Category: Envision Math

Envision Math 1st Grade Textbook Answer Key Topic 2.2 Ordering Three Numbers

Ordering Three Numbers

Home Connection Your child made cube towers and compared three numbers to put them in order from least to greatest.
Home Activity Have your child make a set of number cards from 1 through 12 on slips of paper. Mix up the cards. Have your child select three cards without looking and put them in order from least to greatest and greatest to least

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Guided Practice

Count the cubes.
Write the numbers in order from least to greatest.
Question 1.

Question 2.

Answer:

Do you understand?
Question.
How can you tell which number is least?
Answer:

Independent Practice

Use cubes.
Write the numbers in order from least to greatest.
Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Reasoning Use cubes. Write who has the least.
Question 7.
Pat has 2 fewer cubes than Rosa. Jim has 4 cubes. Rosa has 1 more cube than Jim. ________ has the least
Answer:

Problem Solving

Solve the problems below.
Question 8.
Jen draws 4 trees. Steve draws 8 trees. Luca draws 3 trees. Who draws the least number of trees? Draw a picture to solve.
______________

Answer:

Question 9.
Stacy paints 6 pots. Yin paints 2 pots. Mario paints 4 pots. Which shows the number of pots from least to greatest?

Answer:

Question 10.
Journal Choose three numbers less than 10. Put your numbers in order from greatest to least.
Answer:

Envision Math 1st Grade Textbook Answer Key Topic 1 Test

Test

Oral Directions Say: Mark the correct answer. 1. Rover likes bones. How many bones does he have? 2. Bonnie drew 5 flowers. Then she drew 3 more. How many flowers did Bonnie draw in all? 3–4. Which number does the picture show?

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Oral Directions Say: Mark the correct answer. 5–6. Which number does the picture show? 7. Chuck made 4 paper airplanes. Then he made 4 more. Which model shows how many airplanes Chuck made altogether? 8. Mel’s cat had 5 kittens. Which model shows the number of kittens

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

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 2.7 Subtracting Whole Numbers

Subtracting Whole Numbers

How do you subtract numbers?
Brenda has a total of 221 songs in her computer. Her sister, Susan, has a total of 186 songs in her computer. How many more songs does Brenda have in her computer than Susan?

Choose an Operation Subtract to find how many more songs.

Guided Practice*

Do You Know How?

In 1 through 4, subtract.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Do You Understand?

Question 5.
In the example at the top, why was the 0 in the hundreds place not written in the answer?
Answer:

Question 6.
Brenda would like to have 275 songs on her computer by next year. How many more songs does she need to download?

Independent Practice

In 7 through 26, subtract.

Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Question 14.

Answer:

Question 15.
552 – 228
Answer:

Question 16.
3,711 – 1,683
Answer:

Question 17.
217 – 166
Answer:

Question 18.
562 – 199
Answer:

Question 19.
7,475 – 5,130
Answer:

Question 20.
5,831 – 1,156
Answer:

Question 21.
9,385 – 720
Answer:

Question 22.
1,111 – 589
Answer:

Question 23.
8,476 – 2,185
Answer:

Question 24.
6,251 – 964
Answer:

Question 25.
7,374 – 1,246
Answer:

Question 26.
8,327 – 3,796
Answer:

Step 1

Find 221 – 186.
Estimate: 220 – 190 = 30
Subtract the ones.

Step 2

Subtract the tens.
Subtract the hundreds.

Step 3

Operations that undo each other are inverse operations. Addition and subtraction have an inverse relationship.
The answer checks.

The answer checks.

Problem Solving

Question 27.
A crayon company makes 17,491 green crayons and 15,063 red crayons. How many more green crayons are made than red crayons?
A. 3,463
B. 2,428
C. 10,456
D. 32,554
Answer:

Question 28.
Angela hiked a trail that climbed 526 feet. Raul hiked a trail that climbed 319 feet. How many more feet did Angela climb than Raul?

Answer:

Question 29.
Jermaine and Linda collected aluminum cans for one month. Look at the chart below to see how many aluminum cans each
student collected.
a. Who collected more cans?
b. Find the difference between the number of cans collected.

Answer:

Question 30.
Mount Kilimanjaro is a mountain in Africa. A group of mountain climbers begin their descent from the peak. On Monday, the mountain climbers descended 3,499 feet. On Tuesday, they descended another 5,262 feet. How many feet have the mountain climbers descended?

Answer:

Question 31.
Mike’s team scored 63 points in the first half of a basketball game. His team won the game by a score of 124 to103. How many points did his team score in the second half?
Answer:

Envision Math 4th Grade Textbook Answer Key Topic 2.6 Adding Whole Numbers

Adding Whole Numbers

How do you add whole numbers?

If an artificial coral reef grew 257 inches last year and 567 inches this year, how much did it grow in all?


Estimate: 300 + 600 = 900

Another Example
How do you add more than two numbers?

Find the sum.
9,348 + 102 + 5,802 + 1,933
A. 17,185
B. 17,175
C. 16,175
D. 15,175

Estimate: 9,000 + 100 + 6,000 + 2,000 = 17,100

Step 1

Add the ones.
Regroup if necessary

Step 2

Add the tens.
Regroup if necessary.

Step 3

Add the hundreds, regroup, and then add the thousands.

The correct answer is A

Explain It

Question 1.
How are the ones regrouped in the example above?
Answer:

Question 2.
Reasonableness In Step 3 above, how can you tell that the answer is reasonable?
Answer:

Step 1

Add 257 + 567.
Add the ones.
Regroup if necessary.

Step 2

Add the tens.
Regroup if necessary.

Step 3
Add the hundreds. Regroup if necessary

The reef grew 824 inches in all.

Other Examples

Adding larger numbers
Add 36,424 + 24,842.
Estimate:
36,000 + 25,000 = 61,000

The sum is reasonable because it is close to the estimate of 61,000.

Adding more than two numbers
Add 130,283 + 263,823 + 396,538.
Estimate:
130,000 + 264,000 + 397,000 = 791,000

The sum is reasonable because it is close to the estimate of 791,000.

Guided Practice*

In 1 through 6, find each sum.

Question 1.
821 + 4,543
Answer:

Question 2.
14,926 + 3,832
Answer:

Question 3.
1,321 + 2,246
Answer:

Question 4.
24,593 + 16,861
Answer:

Question 5.

Answer:

Question 6.

Answer:

Do You Understand?

Question 7.
When adding 36,424 and 24,842 above, why is there no regrouping in the 2nd step?
Answer:

Question 8.
Volunteer teams identified 73 fish species, 30 corals, and 71 other invertebrates on the reef. How many species of fish, coral, and
invertebrates were found in all?
Answer:

Independent Practice

In 9 through 24, find each sum.

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Question 14.

Answer:

Question 15.

Answer:

Question 16.

Answer:

Question 17.

Answer:

Question 18.

Answer:

Question 19.
9,634 + 2,958
Answer:

Question 20.
4,673 + 262
Answer:

Question 21.
7,845 + 509 + 3,746
Answer:

Question 22.
526 + 276 + 1,086
Answer:

Question 23.
2,868 + 865
Answer:

Question 24.
15,891 + 527 + 1,086
Answer:

Problem Solving

Question 25.
In 1972, the Apollo 16 lunar rover set the current lunar speed record at 11 miles per hour. In order to break free from Earth’s orbit, Apollo missions had to go 24,989 miles per hour faster than the record speed of the lunar rover. How fast did the Apollo rockets travel?
Answer:

Question 26.
There were 10,453 items checked out of the public library one week. The next week 12,975 items were checked out. A week later, 9,634 items were checked out. How many items were checked out in three weeks?
Answer:

Question 27.
Sandy read 235 pages of a book. She had 192 more pages to read before she was done. How many pages are there in the book?

Answer:

Question 28.
Cheryl and Jason collect baseball cards. Cheryl has 315 cards, and Jason has 186 cards. How many cards do they have altogether?

Answer:

Question 29.
Number Sense The sum of 86, 68, and 38 is 192. What do you know about the sum of 68, 38, and 86?
Answer:

Question 30.
Estimation Maria added 45,273 and 35,687. Will her answer be greater or less than 80,000?
Answer:

Question 31.
The population of New City is 23,945. Eastdale has a population of 12,774. What is the total population of the two communities?
A. 35,719
B. 36,619
C. 36,719
D. 37,619
Answer:

Mixed Problem Solving

Question 1.
Estimate how much higher Mount Shasta is than Lassen Peak.
Answer:

Question 2.
Estimate how much higher above sea level Mount Whitney is than the depth of Death Valley.
Answer:

Question 3.
Estimate the range of the width of Death Valley.

Question 4.
Estimate how many years the Spanish governed California.
Answer:

Question 5.
Estimate which group governed California for a longer period of time: the Spanish government or the Mexican government.
Answer:

Question 6.
About how many years has the United States been governing the State of California?
Answer:

Question 7.
About how many years have passed since the Spanish government first started to govern California?
Answer:

Question 8.
It is about 50 miles from San Jose to San Francisco. From San Francisco to Sacramento, it is about 80 miles. Following that route, about how far is it from San Jose to Sacramento?
Answer:

Question 9.
Mammoth Lakes, elevation 7,920 feet, is the town with the highest elevation in California. Mount Whitney, with an elevation of 14,495,
feet is the highest point in California. Estimate how much higher Mount Whitney is than Mammoth Lakes.
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:

Go through the enVision Math Common Core Kindergarten Answer Key Topic 10 Compose and Decompose Numbers 11 to 19 regularly and improve your accuracy in solving questions.

enVision Math Common Core Kindergarten Answers Key Topic 10 Compose and Decompose Numbers 11 to 19

Essential Question: How can composing and decomposing numbers from 11 to 19 into ten ones and some further ones help you understand place value?

envision STEM Project: Sunlight and Earth’s Surface
Directions Read the character speech bubbles to students. Find Out! Have students find out how sunlight affects Earth’s surface. Say: Talk to friends and relatives about sunlight and how it affects Earth. Journal: Make a Poster Have students make a poster that shows 3 things sunlight does for Earth. Have them draw a sun with 16 rays. Then have them write an equation for parts of 16.

Review What You Know

Question 1.

Answer:

Explanation:
I circled the group that has 16 leafs.

Question 2.

Answer:

Explanation:
I circled the group that has 20 leafs.

Question 3.

Answer:

Explanation:
I circled the group that has less number of leafs.

Question 4.

Answer:

Explanation:
There are 13 leafs in the above picture so, I wrote the number 13.

Question 5.

Answer:

Explanation:
There are 17 leafs in the above picture so, I wrote the number 137

Question 6.

Answer:

Explanation:
There are 15 leafs in the above picture so, I wrote the number 15.

Directions Have students: 1 draw a circle around the group with 16; 2 draw a circle around the group with 20; 3 draw a circle around the group that is less than the other group; 4-6 count the leaves, and then write the number to tell how many.

Pick a Project

A

B

Directions Say: You will choose one of these projects. Look at picture A. Think about this question: How great is the great outdoors? If you choose Project A, you will tell a camping story. Look at picture B. Think about this question: What do mice like to eat? If you choose Project B, you will make a mouse poster.

C

D

Directions Say: You will choose one of these projects. Look at picture C. Think about this question: What do you like to collect? If you choose Project C, you will make a sticker book. Look at picture D. Think about this question: What is in a granola bar? If you choose Project D, you will make a snack-time drawing.

Lesson 10.1 Make 11, 12, and 13

Solve & Share

Answer:

Explanation:
I filled the ten-frame with counters and kept 2 counters outside the frame.
The equation that matches with the number of counters is 10+2=12.

Directions Say: Use counters to fill the ten-frame. Put 1, 2, or 3 counters outside of the ten-frame. Draw all of the counters. What equation can you write to tell how many counters there are in all?

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Directions 1 Have students write an equation to match the number of blocks shown. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Answer:

Explanation:
The equation that matches the number of blocks is 10+1=11.
The equation tells us that there are 10 ones and 1 more one.

Question 3.

Answer:

Explanation:
The equation that matches the number of blocks is 10+3=13.
The equation tells us that there are 10 ones and 3 more ones.

Question 4.

Answer:

Explanation:
I drew 12 counterss to match with the equation 10+2=12
The equation tells us that there are 10 ones and 2 more ones.

Question 5.

Answer:

Explanation:
I drew 13 counters to match with the equation 10+3=13
The equation tells us that there are 10 ones and 3 more ones.

Directions Have students: 2 and 3 write an equation to match the number of blocks shown. Then have them tell how the picture and equation show 10 ones and some more ones; 4 and 5 draw blocks to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 6.

Answer:

Explanation:
I drew 13 counters to match with the equation 10+3=13
The equation tells us that there are 10 ones and 3 more ones.

Question 7.

Answer:

Explanation:
I drew 11 counters to match with the equation 10+1=11
The equation tells us that there are 10 ones and 1 more one.

Question 8.

Answer:

Explanation:
I drew 12 counters to match with the equation 10+2=12
The missing number is 2
The equation tells us that there are 10 ones and 2 more ones.

Question 9.

Answer:

Explanation:
I drew 13 counters to match with the equation 10+3=13
The missing number is 3
The equation tells us that there are 10 ones and 3 more ones.

Directions Have students: 6 draw counters and write an equation to show how to make 13. Then have them tell how the picture and equation show 10 ones and some more ones; 7 draw counters and write an equation to show how to make 11. Then have them tell how the picture and equation show 10 ones and some more ones. 8 Algebra Have students draw counters to find the missing number. Then have them tell how the picture and equation show 10 ones and some more ones. 9 Higher Order Thinking Have students draw counters to find the missing number. Then have them tell how the picture and equation show 10 ones and some more ones.

Lesson 10.2 Make 14, 15 and 16

Solve & Share

Answer:

Explanation:
I drew 15 counters to match with the equation 10+5=15
The equation tells us that there are 10 ones and 5 more ones.

Directions Say: Put 15 counters in the double ten-frame to show 10 ones and some more ones. Then complete the equation to match the counters.

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Directions 1 Have students write an equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Answer:

Explanation:
I drew 15 counters to match with the equation 10+5=15
The equation tells us that there are 10 ones and 5 more ones.

Question 3.

Answer:

Explanation:
I drew 16 counters to match with the equation 10+6=16
The equation tells us that there are 10 ones and 6 more ones.

Question 4.

Answer:

Explanation:
I drew 14 counters to match with the equation 10+4=14
The equation tells us that there are 10 ones and 4 more ones.

Question 5.

Answer:

Explanation:
I drew 15 counters to match with the equation 10+5=15
The equation tells us that there are 10 ones and 5 more ones.

Directions Have students: 2-3 write an equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones; 4-5 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 6.

Answer:

Explanation:
I drew 16 counters to match with the equation 10+6=16
The equation tells us that there are 10 ones and 6 more ones.

Question 7.

Answer:

Explanation:
I drew 14 counters to match with the equation 10+4=14
The equation tells us that there are 10 ones and 4 more ones.

Question 8.

Answer:

Explanation:
The equation 10+5=15 tells us that there are 10 ones and 5 more ones.

Question 9.

Answer:

Explanation:
I drew 16 counters to match with the equation 10+6=16
The missing number is 6
The equation tells us that there are 10 ones and 6 more ones.

Directions Have students: 6 draw counters and write an equation to show how to make 16. Then have them tell how the picture and equation show 10 ones and some more ones; 7 draw counters and write an equation to show how to make 14. Then have them tell how the picture and equation show 10 ones and some more ones, 8 Number Sense Have students write an equation to show 15 as 10 ones and some more ones. 9 Higher Order Thinking Have students draw counters to find the missing number in the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Lesson 10.3 Make 17, 18, and 19

Solve & Share

Answer:

Explanation:
I drew 18 counters to match with the equation 10+8=18
The equation tells us that there are 10 ones and 8 more ones.

Directions Say: Jada made 10 prizes for the school carnival. She makes 8 more. Use counters to show how many prizes Jada made in all. Then write an equation to match the counters, and tell how the counters and equation show 10 ones and some more ones.

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Directions 1 Have students complete the equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Answer:

Explanation:
I counted the number of counters, there are 19 counters.
So, i wrote the equation 10+9=19
The equation tells us that there are 10 ones and 9 more ones.

Question 3.

Answer:

Explanation:
I counted the number of counters, there are 18 counters.
So, i wrote the equation 10+8=18
The equation tells us that there are 10 ones and 8 more ones.

Question 4.

Answer:

Explanation:
I counted the number of cubes, there are 17 cubes
So, i wrote the equation 10+7=17
The equation tells us that there are 10 ones and 7 more ones.

Question 5.

Answer:

Explanation:
I counted the number of cubes, there are 19 cubes
So, i wrote the equation 10+9=19
The equation tells us that there are 10 ones and 9 more ones.

Directions Have students 2 and 3 write an equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones; 4 and 5 complete the equation to match the cubes. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 6.

Answer:

Explanation:
I drew 18 counters to match with the equation 10+8=18
The equation tells us that there are 10 ones and 8 more ones.

Question 7.

Answer:

Explanation:
I drew 17 counters to match with the equation 10+7=17
The equation tells us that there are 10 ones and 7 more ones.

Question 8.

Answer:

Explanation:
I drew 19 counters to match with the equation 10+9=19
The equation tells us that there are 10 ones and 9 more ones.

Question 9.

Answer:

Explanation:
I drew 19 counters to match with the equation 10+9=19
The missing number is 9
The equation tells us that there are 10 ones and 9 more ones.

Directions Have students: 6 draw counters, and then write an equation to show how to make 18. Then have them tell how the picture and equation show 10 ones and some more ones; 7 draw counters, and then write an equation to show how to make 19. Then have them tell how the picture and equation show 10 ones and some more ones; 8 draw counters, and then write an equation to show how to make 17. Then have them tell how the picture and equation show 10 ones and some more ones. 9 Higher Order Thinking Have students draw counters to find the missing number in the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Lesson 10.4 Find Parts of 11, 12 and 13

Solve & Share

Answer:

Explanation:
13 means 10+3
I drew 13 counters to match with the equation 13=10+3
The equation tells us that there are 10 ones and 3 more ones.

Directions Say: 13 students wait for the train. There are only 10 seats in each train car. How many students will have to ride in a second car? Use counters to show your work. Then tell how the counters and equation show 10 ones and some more ones.

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Directions 1 Have students use counters to show 11, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Answer:

Explanation:
13 means 10+3
I drew 13 counters to match with the equation 13=10+3
The equation tells us that there are 10 ones and 3 more ones.

Question 3.

Answer:

Explanation:
There are 10 cubes and 2 more cubes.So, the missing numbers in the equation are 10 and 2
The equation tells us that there are 10 ones and 2 more ones.

Question 4.

Answer:

Explanation:
I drew 11 counters to match with the equation 1=10+1
The equation tells us that there are 10 ones and 1 more one.

Directions Have students: 2 use counters to show 13, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 3 look at the picture of 12 cubes, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 4 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 5.

Answer:

Explanation:
12 means 10+2
I drew 12 counters to match with the equation 12=10+2
The equation tells us that there are 10 ones and 2 more ones.

Question 6.

Answer:

Explanation:
13 means 10+3
I counted the number of cunes, there are 13 cubes.13=10+3
The equation tells us that there are 10 ones and 3 more ones.

Question 7.

Answer:

Explanation:
I drew 11 counters to match with the equation 11=10+1 and 10+1=11.
The equation tells us that there are 10 ones and 1 more ones.

Directions Have students: 5 draw counters to make 12, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 6 color the cubes blue and red to make 13, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones. 7 Higher Order Thinking Have students draw counters to show 11 and write two equations to match the picture. Then have them tell how the picture and equations show 10 ones and some more ones.

Lesson 10.5 Find Parts of 14, 15, and 16

Solve & Share

Answer:

Explanation:
14 means 10+4
I drew 14 counters to match with the equation 14=10+4
The equation tells us that there are 10 ones and 4 more ones.

Directions Say: 14 students go to the zoo. The first bus takes 10 students. The rest of the students go on a second bus. Use counters to describe this situation. Then complete the equation to match the counters and tell how the counters and equation show 10 ones and some more ones.

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Directions 1 Have students use counters to show 15, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Answer:

Explanation:
14 means 10+4
I drew 14 counters to match with the equation 14=10+4
The equation tells us that there are 10 ones and 4 more ones.

Question 3.

Answer:

Explanation:
16 means 10+6
I counted the number of cubes, there are 16 cubes.So, the equation is 16=10+6
The equation tells us that there are 10 ones and 6 more ones.

Question 4.

Answer:

Explanation:
I drew 15 counters to match with the equation 15=10+5
The equation tells us that there are 10 ones and 5 more ones.

Directions Have students: 2 use counters to show 14, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 3 look at the picture of 16 cubes, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 4 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 5.

Answer:

Explanation:
I drew 16 counters to match with the equation 16=10+6
The equation tells us that there are 10 ones and 6 more ones.

Question 6.

Answer:

Explanation:
14=10+4
I colored 14 cubes to match with the equation 14=10+4
The equation tells us that there are 10 ones and 4 more ones.

Question 7.

Answer:

Explanation:
I drew 16 counters to match with the equation 16=10+6 or 10+6=16
The equation tells us that there are 10 ones and 6 more ones.

Directions Have students 5 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones. 6 color the cubes blue and red to show 14, complete the equation to match the picture, and tell how the picture and equation show 10 ones and some more ones. 7 Higher Order Thinking Have students use counters to show 16, draw them in the double ten-frame, and complete two equations to match the picture. Then have them tell how the picture and equations show 10 ones and some more ones.

Lesson 10.6 Find Parts of 17, 18 and 19

Solve & Share

Answer:

Explanation:
I colored 10 boxes blue and the remaining 8 boxes red,
The equation is 10+8=18
The equation tells us that there are 10 ones and 5 more ones.

Directions Say: How can these 18 boxes be split into ten ones and some more ones? Use 2 different color crayons to color the boxes to show your work. Then write an equation to match the picture.

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Directions 1 Have students color 10 cubes blue to show 10 ones, and then draw 10 blue cubes in the top ten-frame. Have them color the remaining cubes in the train red to show more ones, count them, and then draw red cubes in the bottom ten-frame. Then have them write an equation to match the pictures.

Question 2.

Answer:

Explanation:
I colored 10 squares blue to show 10 ones, and then drew 10 blue squares in the top ten-frame.Then i colored the remaining cubes in the train red to show more ones, counted them, and then drew 9 red squares in the bottom ten-frame. Then i wrote the equation 19=10+9 to match the pictures.

Question 3.

Answer:

Explanation:
I colored 10 squares blue to show 10 ones, and then drew 10 blue squares in the top ten-frame.Then i colored the remaining cubes in the train red to show more ones, counted them, and then drew 7 red squares in the bottom ten-frame. Then i wrote the equation 19=10+7 to match the pictures.

Question 4.

Answer:

Explanation:
I counted the above counters, there are 18 counters.So, the equation is 18=10+8
The equation tells us that there are 10 ones an d8 more ones.

Directions Have students: 2 and 3 color 10 squares blue to show 10 ones, and then draw 10 blue squares in the top ten-frame. Have them color the remaining cubes in the train red to show more ones, count them, and then draw red squares in the bottom ten-frame. Then have them write an equation to match the pictures; 4 complete the equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 5.

Answer:

Explanation:
I counted the above counters, there are 17 counters.So, the equation is 17=10+7
The equation tells us that there are 10 ones and 7 more ones.

Question 6.

Answer:

Explanation:
I counted the above counters, there are 19 counters.So, the equation is 19=10+9
The equation tells us that there are 10 ones and 9 more ones.

Question 7.

Answer:

Explanation:
I drew 18 counters to match with the equation 18=10+8 or 10+8=18
The equation tells us that there are 10 ones and 8 more ones.

Directions 5 and 6 Have students complete the equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones. 7 Higher Order Thinking Have students use counters to show 18, draw them in the double ten-frame, and write two equations to match the picture. Then have them tell how the picture and equations show 10 ones and some more ones.

Lesson 10.7 Look For and Use Structure

Problem Solving

Solve & Share

Answer:

Explanation:
I kept 2 counters in the red five-frame. Used a red crayon and wrote the number 2 that tells how many counters are in the red frame. I kept the same number of counters in the blue five-frame. Used a blue crayon and write the number that tells how many counters are in the blue frames.
The red nmber is smaller by ten then the blue number,
The pattern is 2,12.

Directions Say: Put some counters in the red five-frame. Use a red crayon and write the number that tells how many counters are in the red frame. Put the same number of counters in the blue five-frame. Use a blue crayon and write the number that tells how many counters are in the blue frames. Show the numbers to a partner. Compare your answers and look for patterns. How is your blue number like your red number? How is it different?

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Directions 1 Have students find the number with the blue box around it, and then color the number that is 10 greater than the number in the blue box. Have them write an equation to show how the teen number they colored is composed of 10 ones and some more ones. Then have students explain how they decided what parts to add to make the teen number.

Independent Practice

Question 2.

Answer:

Explanation:
I found the number with the blue box around it, it is 7 and then colored the number that is 10 greater than the number in the blue box which is 17.Then wrote an 10+7=17 equation to show how the teen number i colored is composed of 10 ones and 7 more ones.

Question 3.

Answer:

Explanation:
I found the number with the blue box around it, it is 8 and then colored the number that is 10 greater than the number in the blue box which is 18.Then wrote an 10+8=18 equation to show how the teen number i colored is composed of 10 ones and 8 more ones.

Question 4.

Answer:

Explanation:
I found the number with the blue box around it, it is 9 and then colored the number that is 10 greater than the number in the blue box which is 19.Then wrote an 10+9=19 equation to show how the teen number i colored is composed of 10 ones and 9 more ones.

Question 5.

Answer:

Explanation:
The missing numbers in the pattern are 10 and 3.
The equaation is 10+3=13.

Directions Have students: 2-4 find the number with the blue box around it, and color the number that is 10 greater than the number in the blue box. Then have them write an equation to show how the teen number they colored is composed of 10 ones and some more ones; 5 complete the equation to continue the pattern, and then explain the pattern they made.

Problem Solving

Performance Task

Answer:

Directions Read the problem to students. Then have them use multiple problem-solving methods to solve the problem. Say: Mr. Shepard’s class will exchange cards at a holiday party. There are 16 students in the class. The store sells cards in packs of 10. Alex already has 6 cards. Marta already has 7 cards. How many cards will Alex and Marta have after they each buy one pack of cards? 6 Use Structure How can the number chart help you solve the problem? Write the equations for the number of cards Alex and Marto will have. 7 Generalize After you find the number of cards Alex will have, is it easier to find the number of cards Marta will have? 8 Explain Tell a friend why your answers are correct. Then tell the friend about the pattern you see in the number chart and how the equations show 10 ones and some more ones.

Topic 10 Fluency Practice

Find a Match

Activity

Question 1.

Answer:

Explanation:
The clues are 2+3=5=4+1=O, 4-2=2=1+1=G, 5-2=3=4-1=H
I solved the addition and subtraction problems in the above picture and with the help of the clues i found the word HOG.

Question 2.

Answer:

Explanation:
The clues are 2-1=1=5-4=W, 2+2=1+3=4=C, 1-1=0=0+0=O
I solved the addition and subtraction problems in the above picture and with the help of the clues i found the word COW.

Directions 1 and 2 Have students find a partner. Have them point to a clue in the top row, and then solve the addition or subtraction problem. Then have them look at the clues in the bottom row to find a match, and then write the clue letter above the match. Have students find a match for every clue.

Topic 10 Vocabulary Review

Question 1.

Answer:

Question 2.

Answer:

Directions Understand Vocabulary Have students: 1 complete the drawing and the equation to show how many more counters are needed to make 15; 2 complete the drawing and the equation to show how many more counters are needed to make 19.

Topic 10 Reteaching

Set A

Question 1.

Answer:

Explanation:
There are 13 cubres in the above picture.
The equation that matches with the image is 10+3=13
The equation tells us that there are 10 ones and 3 more ones.

Set B

Question 2.

Answer:

Explanation:
I drew 6 more counters to show 16,
The equation 10+6=16 tells us that there are 10 ones and 6 more ones.

Directions Have students: 1 write an equation to match the blocks. Then have them tell how the picture and equation show 10 ones and some more ones; 2 draw counters to show 16, and then write an equation to match the picture. Then tell how the picture and equation show 10 ones and some more ones.

Set C

Question 3.

Answer:

Explanation:
I drew 17 counters to match with the equation 10+7=17
The equation 10+7=17 tells us that there are 10 ones and 7 more ones.

Set D

Question 4.

Answer:

Explanation:
I drew 11 counters to match with the equation 10+1=11
The equation tells us that there are 10 ones and 1 more ones.

Directions Have students: 3 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones; 4 draw counters to make 11, and then complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones.

Set E

Question 5.

Answer:

Explanation:
I drew 14 counters to match with the equation 10+4=14
The missing numbers in the equation are 10 and 4.
The equation tells us that there are 10 ones and 4 more ones.

Set F

Question 6.

Answer:

Explanation:
I found the number with the blue box around it, it is 8 and then colored the number that is 10 greater than the number in the blue box which is 18.Then wrote an 10+8=18 equation to show how the teen number i colored is composed of 10 ones and 8 more ones.

Directions Have students: 5 use counters to show 14, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 6 find the number with the blue box around it, and color the number that is 10 greater than the number in the blue box. Then have them write an equation to match, and then tell how the equation shows 10 ones and some more ones.

Set G

Question 7.

Answer:

Explanation:
I colored 10 cubes blue in the train to show 10 ones, and then drew 10 blue cubes in the top ten-frame.Then colored the remaining 8 cubes in the train red to show 8 more ones, I counted them, and then draw the same number of red cubes in the bottom ten-frame. Then I wrote an equation 18= 10 + 8  to match the pictures.

Directions Have students: 7 color 10 cubes blue in the train to show 10 ones, and then draw 10 blue cubes in the top ten-frame. Have them color the remaining cubes in the train red to show more ones, count them, and then draw the same number of red cubes in the bottom ten-frame. Then have them write an equation to match the pictures.

Topic 10 Assessment Practice

Question 1.

A. 15 = 10 + 5
B. 14 = 10 + 4
C. 13 = 10 + 3
D. 12 = 10 + 2
Answer:

Explanation:
Option A is correct as there are 15 counters in the above ten frames which tell that there are 10 ones and 5 more ones.

Question 2.

A. 10 and 6
B. 10 and 7
C. 10 and 8
D. 10 and 9
Answer:

Explanation:
Option C is correct as there are 18 counters in the above ten frames which tell that there are 10 ones and 8 more ones.

Question 3.
A 10 and 0
B 10 and 1
C 10 and 2
D 10 and 3
Answer:

Explanation:
Option C is correct as there are 12 counters in the above ten frames which tell that there are 10 ones and 2 more ones.

Directions Have students mark the best answer. 1 Say: Mason uses counters in ten-frames to count his marbles. Which equation matches the picture and shows how many marbles Mason has? 2 Say: Sarah counts the number of counters and gets 18. Which two numbers add to 18? Use the equation and double ten-frame for help. 3 Say: Cole has 12 toy trucks. How can Cole split up his trucks into ten ones and some more ones?

Question 4.

Answer:

Explanation:
I found the number with the blue box around it, it is 4 and then colored the number that is 10 greater than the number in the blue box which is 14.Then wrote an 10+4=14 equation to show how the teen number i colored is composed of 10 ones and 4 more ones.

Question 5.

Answer:

Explanation:
I drew 3 more counters to match with the equation 13 = 10 + 3
The equation tells that there are 10 ones and 3 more ones.

Directions Have students: 4 find the number with the blue box around it, and then color the number that is 10 greater than the number in the blue box. Then have them write an equation that shows how the teen number they colored is composed of ten and some more ones; 5 draw counters to make 13, and then complete the equation to match the picture.

Topic 10 Assessment Practice

Question 6.

Answer:

Explanation:
I drew 6 more counters to match with the equation 16 = 10 + 6
The equation tells that there are 10 ones and 6 more ones.

Question 7.

Answer:

Explanation:
I colored 10 cubes blue in the train to show 10 ones, and then drew 10 blue cubes in the top ten-frame.Then colored the remaining 9 cubes in the train red to show 9 more ones, I counted them, and then draw the same number of red cubes in the bottom ten-frame. Then I wrote an equation 18= 10 + 9  to match the pictures

Directions Have students: 6 listen to this story: Gabby has 16 counters. She wants to put her counters into a double ten-frame in order to decompose 16 into tens and ones. Draw counters to match Gabby’s equation. 7 color 10 cubes blue to show 10 ones, and then draw 10 blue cubes in the top ten-frame. Have them color the remaining cubes in the train red to show more ones, count them, and then draw the same number of red cubes in the bottom ten-frame. Then have them write an equation to match the pictures.

Question 8.

Answer:

Explanation:
In the first double ten-frame there are 13 counters, i matched it with the equation 13=10+3
In the Second double ten-frame there are 1 counters, i matched it with the equation 17=10+7
In the third double ten-frame there are 1 counters, i matched it with the equation 11=10+1
In the forth double ten-frame there are 1 counters, i matched it with the equation 14=10+4

Directions 8 Have students choose the equation that matches each double ten-frame.

Question 1.

Answer:

Explanation:
There are 12 marbles in the above ten frame.
I wrote the euqation 10+2=12 to match with the picture.
The equation tll that there are 10 ones and 2 mor eones.

Question 2.

Answer:

Explanation:
I drew 8 more marbles to match with the equation 18 = 10 + 8
The equation tells that there are 10 ones and 8 more ones.

Question 3.

Answer:

Explanation:
I drew 17 yellow marbles to match with the equation 17 = 10 + 7
The equation tells that there are 10 ones and 7 more ones.

Directions Mason’s Marbles Say: Mason collects many different kinds of marbles. He uses ten-frames to help count his marbles. Have students: 1 write the equation to show how many purple marbles Mason has; 2 draw red marbles in the second ten-frame to show 18 red marbles in all, and then complete the equation. Have them tell how the picture and equation show 10 ones and some more ones; 3 draw 17 yellow marbles in the double ten-frame, and then write two equations to match their drawing.

Question 4.

Answer:

Explanation:
I drew 13 green marbles to match with the equation 13 = 10 + 3
The equation tells that there are 10 ones and 3 more ones.

Question 5.

Answer:

Explanation:
I found the number with the blue box around it, it is 4 and then colored the number that is 10 greater than the number in the blue box which is 14.Then wrote an 10+4=14 equation to show how the teen number i colored is composed of 10 ones and 4 more ones.

Directions 4 Have students look at the equation Mason wrote to show how many green marbles he has, and then draw the marbles in the double ten-frame to show the number. Have them tell how the picture shows 10 ones and some more ones. 5 Say: Mason put his striped marbles in a five-frame. Then he buys 10 more striped marbles. Have students write the number to tell how many striped marbles Mason had at first, and then color the part of the number chart to show how many striped marbles he has now. Then have them write an equation and ask them to explain how the picture and equation show 10 ones and some more ones.

Envision Math 2nd Grade Textbook Answer Key Topic 2.4 Adding in Any Order

Adding in Any Order

Question 1.
____ +____ = ____ and ____ + ____ = ____
Answer:

Question 2.
____ +____ = ____ and ____ + ____ = ____
Answer:

Question 3.
____ +____ = ____ and ____ + ____ = ____
Answer:

Home Connection Your child used connecting cubes to show how facts with the same addends have the same sum.
Home Activity Have your child draw a picture to show 3 + 5. Then have him or her turn the picture upside down to show 5 + 3.
AF 1.1 Use the commutative and associative rules to simplify mental calculations and to check results. Also AF 1.0.

Guided Practice

Write the addition fact for the cubes.
Then change the order of the addends.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Do you understand? How is 6 + 3 related to 3 + 6?

Independent Practice

Write the sum.
Then change the order of the addends

Question 5.
4 + 5 = __
__ + __ = ___
Answer:

Question 6.
9 + 3 = __
__ + __ = __
Answer:

Question 7.

Answer:

Question 8.

Answer:

Algebra Write the missing number.
The same shapes are the same numbers.

Question 9.

Answer:

Question 10.

Answer:

Problem Solving

Solve the problems below.

Question 11.
Joy has 4 flowers in her garden. Then she plants 3 more. How many flowers does Joy have now? Draw a picture. Then write facts for this story with the addends in a different order.

____ + ____ = ____
____ + ____ = ____
Answer:

Question 12.
Kate has 6 gears on her helmet. Nick’s helmet has 2 gears. Kate and Nick have 8 gears in all. Choose the facts for this story.

Answer:

Question 13.
Journal Draw a picture for 2 + 4. Then draw a picture for the 4 + 2 fact.

Answer: