practice and homework lesson 1.5 answer key 4th grade

4.5 Multiplicative Comparison and Measurement

• Students interpret, represent, and solve multiplicative comparison problems using an understanding of the relationship between multiplication and division. They use this thinking to convert units of measure within a given system from larger to smaller units.

Section A Goals

• Analyze, describe, and represent multiplicative comparison situations.
• Solve one-step and two-step problems involving multiplicative comparison.

Section B Goals

• Convert from larger units to smaller units within a given system of measurement.
• Solve multi-step problems involving multiplicative comparison and measurement.
• Understand the relative sizes of kilometers, meters and centimeters, liters and milliliters, kilograms and grams, and pounds and ounces.

Section C Goals

Section a: multiplicative comparison.

Practicing Standards:   3.OA.A.1

Write a multiplication expression represented by each diagram.

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Practicing Standards:   3.OA.A.3

Each bottle contains 2 liters of water. How many liters of water are there in 6 bottles?

Practicing Standards:   4.NF.B.4.b

Find the value of each product. Explain or show your reasoning.

\(5 \times \frac{1}{8}\)

\(5 \times \frac{3}{8}\)

• \(4 \times \frac{7}{12}\)

Practicing Standards:   4.NF.B.3.a, 4.NF.B.3.c

Find the value of each expression.

• \(\frac{2}{5} + \frac{4}{5}\)
• \(1\frac{5}{8} - \frac{4}{8}\)
• \(2\frac{1}{6} + 1\frac{5}{6}\)

Here are some connecting cubes.

Select all pictures that show 4 times as many connecting cubes.

Han read 4 books during the summer. Priya read 3 times as many books as Han.

• Draw a diagram that represents the situation.

Write an equation that represents the situation.

Mai exercised 3 times as many hours as Tyler last week. Mai exercised for 15 hours.

• Write an equation to represent the situation.
• How many hours did Tyler exercise last week?

Diego has 8 songs on his playlist. Mai has 3 times as many songs as Diego.

• Explain how the diagram and equation are related.

How many songs are on Mai's playlist?

Lin scored 6 points in her basketball game on Saturday. She scored 3 times as many points in her basketball game on Sunday. How many points did Lin score altogether in the two games? Explain or show your reasoning.

If diagram A represents 15, what does diagram B represent? Explain your reasoning.

• If diagram B represents 100, what does diagram A represent? Explain your reasoning.

Exploration

The diagram represents the books that Diego and Lin brought to the book fair.

Description: diagram. two rectangles. top rectangle, Lin's books. partitioned into 5 equal parts. Bottom rectangle, Diego's books. Partitioned into 7 equal parts. The partitioned parts on the top and bottom are the same size.

For each question, explain or show your reasoning.

• If Lin brought 10 books, how many books did Diego bring?
• If Diego brought 21 books to the fair, how many books did Lin bring?
• If Lin and Diego brought 60 books altogether, how many did they each bring?

Write a comparison story problem.

Trade problems with a partner.

• Draw a diagram and write an equation to represent the situation.
• Solve the story problem.

Section B: Measurement Conversion

Select all measurements that are greater than 1 meter.

the width of a paper clip

the length of your math workbook

the width of the classroom

the height of the door in the classroom

the length of a finger

• The Burj Khalifa is a skyscraper in Dubai. It is 828 meters tall. Is that more or less than 1 kilometer? Explain your reasoning.
• An airplane flies 9,500 meters above the ground. Is that more or less than 1 kilometer? Explain your reasoning.

A bottle of water holds 250 milliliters.

How many of those bottles does it take to make 1 liter?

How many liters of water does the bottle hold?

• Jada's backpack weighs 3.5 kg. How many grams is Jada's backpack? Explain or show your reasoning.

A tuna fish can swim 200 kilometers in a day.

The camel travels 40 kilometers in a day. How many times farther does the tuna fish travel than the camel?

The giant tortoise travels 500 meters in a day. How many kilometers is that?

How many times as far as the giant tortoise does the tuna fish travel?

The average weight of a newborn baby is 7 pounds and 8 ounces. How many ounces is that?

Diego said it took him 1,800 seconds to get home from school yesterday. Lin thinks he is exaggerating.

• It took Diego \(\frac{1}{2}\) hour to get home from school yesterday. How many minutes is that? Explain your reasoning.
• How many seconds is that? Explain or show your reasoning.
• Was Diego's statement correct or is he exaggerating?

Han makes sparkling juice by mixing 1.5 liters of juice and 500 milliliters of sparkling water.

How many milliliters of sparkling juice did Han make?

How many times more juice did Han use than sparkling water?

Jada is trying to decide which option will take less time to make a trip. Here are the details.

Option 1 (Fly)

• 30 minutes to get to the airport
• \(1\frac{1}{2}\) hours waiting at the airport
• 45 minute flight
• \(1 \frac{1}{4}\) hours to get to destination

Option 2 (Drive)

• \(3\frac{3}{4}\) hour drive
• \(\frac{1}{2}\) hour stop for lunch

Which option takes less total time? Explain your reasoning.

There are different hikes leaving from the same location. Here are the distances:

Trail A: 800 m

Trail B: 2.5 km

Trail C: 1,300 m

Trail D: 3 km

• Andre hiked a total of more than 3 km but less than 4 km. Which trails might Andre have taken?
• Jada hiked more than 2 km but less than 3 km. Which trails might Jada have taken?

Section C: Let’s Put it to Work

• The third graders at Jada’s school drank 3 times as much milk as Jada’s class. How many quarts is that?

Diego saw a snake that is 9 inches long at the pet store. The world's longest snake, a python, is 10 yards long. How many times longer is the python than the snake Diego saw? Explain or show your reasoning.

• Andre drew a rectangle that is 5 centimeters long and 6 centimeters wide. What is the perimeter of Andre’s rectangle?
• Jada drew a rectangle whose side lengths are 4 times as long as those of Andre’s rectangle. What is the perimeter of Jada's rectangle?
• A rectangle has perimeter 19 cm. One side is 4 cm. How long is the other side of the rectangle?

A square has perimeter 19 cm. How long is each side of the square? Explain or show your reasoning.

A furlong is 220 yards. It is a unit usually used to measure the distance of horse races. A mile is 5,280 feet. Mai read that a furlong is \(\frac{1}{8}\) mile. Is this true? Explain or show your reasoning.

Many of the length measurements that we use today have interesting histories. Choose one of them, such as a foot, a yard, or a marathon and investigate its origin.

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enVision MATH Common Core 5, Grade: 5 Publisher: Scott Foresman Addison Wesley

Envision math common core 5, title : envision math common core 5, publisher : scott foresman addison wesley, isbn : 328672637, isbn-13 : 9780328672639, use the table below to find videos, mobile apps, worksheets and lessons that supplement envision math common core 5., textbook resources.

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Eureka Math Grade 5 Module 4 Lesson 23 Answer Key

Engage ny eureka math 5th grade module 4 lesson 23 answer key, eureka math grade 5 module 4 lesson 23 problem set answer key.

a. 3.4 × _______ = 3.4

Answer: 3.4 × 1.00 = 3.4

b. _______ × 0.21 > 0.21

Answer: 1.021 × 0.21 > 0.21.

c. 8.04 × _______ < 8.04

Answer: 8.04 × 0.989 < 8.04.

Question 2. a. Sort the following expressions by rewriting them in the table.

b. Explain your sorting by writing a sentence that tells what the expressions in each column of the table have in common.

Answer: Here, in the first column, the boxed number is multiplied by a scaling factor less than 1. So the product will be less than the boxed number. In the second column, the boxed number is multiplied by a scaling factor greater than 1.

Question 3. Write a statement using one of the following phrases to compare the value of the expressions. Then, explain how you know.

a. 4 × 0.988 _________________________________ 4

b. 1.05 × 0.8 _________________________________ 0.8

c. 1,725 × 0.013 _________________________________ 1,725

d. 989.001 × 1.003 _________________________________ 1.003

e. 0.002 × 0.911 _________________________________ 0.002

Answer: a. 4 × 0.988 is less than slightly 4 because 0.988 is slightly less than 1.

b. 1.05 × 0.8 is slightly more than 0.8 because 0.1 is a little more than 1.

c. 1,725 × 0.013 is a lot less than 1,725 because 0.013 is a lot less than 1.

d. 989.001 × 1.003 is a lot more than 1.003 because 989.001 is a lot more than 1.

e. 0.002 × 0.911 is slightly less than 0.002 because 0.911 is a little less than 1.

Question 4.

During science class, Teo, Carson, and Dhakir measure the length of their bean sprouts. Carson’s sprout is 0.9 times the length of Teo’s, and Dhakir’s is 1.08 times the length of Teo’s. Whose bean sprout is the longest? The shortest? Explain your reasoning.

Answer: Dhakir’s bean sprouts are the longest and Teo’s bean sprouts are the shortest.

Explanation: Here, Dhakir’s bean sprouts are the longest, because it is slightly more than 1 time. The length of the Teo’s bean sprouts. Carson bean sprout is the shortest because it is a little less than 1 time the length of the Teo’s.

Question 5. Complete the following statements; then use decimals to give an example of each. • a × b > a will always be true when b is…

Answer: It’s true when b is greater than one.

Explanation: Let’s take an example of a × b > a 3.15 × 1.3 = 4.095 and here 4.095 > 3.15 and it is true when b is greater than one.

• a × b < a will always be true when b is…

Answer: It’s true when b is less than one.

Explanation: Let’s take an example of a × b < a 3.15 × 0.7 = 2.205 and here 2.205 < 3.15 and it is true when b is less than one.

Eureka Math Grade 5 Module 4 Lesson 23 Exit Ticket Answer Key

a. 3.06 × _______ < 3.06

b. 5.2 × _______ = 5.2

c. _______ × 0.89 > 0.89

Answer: a. 3.06 × 0.898 < 3.06.

b. 5.2 × 1.00 = 5.2.

c. 1.009× 0.89 > 0.89.

Question 2. Will the product of 22.65 × 0.999 be greater than or less than 22.65? Without calculating, explain how you know.

Answer: It will be less.

Explanation: It’s a decimal so it’ll be a bit less than 22.65.

Eureka Math Grade 5 Module 4 Lesson 23 Homework Answer Key

Question 1. Sort the following expressions by rewriting them in the table.

b. What do the expressions in each column have in common?

b. 1.01 × 2.06 _______________________________ 2.06

c. 1,955 × 0.019 _______________________________ 1,955

d. Two thousand × 1.0001 _______________________________ two thousand

e. Two-thousandths × 0.911 _______________________________ two-thousandths

a. 14 × 0.999 is slightly less than 14.

b. 1.01 × 2.06 is slightly more than 2.06.

c. 1,955 × 0.019 a lot less than 1,955.

d. Two thousand × 1.0001 is slightly more than two thousand.

e. Two-thousandths × 0.911 is slightly less than two-thousandths.

Question 3. Rachel is 1.5 times as heavy as her cousin, Kayla. Another cousin, Jonathan, weighs 1.25 times as much as Kayla. List the cousins, from lightest to heaviest, and explain your thinking.

Answer: Kayal, Jonathan, Rachel.

Explanation: Here, Kayal is the lightest after Kayal Jonathan and then Rachel is the heaviest

Answer: Greater than 1

Explanation: 4.15 × 1.3 = 4.095 and here 5.395 > 4.15 and it is true when b is greater than one. 2.5 × 0.5 = 1.25 and here 1.25 < 2.5 and it is true when b is less than one.

Explanation: Let’s take an example of a × b < a 3.15 × 0.7 = 2.205 and here 2.205 < 3.15 and it is true when b is less than one. 5.2 × 1.6 = 8.32 and here 8.32 > 5.2 and it is true when b is greater than one.

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Texas Go Math Grade 7 Lesson 8.4 Answer Key Solving Two-Step Inequalities

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 8.4 Answer Key Solving Two-Step Inequalities.

Use algebra tiles to model and solve each inequality.

Circle any given values that make the inequality true.

Texas Go Math Grade 7 Lesson 8.4 Guided Practice Answer Key

Solve each inequality. Graph and check the solution. (Example 2)

Circle any given values that make the inequality true. (Example 3)

Essential Question Check-In

Question 7. How do you solve a two-step inequality? Answer: First, isolate the variable. On one side of the inequality we put the variable, and on other side we put what’s left. If the variable is multiplied by some number, we have to divide inequality by that number. If we divide or multiply by a negative number, we have to reverse the direction of inequality.

Texas Go Math Grade 7 Lesson 8.4 Independent Practice Answer Key

Solve each inequality. Graph and check the solution.

Texas Go Math Grade 7 Lesson 8.4 H.O.T. Focus On Higher Order Thinking Answer Key

c. Describe the solution set of the compound inequality x < 2 and x > 7. Answer: The solution set is the intersection of sets where x is greater than 2 and less than 7, x ε (2, 7).

d. Describe the solution set of the compound inequality x > 2 or x < 7. Answer: The solution set is the union of sets where x is less than 2 and greater than 7, x ε (-∞, 2) ∪ (7, ∞).

Go Math Lesson 8.4 7th Grade Solving Two-Step Inequalities Question 22. Communicate Mathematical Ideas Joseph used the problem-solving strategy Work Backward to solve the inequality 2n+ 5 < 13. Shawnee solved the inequality using the algebraic method you used in this lesson. Compare the two methods. Answer: Working backward consists of mentally performing the following operations: Subtract 5 from 13 to obtain 8 and dividing by 2 gives us that n must be less than 4. Let’s perform the algebraic operations: 2n + 5 < 13 Write the inequality 2n + 5 – 5 < 13 – 5 Subtract 5 from both sides 2n < 8 Simplify \(\frac{2 n}{2}\) < \(\frac{8}{2}\) Divide both sides by 2 n < 4 Simplify The two methods are basically the same. Working backward consists of mostly working mentally, while the algebraic method is mostly written, but the operations performed are the same. The two methods are basically the same. The backward method works mentally while the algebraic method is a written solution.

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