercise 5 to find how many points Kat will have if she answers 9, 13, and 24 questions correctly.
Answer:

Explanation:

Question 7.
Jordan is playing in a charity basketball game. The local barber pledged to pay $2 for every point he scores. The local grocery store will give a one-time donation of $75. Which expression represents how much money Jordan will raise if he scores x points?
A. 75 + 2x
B. 77x
C. 75 + 4x
D. 75 – 2x
Answer:
A. 75 + 2x
Explanation:

Question 8.
Jeremy started a club to help senior citizens use computers. On the first day, he was the only member. On the second day, two friends joined. Each day after that, two more members joined. If x equals the number of days, evaluate the expression 1 + 2(x – 1) to find the membership of the club on the 10th day.
Answer:
19 people
Explanation:

Question 9.
The camp chef is making waffles for breakfast. The recipe calls for 3 cups of milk for every batch. If x equals the number of batches, copy and complete the table to show how much milk the chef needs for 3, 7, and 10 batches.
Answer:

Explanation:

Independent Practice

Use the information at right for 10 through 14.

Question 10.
Carver bought some plants at the Garden Center sale. On his bill, he saw that he had paid $20 for 5 plants. What size did Carver buy?
Answer:
He bought 5 large plants.
Explanation:

Question 11.
Sally and her mother went to the sale at the Garden Center. Sally bought x large plants and y small plants. She paid with a twenty-dollar bill. Make a table using the expression 20 – (4x + 2y) to show how much change she received if she bought 2 large plants and 4 small plants; 4 large plants and 2 small plants; or 1 large plant and 7 small plants.
Answer:
See margin.
Explanation:

Tips: Make a separate column for each variable.
Question 12.
Elyse has a small flower garden in her backyard. She wants to plant seven rows of flowers. She drew a plan of her garden.

a. If each row can hold 3 large plants, 4 medium plants, or 8 small plants, how many of each should Elyse buy?
Answer:
See margin.
Explanation:

b. What will the total cost be for all of Elyse’s plants?
Answer:
$100
Explanation:

Question 13.
Maggie wants to plant a 10 ft row of large plants. A large plant needs 1.5 ft between plants. Maggie will put her first plant 0.5 ft in from the end. How much money will Maggie need to fill the row? Explain how you found your answer.
Answer:
$28; sample answer; I drew a picture to show 7 plants.
Explanation:

Question 14.
Art has $32. How many large plants could he buy? Medium plants? Small plants?
Answer:
8 large; 10 medium; 16 small
Explanation:

Think About the Process
Question 15.
William and Anne are selling magazines. For each magazine sold, their soccer team raises $2.25. Which value completes this table?

A. 19.25
B. 382.5
C. 3825
D. 38.25
Answer:
D. 38.25

Question 16.
Tanya has a job delivering newspapers. Every week, her customers pay her $1.50. She also receives an allowance of $5 a week. If Tanya has x newspaper clients, which expression best describes how much money Tanya receives each week?
A. 5x – 1.5
B. 5x + 1.5
C. 5 + 1.5x
D. 5 – 1.5x
Answer:

Stop and Practice

Skills Review Write each phrase as an algebraic expression.
Question 1.
7 less than a number x
Answer:

Question 2.
5 times a number p
Answer:

Question 3.
4 times a number m, minus 3 times a number k
Answer:

Question 4.
8 plus two times a number j
Answer:

Use the properties of operations to fill in the blanks in each expression.
Question 5.
28 × 5 = 5 × ☐
Answer:

Question 6.
12 × 25 × 32 = 12 × ☐ × 25 × 32
Answer:

Question 7.
7 + (30 + 15) = (7 + 30) + ☐
Answer:

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

Evaluate each expression for x = 3 and y = 5.
Question 9.
5x + 8
Answer:

Question 10.
(10 – y) (10)
Answer:

Question 11.
10y + 23
Answer:

Question 12.
Write an algebraic expression for the value of y that explains the relationship between x and y. Then finish the table.

Answer:

Error Search Find each answer that is not correct. Write it correctly and explain the error.
Question 13.
8 + 2 × 6 = 60
Answer:

Question 14.
8 × 0 + (4 × 1) = 4
Answer:

Question 15.
4(24) = 4(6) + 4(4)
Answer:

Question 16.
32 + 73 = (30 + 70) + (2 + 3)
Answer:

Question 17.
58(40) = 50(40) × 8(40)
Answer:

Question 18.
4(51 + 32) = 4(80) + 4(3)
Answer:

Number Sense

Insert parentheses to make each sentence true.
Question 19.
3 × 8 + 3 × 2 = 66
Answer:

Question 20.
2 × 5 + 4 – 8 = 10
Answer:

Question 21.
15 – 2 × 3 + 5² = 64
Answer:

Question 22.
4x – 5 = 4x – 20
Answer:

Question 23.
6 + 8 – 3 × 7 = 41
Answer:

Question 24.
4 + 4 × 3 + 5 = 29
Answer:

Question 25.
3² – 8 × 0 = 9
Answer:

Question 26.
80 ÷ 2 × 2 + 2 × 3 = 26
Answer:

Question 27.
25 – 10 + 3 ÷ 2 + 4 = 3
Answer: