Category: Envision Math

Go through the enVision Math Common Core Grade 4 Answer Key Topic 14 Algebra: Generate and Analyze Patterns regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 14 Algebra Generate and Analyze Patterns

Essential Questions:
How can you use a rule to continue a pattern? How can you use a table to extend a pattern? How can you use a repeating pattern to predict a shape?

enVision STEM Project: Patterns and Waves
Journal: Write a Report Include what you found. Also in your report:
Do Research Use the Internet or other sources to learn about 2 industries where oscilloscopes can be used. Name the industry and what can be observed using the oscilloscope.

Oscilloscopes are used to observe patterns in waves. Suppose a scientist created a pattern with three levels of sounds: quiet, loud, medium. If the scientist repeats the pattern of sounds, what would be the 41st sound in the pattern? Explain.

Review What You Know

Vocabulary
Choose the best term from the box. Write it on the blank.

• even number
• odd number
• inverse operations
• variable

Question 1.
A(n) ________ can be divided into groups of 2 without a remainder.
Answer:
Even number
Explanation:
Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.

Question 2.
A symbol or letter that stands for a number is called a(n) ___________.
Answer: Variable
Explanation:
A variable is a letter or symbol used as a placeholder for an unknown value

Question 3.
Operations that undo each other are called _________
Answer: Inverse Operation.
Explanation:
Inverse operations are operations that are opposite or “undo” each other.
For example, addition undoes subtraction and division undoes multiplication.
Inverse operations are useful when solving equations

Addition and Subtraction Patterns

Add or subtract to find the missing number in each pattern.
Question 4.
3, 6, 9, 12, ____,18
Answer: 15
Explanation:
Pattern : Add 3

Question 5.
4,8, 12, ____, 20, 24
Answer: 16
Explanation:
Pattern : Add 4

Question 6.
8, 7, 6, ____,4, 3
Answer: 5
Explanation:
Pattern : Add 1 then less 1

Question 7.
30, 25, 20, 15, ____,5
Answer: 10
Explanation:
Pattern : Subtract 5

Question 8.
1, 5, 9, ____, 17, 21
Answer: 13
Explanation:
Pattern : Add 4

Question 9.
12, 10, 8, 6, ___, 2
Answer: 4
Explanation:
Pattern : Subtract 2

Multiplication and Division Patterns

Multiply or divide to find the missing number in each pattern.
Question 10.
1, 3, 9, 27, ___, 243
Answer: 81
Explanation:
Pattern : Multiply 3

Question 11.
64, 32, 16, ____, 4, 2
Answer:  8
Explanation:
Pattern : Divide by 2

Question 12.
1,5, 25, ____, 625
Answer: 125
Explanation:
Pattern : Multiply 5

Question 13.
1, 2, 4, 8, ____, 32
Answer:
Explanation:
Pattern : Multiply by 2

Question 14.
1, 4, 16, ____, 256
Answer: 64
Explanation:
Pattern : Multiply by 4

Question 15.
729, 243, 81,27, 9, ____
Answer: 3
Explanation:
Pattern : Divided by 3

Problem Solving

Question 16.
Look for Relationships James places 1 counter in the first box. He places 2 counters in the second box, 4 counters in the third box, 8 counters in the fourth box, and continues the pattern until he gets to the tenth box. How many counters did James place in the tenth box?

Answer: 512
Explanation:
Pattern is multiply by 2

Pick a Project

PROJECT 14A
How have roller coasters changed through the years?
Project: Make a Model Roller-Coaster Car

PROJECT 14B
How can you use currency from different countries?
Project: Make Your Own Currency

PROJECT 14C
How can patterns be used in sidewalks?
Project: Design Your Own Sidewalk

PROJECT 14D
How many stadiums in the United States have retractable roofs?
Project: Make a Seating Diagram

Lesson 14.1 Number Sequences

Solve & Share
Look at the rules and starting numbers below. What are the next 6 numbers in each pattern? Tell how you decided. Describe features of the patterns. Solve these problems any way you choose.
I can … use a rule to create and extend a number pattern and identify features of the number pattern not described by the rule.

Look Back! Look for Relationships Create two patterns that use the same rule but start with different numbers. Identify a feature of each pattern. For example, identify whether the numbers are all even, all odd, or alternate between even and odd.

Essential Question
How Can You Use a Rule to Continue a Pattern?

Visual Learning Bridge
The house numbers on a street follow the rule “Add 4.” If the pattern continues, what are the next three house numbers? Describe a feature of the pattern.

You can use a number line to help make sense of the problem and find the next three house numbers.

Use a number line to continue the pattern.
A rule is a mathematical phrase that tells how numbers or shapes in a pattern are related. The rule for the house numbers is “Add 4.”

The next three house numbers are 20, 24, and 28.

Describe features of the pattern.
Some patterns have features that are not given in the rule.
16, 20, 24, 28
One of the features of this pattern is all of the house numbers are even numbers.
Another feature is all of the house numbers are multiples of 4.

Convince Me! Generalize Can you use the rule “Add 4” to create a different pattern with all odd numbers? Explain.
Explanation:
No, we cannot apply this rule on odd numbers
when u add 4 to a odd number the answers all will be in odd numbers
but not the multiples.

Another Example!
On another street, the house numbers follow the rule “Subtract 5.” What are the next three house numbers after 825? Describe a feature of the pattern.

The next three house numbers are 820, 815, and 810. All of the house numbers are multiples of 5.

Guided Practice

Do You Understand?
Question 1.
Rudy’s rule is “Add 2.” He started with 4 and wrote the numbers below. Which number does NOT belong to Rudy’s pattern? Explain. 4,6, 8, 9, 10, 12
Answer: 9
Explanation:
9 number does NOT belong to Rudy’s pattern
Because it is not the multiple of 2

Do You Know How?
Continue the pattern. Describe a feature of the pattern.
Question 2.
Subtract 6
48, 42, 36, 30, 24, _____, _____, ______
Answer: 18,12,6.
Explanation:
Pattern = multiples of 6

Independent Practice

For 3-6, continue each pattern. Describe a feature of each pattern.
Question 3.
Subtract 3: 63, 60, 57, _____, _____
Answer: 54,51,48
Explanation:
Pattern is multiples of 3

Question 4.
Add 7: 444, 451, 458, _____, _____
Answer: 465,472.
Explanation:
pattern = Multiples of 7

Question 5.
Add 25: 85, 110, 135, _____, _____
Answer: 160,185
Explanation:
The sequence is completed by adding 25

Question 6.
Subtract 4: 75, 71, 67, _____, _____
Answer: 63,59
Explanation:
The sequence is completed by  subtracting 4

For 7-12, use the rule to generate each pattern.
Question 7.
Rule: Subtract 10
90, _____, _____
Answer: 80,70
Explanation:
The sequence is completed by subtracting 10

Question 8.
Rule: Add 51
16, _____, _____
Answer: 67,83
Explanation:
The sequence is completed by adding 51

Question 9.
Rule: Add 5
96, _____, _____
Answer: 101, 106
Explanation:
The sequence is completed by adding 5

Question 10.
Rule: Add 107
43, _____, _____
Answer:  150, 257
Explanation:
The sequence is completed by adding 107

Question 11.
Rule: Subtract 15
120, _____, _____
Answer: 105, 90
Explanation:
The sequence is completed by Subtracting 15

Question 12.
Rule: Subtract 19
99, _____, _____
Answer: 80, 61
Explanation:
The sequence is completed by Subtracting 19

Problem Solving

Question 13.
Reasoning Orlando delivers mail. He sees one mailbox that does not have a number. If the numbers are in a pattern, what is the missing number?

Answer: 31
Explanation:
Pattern : Add 2
The missing number is 31

Question 14.
A bus tour runs 9 times a day, 6 days a week. The bus can carry 30 passengers. Find the greatest number of passengers who can ride the tour bus each week.
Answer: 1620
Explanation:
6 x 9 = 54 trips
54 x 30 = 1620
The greatest number of passengers who can ride the tour bus each week is 1620 passengers.

Question 15.
The year 2017 was the year of the Rooster on the Chinese calendar. The next year of the Rooster will be 2029. The rule is “Add 12.” What are the next five years of the Rooster?

Answer: 2041, 2053, 2065, 2077, 2089
Explanation:
The next five years of the Rooster are 2041, 2053, 2065, 2077, 2089

Question 16.
Describe a feature of the year of the Rooster pattern.
Answer: Multiples of 12
Explanation:
Feature of the year of the Rooster pattern is multiples of 12

Question 17.
Vocabulary Define rule. Create a number pattern using the rule “Subtract 7.”
Answer: Rule = multiples of 7
Explanation:
70, 63, 56, 49
Is the pattern of Subtract 7

Question 18.
Higher Order Thinking Some patterns use both addition and subtraction in their rules. The rule is “Add 3, Subtract 2.” Find the next three numbers in the pattern.
1, 4, 2, 5, 3, 6, 4, 7, _____, _____, _____
Answer: 5, 8 , 6
Explanation:
The next three numbers in the pattern is 5, 8 , 6

Assessment Practice

Question 19.
Rima used “Subtract 3” as the rule to make a pattern. She started with 60, and wrote the next six numbers in her pattern. Which number does NOT belong in Rima’s pattern?

A. 57
B. 54
C. 45
D. 26
Answer: D
Explanation:
26 number does NOT belong in Rima’s pattern

Question 20.
Ivan counted all the beans in a jar. If he counted the beans in groups of 7, which list shows the numbers Ivan could have named?
A. 77, 84, 91, 99
B. 301, 308, 324, 331
C. 574, 581, 588, 595
D. 14, 24, 34, 44
Answer: B
Explanation:
301, 308, 324, 331 list shows the numbers Ivan could have named

Lesson 14.2 Patterns: Number Rules

Solve & Share
There are 6 juice boxes in 1 pack, 12 in 2 packs, and 18 in 3 packs. How many juice boxes are in 4 packs? in 5 packs? in 6 packs? Use the rule to complete the table. Describe features of the pattern. Then find how many juice boxes are in 10 packs and 100 packs.
I can … use a rule to extend a number pattern, identify features of the number pattern, and use the number pattern to solve a problem.

Look Back! Reasoning Create a table showing the relationship between the number of bicycles and the number of bicycle wheels. Start with 1 bicycle. Complete 5 rows of the table using the rule “Multiply by 2.” Describe features of the pattern.
gf

Essential Question
What is the Pattern?

Visual Learning Bridge
There are 3 leaflets on 1 cloverleaf. There are 6 leaflets on 2 cloverleaves. There are 9 leaflets on 3 cloverleaves. How many leaflets are on 4 cloverleaves? How many cloverleaves will have 12 leaflets?

You can use a table to create, extend, and identify features of a pattern.

How many leaflets are on 4 cloverleaves?

There are 12 leaflets on 4 cloverleaves. The number of leaflets is a multiple of the number of cloverleaves.

How many cloverleaves for 12 leaflets?

There are 4 cloverleaves for 12 leaflets. The number of cloverleaves is a factor of the number of leaflets.

Convince Me! Model with Math If you know the number of leaflets, l, what expression can you use to find the number of cloverleaves, c? If you know the number of cloverleaves, what expression can you use to find the number of leaflets?

Guided Practice

Do You Understand?
Question 1.
The rule for this table is “Multiply by 4.” What number does not belong?

Answer: 15
Explanation:
4 x  4 = 16
15 does not belong to the  group

Do You Know How?
Complete the table. Describe a feature of the pattern.
Question 2.
Rule: Divide by 4

Answer: 5

Explanation:
5 x 4 = 20
Multiply by 4 is the pattern

Independent Practice

For 3-6, use the rule to complete each table. Describe a feature of each pattern.
You can multiply or divide to find the patterns in these tables.
Question 3.
Rule: Multiply by 8

Answer:

Explanation:
2 x 8 = 16
5 x 8 = 40
The sequence is completed by the multiplies of 8

Question 4.
Rule: Divide by 5

Answer:

Explanation:
The sequence is completed by Divide by 5

Question 5.
Rule: Multiply by 16

Answer:

Explanation:
The sequence is completed by the multiples of 16

Question 6.
Rule: Divide by 2

Answer:

Explanation:
The sequence is completed by dividing with 2
500 divided by 2 is 250
730 divided by 2 is 365

Problem Solving

Question 7.
The table shows how much money Joe makes painting. How much money will Joe make when he paints for 6 hours?
Rule: Multiply by 45

Answer: 270

Explanation:
$270 money will Joe make when he paints for 6 hours

Question 8.
The table shows the total number of pounds of potatoes for different numbers of bags. How many bags does it take to hold 96 pounds of potatoes?
Rule: Divide by 8

Answer: 12

Explanation:
12 bags it take to hold 96 pounds of potatoes

Question 9.
Number Sense What is the greatest number you can make using each of the digits 1,7,0, and 6 once?
Answer: 7106
Explanation:
7106  is the greatest number you can make using each of the digits 1,7,0, and 6 once

Question 10.
Algebra A penguin can swim 11 miles per hour. At this speed, how far can it swim in 13 hours? Use s as a variable. Write and solve an equation.
Answer: 143 miles
Explanation:
s = 11 x 13
s = 143 miles

For 11-12, the rule is “Multiply by 3.”

Question 11.
Reasoning Using the rule, how many batteries do 8 flashlights need?
Answer: 24
Explanation:
8 x 3 = 24
24 batteries has 8 flashlights needed.

Question 12.
Higher Order Thinking How many more batteries do 20 flashlights need than 15 flashlights? Explain.
Answer:
15 x 3 = 45
20 x 3 = 60
60 – 45 = 15
Explanation:
15 more batteries do 20 flashlights need than 15 flashlights

Assessment Practice

Question 13.
There are 6 rolls in each package. Use the rule “Divide by 6” to show the relationship between the number of rolls and the number of packages. Use each digit from the box once to complete the table.

Answer:

Explanation:
Used each digit from the box once to complete the table.

Lesson 14.3 Patterns: Repeating Shapes

Solve & Share
The rule for the repeating pattern below is “Square, Triangle.” What will be the 37th shape in the pattern? Explain. Solve this problem any way you choose.
I can … use a rule to predict a number or shape in a pattern.

Look Back! When the pattern has 37 shapes, how many are triangles?
Answer:
37 divided by 2 is 18 times triangles
37 is the triangle

Essential Question
How Can You Use a Repeating Pattern to Predict a Shape?

Visual Learning Bridge
Rashad is making a repeating pattern for the rule “Triangle, Square, Trapezoid.” What will be the 49th shape in the pattern?
A repeating pattern is made up of shapes or numbers that form a part that repeats.

Explanation:
49th shape is triangle
48 divided by 3 is 16
so, the next is triangle

Look for Features of the Repeating Pattern

The trapezoid is the 3^rd, 6^th, and 9^th shape in the pattern. The positions of the trapezoids are multiples of 3.

The triangle is the 15^th, 4^th, and 7^th shape in the pattern. The positions of the triangles are 1 more than a multiple of 3.

The square is the 2^nd, 5^th, and 8^th shape in the pattern. The positions of the squares are 1 less than a multiple

Use the Repeating Pattern to Solve
When you divide 49 by 3, the quotient is 16 R1. The pattern repeats 16 times. The 1st shape in the repeating pattern, a triangle, then appears.

49 is one more than a multiple of 3.
The 49th shape is a triangle.

Convince Me! Be Precise Suppose the rule is “Square, Triangle, Square, Trapezoid” in a repeating pattern. What is the 26th shape in the pattern? Describe features of the repeating pattern. Be precise in your description.

Another Example!
Write the next three numbers in the repeating pattern. Then name the 100th number in the pattern.

Rule: 1, 3, 5, 7 1, 3, 5, 7, 1, 3, 5, 7, 1, 3, 5, 7, 1, 3, 5 …
There are 4 items in the repeating pattern. To find the 100^th number, divide by 4. The pattern repeats 25 times. The 100^th number is 7.

Guided Practice

Do You Understand?
Question 1.
In the “Triangle, Square, Trapezoid” example on the previous page, what will be the 48^th shape? the 50^th shape? Explain.
Answer: 48th is trapezoid, 50th is square
Explanation:
When you divide 49 by 3, the quotient is 16 R1. The pattern repeats 16 times. The 1st shape in the repeating pattern, a triangle, then appears.

Do You Know How?
Question 2.
What is the 20^th shape? The rule is “Triangle, Circle, Circle.”

Answer: circle
Explanation:
When you divide 20 by 3, the quotient is 6 R2. The pattern repeats 6 times. The 1st shape in the repeating pattern, a circle, then appears.

Question 3.
Write the next three numbers. The rule is “9, 2, 7, 6.”
9, 2, 7, 6, 9, 2, 7, 6, ____, _____, ______
Answer: 9,2,7
Explanation:
The next three numbers 9, 2, 7

Independent Practice

For 4-7, draw or write the next three items to continue each repeating pattern.
Question 4.
The rule is “Square, Triangle, Square.”

Answer:

Explanation:
The pattern is completed with the help of rule

Question 5.
The rule is “Up, Down, Left, Right.”

Answer:

Explanation:
The pattern is completed with the help of rule

Question 6.
The rule is “1, 1, 2.”
1, 1, 2, 1, 1, 2, ____ , ____, ____ ……
Answer: 1,1,2
Explanation:
The pattern is completed with the help of rule

Question 7.
The rule is “5, 7, 4, 8.”
5, 7, 4, 8, 5, 7, 4, 8, 5, 7, ____, ____, ____ ……
Answer: 4, 8, 5
Explanation:
The pattern is completed with the help of rule

For 8-9, determine the given shape or number in each repeating pattern.
Question 8.
The rule is “Tree, Apple, Apple.” What is the 19^th shape?

Answer:
Explanation:
When you divide 19 by 3, the quotient is 6 R1. The pattern repeats 6 times. The 1st shape in the repeating pattern, a tree, then appears.

Question 9.
The rule is “1, 2.” What is the 42^nd number?
1, 2, 1, 2, 1, 2, …
Answer:
Explanation:
When you divide 42 by 2, the quotient is 21 R0. The pattern repeats 21 times.
The pattern is closed so the pattern end with 2.

Problem Solving

Question 10.
Create a repeating pattern using the rule “Triangle, Square, Square.”
Answer:

Explanation:
Created a repeating pattern using the rule “Triangle, Square, Square.”
Ends with the triangle.

Question 11.
enVision® STEM Margot measured the distance for 6 wavelengths of visible light as 2,400 nanometers. What is the distance for 1 wavelength?
Answer:
2400 divided by 6 = 400
Explanation:
400 is the distance for 1 wavelength

Question 12.
Look for Relationships Hilda is making a repeating pattern with the shapes below. The rule is “Heart, Square, Triangle.” If Hilda continues the pattern, what will be the 11th shape?

Answer:
Explanation:
When you divide 11 by 3, the quotient is 3 R2. The pattern repeats 3 times.
The 2nd shape in the repeating pattern, a square, then appears.

Question 13.
Look for Relationships Josie puts beads on a string in a repeating pattern. The rule is “Blue, Green, Yellow, Orange.” There are 88 beads on her string. How many times did Josie repeat her pattern?
Answer: 22 times
Explanation:
When you divide 88 by 4, the quotient is 22 R0. The pattern repeats 22 times.
The pattern is closed so the pattern end with yellow

Question 14.
How many more years passed between the first steam locomotive and the gasoline-powered automobile than between the gasoline-powered automobile and the first diesel locomotive?

Answer: 81 , 27
Explanation:
steam locomotive and the gasoline-powered automobile
1885 – 1804 = 81
81 years
gasoline-powered automobile and the first diesel locomotive
1912 – 1885= 27

Question 15.
Louisa used the rule “Blue, Green, Green, Green” to make a bracelet with a repeating pattern. She used 18 green beads. How many beads did Louisa use to make the bracelet? How many beads were NOT green?
Answer:
18 divided by 3 is 6
so, pattern repeated 6 times
6 x 4 = 24
24 – 18 = 6
Explanation:
6 beads were NOT green

Question 16.
Higher Order Thinking Marcus is using shapes to make a repeating pattern. He has twice as many circles as squares. Make a repeating pattern that follows this rule.
Answer: The rule is circle , square , square

Explanation:
The pattern is made according to the rule.

Assessment Practice

Question 17.
Which rules give a repeating pattern that has a square as the 15th shape? Select all that apply.
☐ Square, Circle
☐Circle, Square, Triangle
☐ Square, Circle, Triangle
☐ Circle, Triangle, Square
☐ Trapezoid, Circle, Square
Answer:

Explanation:
Selected all that apply
where the 15th shape is a square.

Question 18.
Which rules give a repeating pattern that has a 7 as the 15^th number? Select all that apply.
☐ 1, 7
☐ 1, 7, 9
☐ 1, 9, 7
☐ 1, 7, 7
☐ 7, 1, 9
Answer:

Explanation:
selected pattern rules give a repeating pattern that has a 7 as the 15^th number

Lesson 14.4 Problem Solving

Look For and Use Structure
Solve & Share
Evan’s baby brother is stacking blocks. Using the rule “Add 1 block to the number of blocks in the previous stack,” how many blocks will be in the 6th stack? Explain. Justify your answer.
I can … use patterns to help solve problems.

Thinking Habits
• What patterns can I see and describe?
• How can I use the patterns to solve the problem?
· Can I see expressions and objects in different ways?

Look Back! Look For Relationships How many blocks are in the 10th stack? Explain.

Essential Question
How Can I Look For and Make Use of Structure?

Visual Learning Bridge
Alisa made three walls with cubes. She recorded her pattern. If she continues the pattern, how many cubes will be in a 10-layer wall? a 100-layer wall?

What do you need to do to find the number of cubes in a 10-layer and 100-layer wall?
I need to continue the pattern using the rule and analyze the pattern to find features not stated in the rule itself.

How can I make use of structure to solve this problem?
I can

• look for and describe patterns in three dimensional shapes.
• use the rule that describes how objects or values in a pattern are related.
• use features of the pattern not stated in the rule to generate or extend the pattern.

Here’s my thinking.
Make a table and look for patterns.

There are 4 cubes in each layer. Multiply the number of layers by 4 to calculate the number of cubes.
A 10-layer wall contains 10 × 4 = 40 cubes.
A 100-layer wall contains 100 × 4 = 400 cubes.

Convince Me! Look for Relationships How could you use multiples to describe Alisa’s pattern?

Guided Practice

Use Structure
Leah arranged triangular tiles in a pattern like 1 row the one shown. She used the rule “Multiply the number of rows by itself to get the number of small triangles.” How many small triangles would be in the pattern if there were 10 rows?

Question 1.
Complete the table to help describe the pattern.

Answer:

Explanation:
Multiplied the number by itself

Question 2.
Describe the pattern another way.
Answer:
4 x 4 = 12
5 x 5 = 25
Explanation:
used the rule “Multiply the number of rows by itself to get the number of small triangles

Question 3.
How many triangles would be in 10 rows?
Answer: 100
Explanation:
10 x 10= 100
used the rule “Multiply the number of rows by itself to get the number of small triangles

Independent Practice

Look for Relationships
Alan built the towers shown using the rule “Each story has 2 blocks.” How many blocks will a 10-story tower have? Use Exercises 4-6 to answer the question.

Question 4.
Complete the table to help describe the pattern.

Answer: 10 x 2 = 20

Explanation:
Pattern is add by 2

Question 5.
What is another way to describe the pattern that is not described by the rule?
Answer:
Explanation:
Pattern is add by 2

Question 6.
How many blocks are in a 10-story tower? Explain.
Answer: 10 x 2 = 20
Explanation:
used the rule “Multiply the number with 2″

Problem Solving

Performance Task

Glass Stairs
An art gallery staircase is built using glass cubes. The diagram below shows 4 steps are 4 cubes high and 4 cubes across. Five steps are 5 cubes high and 5 cubes across. How many glass cubes are used to make 7 steps? Use Exercises 7-10 to answer the question.

Question 7.
Make Sense and Persevere What do you know, and what do you need to find?
Answer:
4 steps are 4 cubes high and 4 cubes across. Five steps are 5 cubes high and 5 cubes across
is what we know
7 steps is to find
seven steps are 7 cubes high and 7 cubes across

Question 8.
Reasoning Complete the table.

Answer:

Explanation:
Pattern = multiply by 3

Question 9.
Look For Relationships What pattern can you determine from the table?

Answer: Pattern = multiply by 3
Explanation:
multiply by 3 pattern can you determine from the table

Question 10.
Reasoning How many cubes are needed for 7 steps? Write and solve an equation.
Answer: 49 cubes
Explanation:
7 x 7 = 49
seven steps are 7 cubes high and 7 cubes across
49 cubes are needed for 7 steps

Topic 14 Fluency Practice Activity

Point & Tally
Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue. Partner 1 and Partner 2 each point to a black number at the same time. Each partner adds the two numbers. If the answer is on your color, you get a tally mark. Work until one partner has twelve tally marks.
I can … add multi-digit whole numbers.

Topic 14 Vocabulary Review

Understand Vocabulary
Word List

• equation
• even number
• factor
• multiple
• odd number
• repeating pattern
• rule
• unknown

Question 1.
Circle the term that best describes 28.
even
odd
equation
unknown
Answer: Even
Explanation:
Even is the word which is divisible by 2

Question 2.
Circle the term that best completes this sentence: 4 is a _________ of 16.
even
odd
factor
multiple
Answer: factor
Explanation:
2, 4 , 8 are the factors of 16

Question 3.
Circle the term that best describes 17.
even
odd
equation
unknown
Answer: Odd
Explanation:
Odd numbers are the numbers that cannot be divided by 2 evenly.

Question 4.
Circle the term that best completes this sentence: 9 is a _________ of 3.
even
odd
factor
multiple
Answer: Multiple of 3
Explanation:
3 x 3 = 9
9 is the multiple of 3

Question 5.
Draw a line from each term to its example.

Answer:

Explanation:
The preview  words are matched with the correct answers.

Use Vocabulary in Writing
Question 6.
Use at least 3 terms from the Word List to describe the pattern.
50, 48, 46, 44, 42 …
Answer:
Even numbers
Multiple
Rule
Explanation:
The above all numbers are even numbers
They are multiples of 2
Rule= less 2

Topic 14 Reteaching

Set A pages 521-524

You can use the rule “Subtract 3” to continue the pattern.

The next three numbers in the pattern are 9,6, and 3
A feature of the pattern is all the numbers are multiples of 3.
Another feature is all the numbers in the pattern alternate even, odd.

Remember to check that the numbers in your pattern follow the rule.

Use the rule to continue each pattern. Describe a feature of the pattern.
Question 1.
Rule: Add 20
771, 791, 811, _____, _____, _____
Answer: 831, 851
Explanation:
A feature of the pattern is all the numbers are odd numbers

Question 2.
Rule: Subtract 12
122, 110, 98, _____, _____, ______
Answer: 86, 74, 62
Explanation:
A feature of the pattern is all the numbers are even numbers

Set B pages 525-528

The regular price is twice the sale price. You can use the rule “Divide by 2” to continue the pattern.

Remember to look for features of the pattern not described by the rule.

Use the rule to continue each pattern. Describe a feature of the pattern.
Question 1.
Rule: Multiply by 18

Answer:

Explanation:
A feature of the pattern is all the numbers are even numbers

Question 2.
Rule: Divide by 9

Answer:  $100

Explanation:
A feature of the pattern is all the numbers are even and odd numbers

Question 3.
Rule: Multiply by 24

Answer:

Explanation:
A feature of the pattern is all the numbers are even

Set C pages 529-532

You can use the rule “Circle, Triangle, Square” to continue the repeating pattern.

You can use the rule to find the 25^th shape in the pattern.
25 ÷ 3 = 8 R1.
The pattern will repeat 8 times, then the 1^st shape will appear.
The circle is the 25^th shape in the pattern.

Remember to use the rule to continue the pattern.

Question 1.
a. Draw the next three shapes in the repeating pattern. The rule is “Right, Up, Up.”

Answer:

Explanation:
Up, Up, Right is the next three shapes in the repeating pattern

b. Draw the 50^th shape in the pattern.
Answer:
Explanation:
You can use the rule to find the 50^th shape in the pattern.
50 ÷ 3 = 16 R2.
The pattern will repeat 16 times, then the 1^st shape will appear.
The up is the 50^th shape in the pattern.

Question 2.
a. Write the next three numbers in the repeating pattern. The rule is “3, 5, 7, 9.”
3, 5, 7, 9, 3, 5, 7, ____, _____, ______
Answer: 9, 3, 5, 7
Explanation:
9, 3, 5, 7 the next three numbers in the repeating pattern

b. What will be the 100^th number in the pattern?
Answer:
Explanation:
You can use the rule to find the 100^th number in the pattern.
100 ÷ 4 = 25 R0.
The pattern will repeat 25 times,
There the pattern ends so, the 100th  number is 7

Set D pages 533-536

Think about these questions to help you Look For and Use Structure.
Thinking Habits

• What patterns can I see and describe?
• How can I use the patterns to solve the problem?
• Can I see expressions and objects in different ways?
  

Remember to use the rule that describes how objects or values in a pattern are related.

Sam creates a pattern using the rule “Each story has 3 blocks.”

Question 1.
Draw the next shape in Sam’s pattern.
Answer:

Explanation:
4 x 4 is the Sam’s next shape

Question 2.
Use the rule to continue Sam’s pattern.

Answer:

Explanation:
pattern = multiple of 3

Question 3.
How many blocks are in the 10th shape in Sam’s pattern?
Answer:
10 x 10 = 100
Explanation:
100 blocks are in the 10th shape in Sam’s pattern.

Topic 14 Assessment Practice

Question 1.
Football players come out of the tunnel, and their jerseys have the number pattern shown below. They follow the rule “Add 4.”

A. What number belongs on the front of the blank jersey? Explain.
Answer: 24
Explanation:
Number 24 belongs on the front of the blank jersey

B. Describe two features of the pattern.
Answer:
Explanation:
A feature of the pattern is all the numbers are even
A feature of the pattern is all the numbers are multiples of  4

Question 2.
One dozen eggs is 12 eggs. Two dozen eggs is 24 eggs. Match the number of dozens to the number of eggs. The rule is “Multiply by 12.”

Answer:

Explanation:
Matched the eggs with the dozen

Question 3.
Use the rule “Multiply by 6” to continue the pattern. Then describe a feature of the pattern.

Answer:

Explanation:
A feature of the pattern is all the numbers are even

Question 4.
Use the rule “Divide by 3” to continue the pattern. Then write 4 terms of a different pattern that follows the same rule.
729, 243, 81, ____, _____
Answer: 27, 9 , 3, 1
Explanation:
4 terms of a different pattern that follows the same rule is 27, 9 , 3, 1

Question 5.
Nicole arranges her shopping purchases by price. Each item costs $6 more than the last. The first item costs $13. The last costs $61. Her brother John says that the price of each item is an odd number. Is John correct? Find the cost of each item to explain.
Answer: 19 , 25 , 31, 37 , 43, 49, 55, 61.
Explanation:
John says that the price of each item is an odd number. yes, John correct

Question 6.
The rule for the repeating pattern is “5, 7, 2, 8.” Write the next three numbers in the pattern. Then tell what will be the 25th number in the pattern. Explain.
5, 7, 2, 8, 5, 7, 2, 8, 5, _____, _____, _____
Answer:
5, 7, 2, 8, 5, 7, 2, 8, 5, 7, 2, 8
Explanation:
You can use the rule to find the 25^th number in the pattern.
25 ÷ 4 = 6 R1.
The pattern will repeat 6 times,
then the 1^st number will appear.
The 5 is the 25^th number in the pattern

Question 7.
Jackson wrote different patterns for the rule “Subtract 5.” Select all of the patterns that he could have written. Then write 4 terms of a different pattern that follows the same rule.
☐ 27, 22, 17, 12,7
☐ 5, 10, 15, 20, 25
☐ 55, 50, 35, 30, 25
☐ 100, 95, 90, 85, 80
☐ 75, 65, 55, 45, 35
Answer:

Explanation:
different patterns for the rule “Subtract 5.”
Selected all of the patterns that he could have written

Question 8.
The rule is “Subtract 7.” What are the next 3 numbers in the pattern? Describe two features of the pattern.
70,63, 56, 49, 42,35
Answer: 28, 21, 14, 7
Explanation:
28, 21, 14, 7 the next 3 numbers in the pattern

Question 9.
The table shows the different number of teams formed by different numbers of players. The rule is “Divide by 8.”

A. How many teams can be formed with 40 players?
_______ teams
Answer: 5
Explanation:
5 teams can be formed with 40 players

B. How many players are there on 13 teams? How do you know?
Answer: 104
Explanation:
104 players are there on 13 teams

Question 10.
A. Select all the true statements for the repeating pattern. The rule is “Circle, Heart, Triangle.”

☐ The next shape is the circle.
☐ The circle only repeats twice.
☐ The 10^th shape is the heart.
☐ The 12^th shape is the triangle.
☐ The circle is the 1^st, 4^th, 7^th, etc. shape.
Answer:

Explanation:
Selected all the true statements for the repeating pattern.

B. How many triangles are there among the first 22 shapes?
Answer: 7
Explanation:
7 triangles are there among the first 22 shapes

Topic 14 Performance Task

Wall Hangings Michael uses knots to make wall hangings to sell.

Question 1.
The Michael’s Basic Wall Hanging figure shows a simple wall hanging Michael makes by repeating the shapes shown. What is the 16th shape in the repeating pattern? The rule is “Circle, Triangle, Square.” Explain.
Answer:
Explanation:
You can use the rule to find the 25^th number in the pattern.
16 ÷ 3 =  R1.
The pattern will repeat 5 times,
then the 1^st shape will appear.
The circle is the 16^th shape in the pattern

Question 2.
The Snowflake Design figure shows a knot Michael likes to use.

Part A
List the number of knots that Michael uses to form 1 to 6 snowflake designs. The rule is “Add 11.”
Answer: 11 , 22, 33, 44, 55, 66
Explanation:
The number of knots that Michael uses to form 1 to 6 snowflake designs 11 , 22, 33, 44, 55, 66

Part B
Describe a feature of the pattern you listed in Part A that is not part of the rule. Explain why it works.
Answer:
Explanation:
A feature of the pattern is all the numbers are even and odd

Question 3.
The Michael’s Wall Hanging figure shows the design of a wall hanging Michael makes using the Snowflake Design. Answer the following to find how many knots Michael ties to make a wall hanging with 28 snowflakes.

Part A
Each column of 4 snowflakes has 4 connectors. There are also 4 connectors between columns. Complete the Connectors table using the rule “Add 8 connectors for each column.” Describe a feature of the pattern.

Answer:

Explanation:
Completed the table by following the rule

Part B
Complete the Total Knots table using the following rules.
Snowflake Knots rule: Multiply the number of snowflakes by 11.
Connector Knots rule: Multiply the number of connectors from the Connectors table by 3.
Total Knots rule: Add the number of snowflake knots and the number of connector knots.

Answer:

Explanation:
Snowflake Knots rule: Multiply the number of snowflakes by 11.
Connector Knots rule: Multiply the number of connectors from the Connectors table by 3.
Total Knots rule: Add the number of snowflake knots and the number of connector knots.

Go through the enVision Math Common Core Kindergarten Answer Key Topic 12 Identify and Describe Shapes regularly and improve your accuracy in solving questions.

enVision Math Common Core Kindergarten Answers Key Topic 12 Identify and Describe Shapes

Essential Question:
How can two- and three-dimensional shapes be identified and described?
Answer
A two-dimensional (2D) shape has only two measurements, such as length and height.
A square, triangle, and circle are all examples of a 2D shape.
However, a three-dimensional (3D) shape has three measurements, such as length, width, and height.
A cube, prism and cylinder are example of 3D shapes.

enVision STEM project: Pushing and Pulling Objects
Directions Read the character speech bubbles to students. Find Out! Have students investigate different kinds of wheels. Say: Not all wheels look alike, but they are all the same shape. Talk to your friends and relatives about the shape of a wheel and ask them how it can help when you need to push and pull objects. Journal: Make a Poster Have students make a poster that shows various objects with wheels. Have them draw up to 5 different kinds of objects that have wheels.
Answer:
Yes, students can investigate different kinds of wheels by recollecting means of transport like bus, car, bike and so on., while travelling.
Not all wheels look alike, but they are all the same shape.
With this we can bring the concept of circle shape to the students
Wheels are everywhere in our world today, in very obvious places like car, bus trucks etc., but also hidden inside everything from computer hard drives, dishwashers. Six thousand years ago, there weren’t any wheels at all. The rise of the wheel, from a basic turntable that helped people mold clay pots to a key component in hundreds of important invention owes everything to the simple and effective way it helps us capture and harness energy and transform forces. So we need wheels to push and pull the objects.
Poster:

Review What You Know

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Directions Have students: 1 draw a circle around the set of numbers that shows a pattern of counting by tens; 2 draw a circle around the hundred chart; 3 draw a circle around the numbers fifty-five and ninety-nine; 4 count the objects, write the numbers, and then draw a circle around the number that is greater than the other number; 5 count the objects, and then write the number; 6 draw a circle around the number that tells how many counters.

Pick a Project

A

Project A:
Answer:
Bone is specific to vertebrates, and originated as mineralization around the basal membrane of the throat or skin, giving rise to tooth-like structures and protective shields in animals with a soft cartilage-like endoskeleton. The bones gives the shape and posture to the body.
Steps to be followed for Dinosaur puzzles:
The primary material that you need for this project is corrugated cardboard or double layered cardboard.
The first thing that you need to do is find a template or draw the picture of Dinosaur.
Now that you have a template, you need to print it out in the size that you want.
Then attach the templates to the cardboard, you can use tape or a removable glue.
Then you need to mark the outline of each piece on the cardboard. You can do this by tracing each piece with a dark pen. You could also use a sharp object such as a knife or a needle to pierce through the template and into the cardboard.
Cut out the puzzle pieces and now comes the fun part i.e., putting the puzzle together.

B

PROJECT: B

Directions Say: You will choose one of these projects. Look at picture A. Think about this question: Where did all those bones come from? If you choose Project A, you will create dinosaur puzzles. Look at picture B. Think about this question: Would you rather design buildings or build them? If you choose Project B, you will design and build a structure.

C

Project C
Answer:
Depending on its size, it could be a pyramid, a clown’s hat, a slice of pie, a bird’s beak.
Depending on how they’re placed, they might suggest a mountain range or a tent encampment, a pine tree farm, or a schooner’s etc.,

D

Project D
Preparation of cookies

Lesson 12.1 Two-Dimensional(2-D) and Three-Dimensional (3-D) Shapes

Answer:
Solid figures are identified according to the features that are unique to each type of solid. Specifically, one can observe the numbers of faces, edges, and vertices, as well as the shape of the base.
A plane horizontal surface with no depths is called the flat surface.
The following groups are different based upon their shape and structure.
Classified into 2 dimensional and 3 dimensional shapes.
Flat and Solid shapes.

Directions Say: Pick 6 shapes from a bag. Put the shapes into two groups. Tell how the groups are different. Then draw a picture of the shapes you put on each table.

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Directions 1 Have students draw a circle around the objects that are flat, and mark an X on the objects that are solid.

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:
4 marked on X on the objects that are NOT flat

Question 5.

Answer:

5 marked on X on the objects that are NOT Solid.

Directions Have students 2 and 3 draw a circle around the objects that are flat, and mark an X on the objects that are solid. 4 mark on X on the objects that are NOT flat; 5 mark on X on the objects that are NOT Solid.

Independent Practice

Question 6.

Answer:

X marked on the objects that are solid. circled around the objects that are flat

Question 7.

Answer:
Marked an X on the objects that are NOT solid

Question 8.
Answer:
Yes, students can draw the Picture of an objects that are solid based upon previous concept of 2 dimensional and 3 dimensional shapes.

Directions Have students: 6 mark an X on the objects that are solid. Then have them draw a circle around the objects that are flat; 7 mark an X on the objects that are NOT solid 8 Higher Order Thinking Have students draw a picture of an object that is solid.

Lesson 12.2 Circles and Triangles

Directions Say: Go on a shape hunt. Find shapes and objects in the classroom or outside that look like the shapes shown on the page. Draw the shapes. Use your own words to tell where you found them. Then say: Tell how the shapes are different.
Answer:
Answer may vary according to the visualization of students.
The shapes and objects that are found in the classroom or outside are:
Football, cricket ball, basket ball, flying disc, pyramid etc., are found outside the classroom.
Clock, birthday caps etc., are found in classroom.
Both circle and triangle are different from each other as circle is round in shape and triangle has 3 sides.

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Question 2.

Answer:

Directions 1 and 2 Have students color the circle in each raw, and then mark an X on each triangle.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Directions 3 Have students color the circle and mark an X on the triangle. 4 Number Sense Have students mark an X on the shape that has 3 sides. 5 Have students mark an X on the objects that look like a triangle, and then draw a box around the objects that look like a circle.

Independent Practice

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

Question 10.
Answer:
Yes, by understanding the concept of shapes students can able to draw a picture of an object that is shaped like a triangle.
Picture of an object may vary from student to student.

Directions 6-9 Have students color the circles and mark an X on the triangles in each row. 10 Higher Order Thinking Have students draw a picture of an object that is shaped like a triangle.

Lesson 12.3 Squares and Other Rectangles

Solve & Share

Directions Say: Emily has a large quilt on her bed. The shape outlined with black lines is a rectangle. The rectangular quilt is made up of square rectangles of different colors. How many other rectangles can you find in the picture? How many of the rectangles are squares? Count the shapes and tell where you see them.
Answer:
only 1 rectangle
6 squares are rectangle
6 square shapes on the quilt

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Question 2.

Answer:

Directions 1 and 2 Have students color the rectangles in each row, and then mark an X on each rectangle that is also a square.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

EXPLANATION:
Have students tell how they know which objects to mark with an X.
Yes, know the students can identify the shapes of rectangle and square.
Rectangles and squares are the same?
No
How are they different?
They differ in Lengths of sides are not same as in Square( where all sides are of same length)

Directions Have students: 3 and 4 color the rectangles in each row, and then mark an X on each rectangle that is also a square; 5 draw a circle around the objects that look like a rectangle, and then mark an X on each object that also looks like a square. Have students tell how they know which objects to mark with an X. Say: How are rectangles and squares the same? How are they different?

Independent Practice

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

Question 10.
Answer:

Directions
6-9 Have students color the rectangles in each row, and then mark an X on each rectangle that is also a square. 10 Higher Order Thinking Have students draw a green rectangle, and then draw a yellow square.

Lesson 12.4 Hexagons

Solve & Share

Directions Say: Emily wants to buy art that has six-sided shapes in it like the yellow pattern block. Draw a circle around all the pieces of art that she can buy.

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Question 2.

Answer:

Directions 1 and 2 Have students color the hexagon in each row.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:
By understanding the concept of hexagon and counting the number of sides of an object students can able to draw a circle around the hexagon.

Question 6.

Answer:
By understanding the concept of hexagon and counting the number of sides of an object students can able to draw a circle around the hexagon.

Directions Have students: 3 and 4 color the hexagon; 5 and 6 draw a circle around the object that looks like a hexagon. Then have students tell how they decided which object to circle.

Independent Practice

Question 7.

Answer:

Question 8.
Answer:

Directions 7 Have students draw a circle around the objects that look like a hexagon, 8 Higher Order Thinking picture using at least I hexagon.

Lesson 12.5 Solid Figures

Directions Say: Jackson wants to find objects that have the same shape as the solid figures. How can he find objects that have the some shape? Draw objects below each solid figure that have the same shape.
Answer:
Solid figures are identified according to the features that are unique to each type of solid. Specifically, one can observe the numbers of faces, edges, and vertices, as well as the shape of the base. He can find by seeing the shape and pattern of an object whether they are cone, cylinder, sphere or circle and cube.

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Question 2.

Answer:

Directions 1 and 2 Have students name the solid figure on the left, and then draw a circle around the solid figure on the right that is the same shape.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Explanation:
Students can find objects like chalk piece in the shape of cylinder, sharped pencil tip as cone, clock as sphere.

Directions 3 and 4 Have students name the solid figure on the left, and then draw a circle around the solid figure on the right that is the same shape, 5-8 Have students name the solid figure on the left, and then draw a circle around the object on the right that looks like that shape. Then have students see if they can find objects in the classroom that look like a cone, a cylinder, or a sphere.

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Directions Have students: 9 and 10 look at the object on the left, and then draw a circle around the solid fig are on the right that looks like that shape; 11 name the solid figure on the left, and then draw a circle around the objects on the right that look like that shape 12 Higher Order Thinking Have students name the solid figure on the left, and then draw 2 mare objects that look like that shape.

Lesson 12.6 Describe Shapes in the Environment

Directions Say: Draw a circle around two of the shapes on the work mat. Name the shapes. Can you find the shapes you circled in your classroom? Use your own words to tell where you found them. Draw a picture of the objects and their surroundings.

Answer:

Yes – classroom board is in the shape of Rectangle and the clock is in the shape of circle

Visual Learning Bridge

Guided Practice

Question 1.

Answer:

Directions 1 Have students mark an X on the object next to the pencil that looks like a rectangle. Have students draw on object that looks like a square in front of the mug. Then have them draw an object that looks like a cone next to the table.

Question 2.

Directions 2 Vocabulary Have students name the shape of the objects in the picture and use position words to describe their location. Then have them draw an X on the object in front of the sand castle that looks like a cylinder. Have students draw an object that looks like o sphere beside Jackson, and then an object that looks like a rectangle next to the sandbox.

Answer:
Cylinder shaped hat and Sphere shaped ball is located on the sand and in side the rectangular box

Independent Practice

Question 3.

Answer:

Question 4.

Answer:
Circle above the tree and a triangle behind the fence

Directions 3 Have students point to objects in the picture and name each shape. Then have them draw a circle around the objects that look like a cylinder, and mark an X on the objects that look like a cone. 4 Higher Order Thinking Have students: mark an X on the object below the tree that looks like a rectangle; draw an object that looks like a circle above the tree; and draw an object that looks like a triangle behind the fence. Then have them name the shape of objects in the picture and use position words to describe their locations

Lesson 12.7 Precision

Problem Solving

Solve & Share

Directions Say: Emily’s teacher teaches her class a game. She uses I blue cube, I red cube, I yellow counter, and I red counter and puts each of them somewhere on the farm picture. Play this game with a partner. Place the fools on the page, and then describe where one of them is located. Do NOT tell your partner which one you are talking about. How can your partner tell which one you are describing? Change places and play again.

Guided Practice

Question 1.

Answer:

Directions 1 Have students mark an X on the object above the bed that looks like a cube. Then have them explain how they know they are correct. Then have them draw a shape that looks like a rectangle next to the bed.
Answer:
As the students learnt the concept of solid shapes in 12.5 solid figures one easily identify cube.

Independent Practice

Question 2.

Answer:

Rectangle has 4 sides and 6 faces , cylinder has 2 faces, sphere shaped ball is behind the Shuttle cock of cone shaped

Question 3.

Answer:
Cone dose not exist in the Solid pictures, Sphere is given in the left side which is looks like water melon of shaped sphere

Directions 2 Have students name the shapes of the objects in the picture. Then have them mark an X on the object that is behind another object, and is next to the object that looks like a cylinder. Have them explain how they decided which shape to mark. 3 Have students find the object in the picture that is NOT beside the box of tissues, and then mark an X on the solid it looks like on the left. Have them explain why a sphere is NOT the right answer Then have them name the shapes of the objects in the picture.

Problem Solving

Performance Task

Directions Read the problem to students. Then have them use multiple problem-solving methods to solve the problem. Say: Carlos wants to tell a friend about different things in the locker room and where they are located. What words can he use? 4 Be Precise Mark an X on the object that looks like a cylinder that is beside the object that looks like a cube. What words helped you find the correct object?
Answer:
cube is used to mark the cylinder X

5 Reason Carlos says the soccer ball is behind the water bottle. What is another way to explain where the water bottle is?
Answer:
The water bottle is under the Rectangular table

6 Explain Carlos describes the rectangle poster as being above the circle clock. Do you agree or disagree? Explain how you know you are correct.
Answer:
No, below the circle clock
The circle clock is above the rectangle poster

Topic 12 Fluency Practice Activity

Question 1.

Answer:
In this activity if you add or subtract any set of numbers to get 2, finally we can find an alphabet ‘H’.

Question 2.

Answer:

Directions Have students: 1 color each box that has a sum or difference that is equal to 2; 2 write the letter that they see.

Topic 12 Vocabulary Review

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.
Answer:

Question 5.
Answer:

Directions Understand Vocabulary Have students: 1 draw a circle around the two-dimensional shape; 2 draw a circle around the three-dimensional shape; 3 draw a circle around the vertices of the triangle; 4 draw a circle; 5 draw a shape that is NOT a square.

Topic 12 Reteaching

Set A

Question 1.

Answer:

Set B

Question 2.

Answer:

Directions Have students: 1 draw a circle around the objects that are flat, and then mark an X on the objects that are solid; 2 draw c circle around the objects that look like a circle, and then mark an X on the objects that look like a triangle.

Set C

Question 3.

Answer:

Set D

Question 4.

Answer:

Directions Have students: 3 color the rectangles, and then mark on X on the rectangle that is a square; 4 color the hexagons.

Set E

Question 5.

Answer:

Set F

Question 6.

Answer:

Directions Have students: 5 name the solid figure on the left, and then draw a circle around the solid figure that looks like that shape on the right; 6 point to each object in the picture and tell what shape each looks like. Then have them draw a circle around the objects that are solid, and mark an X on objects that are flat.

Question 7.

Answer:

Set G

Question 8.

Answer:

Directions Have students: 7 mark an X on the object that is next to the blue book, end then draw a circle around the object that is below the object that is shaped like a sphere; 8 mark an X on the objects that look like a circle that are behind the abject that is shaped like a sphere.

Topic 12 Assessment Practice

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Directions Have students mark the best answer. 1 Which object is NOT solid? 2 Which object is NOT a triangle? 3 Choose two objects that look like a hexagon, 4 Which object looks like a square?

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Directions Have students: 5 mark an X on the objects that do NOT look like a circle; 6 name the shapes, color the rectangles, and then mark on X on the rectangle that is a square; 7 look at the solid figure an the left, and then draw a circle around the object that looks like that shape.

Question 8.

Answer:

Question 9.

Answer:

Directions Have students: 8 draw an object that looks like a cylinder in front of the vase. Then mark on X on the object that looks like a square next to the cat; 9 choose flat or solid for each image.

Question 10.
Answer:

Question 11.
Answer:

Question 12.

Answer:

Directions Have students: 10 draw a picture of an object that looks like a sphere below a book and next to a cup; 11 draw a picture of an object that is flat. Then have them draw on object that is solid; 12 draw a circle around the objects that look like a circle, and then mark an X on the objects that look like a rectangle.

Topic 12 Performance Task

Question 1.

Answer:

Question 2.

Answer:

Directions Play Time! Say: Supna and her friends are playing with toys. Have students: 1 draw a circle Ground the toys that look like a cube. Have students mark an X on the toys that look like a cylinder; 2 draw a circle around the toys that look like a rectangle. Then have them mark an X on the rectangles that are squares.

Question 3.
Answer:

Question 4.
Answer:

Question 5.

Answer:

Directions Have students: 3 mark an X on the object in the playroom that looks like a hexagon; 4 draw an object next to the shelves that looks like a cone; 5 listen to the clues, and then draw a circle around the object the clues describe. Say: The object is above the blocks. It looks like a sphere. It is next to a green ball. The object is NOT yellow.

Go through the enVision Math Common Core Grade 4 Answer Key Topic 13 Measurement: Find Equivalence in Units of Measure regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 13 Measurement: Find Equivalence in Units of Measure

Essential Questions:
How can you convert from one unit to another? How can you be precise when solving math problems?

enVision STEM Project: Erosion and Measurement
Do Research The Colorado River has played a large part in shaping North America. Use the Internet and other resources to research the states through which the river travels.
Journal: Write a Report Include what you found. Also in your report:

• Look up geology and geometry in the dictionary. Write the definitions and explain how these words are related. What does the prefix “geo” mean in both words?
• A.J. takes a 4-mile tour of the Grand Canyon. Explain how to convert the length of A.J.’s tour from miles to feet.

Review What You Know

Vocabulary

Choose the best term from the box. Write it on the blank.

• capacity
• gram
• liter
• mass

Question 1.
The amount of liquid a container can hold is called its ________.
Answer:
The amount of liquid a container can hold is called its __capacity______.

Question 2.
________ is the amount of matter that something contains.
Answer:
___Mass_____ is the amount of matter that something contains.

Question 3.
One metric unit of capacity is a ________.
Answer:
One metric unit of capacity is a __Liter______.

Perimeter
Find the perimeter of each shape.
Question 4.

Answer:
Perimeter of the given rectangle shape = 134 centimeters.

Explanation:
Length of the given rectangle shape = 42 centimeters.
Width of the given rectangle shape = 25 centimeters.
Perimeter of the given rectangle shape = 2 × (Length of the given rectangle shape × Width of the given rectangle shape)
= 2 × (42 + 25)
= 2 × 67
= 134 centimeters.

Question 5.

Answer:
Perimeter of the given square shape = 28 feet.

Explanation:
Length of the given square shape = 7 feet.
Perimeter of the given square shape = 4 × Length of the given square shape
= 4 × 7
= 28 feet.

Question 6.

Answer:
Perimeter of the given Triangular shape = 9 yards.

Explanation:
Length of the given Triangular shape = 3 yards.
Perimeter of the given Triangular shape =  Length of the given Triangular shape + Length of the given Triangular shape + Length of the given Triangular shape
= 3 + 3 + 3
= 9 yards.

Question 7.

Answer:
Perimeter of the given Quadrilateral shape = 62 inches.

Explanation:
Length of the given Quadrilateral shape:
Side 1 length = 17 inches.
Side 2 length = 12 inches.
Side 3 length = 21 inches.
Side 4 length = 12 inches.
Perimeter of the given Quadrilateral shape = Side 1 length + Side 2 length + Side 3 length + Side 4 length
= 17 + 12 + 21 + 12
= 29 + 21 + 12
= 50 + 12
= 62 inches.

Question 8.

Answer:
Perimeter of the given hexagon shape = 90 centimeters.

Explanation:
Length of the given hexagon shape = 15 centimeters.
Perimeter of the given hexagon shape = 6 × Length of the given hexagon shape
= 6 × 15
= 90 centimeters.

Question 9.

Answer:
Perimeter of the given rectangle shape = 40.67 feet.

Explanation:
Length of the given rectangle shape = 19 (11/12) feet.
Width of the given rectangle shape =  7 (5/12) feet.
Perimeter of the given rectangle shape = 2 × (Length of the given rectangle shape × Width of the given rectangle shape)
= 2 × (19 11/12 + 7 5/12)
= 2 × (209/12 + 35/12)
= 2 × 244/12
= 488/12
= 40.67 feet.

Area
Find the area of each shape.
Question 10.

Answer:
Area of the given rectangle shape = 10 square yards.

Explanation:
Length of the given rectangle shape = 5 yards.
Width of the given rectangle shape =  2 yards.
Area of the given rectangle shape = Length of the given rectangle shape × Width of the given rectangle shape
= 5 × 2
= 10 square yards.

Question 11.

Answer:
Area of the given rectangle shape = 1/2 or 0.5 inches.

Explanation:
Length of the given rectangle shape = 2 inches.
Width of the given rectangle shape =  1/4 inches.
Area of the given rectangle shape = Length of the given rectangle shape × Width of the given rectangle shape
= 2 × 1/4
= 1/2 or 0.5 inches.

Question 12.

Answer:
Area of the given rectangle shape = 21 square centimeters.

Explanation:
Length of the given rectangle shape = 7 centimeters.
Width of the given rectangle shape = 3 centimeters.
Area of the given rectangle shape = Length of the given rectangle shape × Width of the given rectangle shape
= 7 × 3
= 21 square centimeters.

Problem Solving
Question 13.
Make Sense and Persevere A league is a nautical measurement equal to about 3 miles. If a ship travels 2,000 leagues, about how many miles does the ship travel?
Answer:
Number of miles the ship travelled = 6000 miles.

Explanation:
1 league = 3 miles.
Number of leagues the ship travelled = 2000.
Number of miles the ship travelled = 3 × Number of leagues the ship travelled
=> 3 × 2000
=> 6000 miles.

Pick a Project
PROJECT 13A
What makes the St. Johns River special?
Project: Make a Travel Brochure About Rivers in Your Home State

Answer:

PROJECT 13B
How are tin cans useful?
Project: Cooking on a Budget

Answer:
Ways to Cook on a Budget

PROJECT 13C
Who invented the jigsaw puzzle?
Project: Make Your Own Jigsaw Puzzle

Answer:

3-ACT MATH PREVIEW

Math Modeling
A Pint’s a Pound

I can … model with math to solve a problem that involves estimating and computing with units of weight and capacity.

Lesson 13.1 Equivalence with Customary Units of Length

Solve & Share
Jeremy jogged 75 yards from his house to school. How many feet did Jeremy jog? Solve this problem any way you choose.
I can … convert customary units of length from one unit to another and recognize the relative size of different units.

Look Back! Look for Relationships What do you notice about the relationship between the number of yards and the number of feet Jeremy jogged?
Answer:
The relationship between the number of yards and the number of feet Jeremy jogged is 3 times more than the number of yards Jeremy jogged.

Explanation:
Number of yards Jeremy jogged = 75.
Number of feet Jeremy jog = 3 × Number of yards Jeremy jogged
= 3 × 75
= 225 feet.

Essential Question
How Can You Convert from One Unit of Length to Another?
Answer:
We can Convert from One Unit of Length to Another, by following steps:
1. Write the conversion as a fraction (that equals one)
2. Multiply it out (leaving all units in the answer)
3. Cancel any units that are both top and bottom.

Visual Learning Bridge
Maggie has a tree swing. How many inches long is each rope from the bottom of the branch to the swing?

Step 1
Find the length of the rope in feet. r = 10 – 2\(\frac{1}{4}\)

Each rope is 7\(\frac{3}{4}\) feet long.

Step 2
Convert the length of the rope to inches.

Each rope is 93 inches long.

Convince Me! Generalize How do you know the answer is reasonable when converting a larger unit to a smaller unit?
Answer:
When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide. Hence, the answer is reasonable when converting a larger unit to a smaller unit.

Another Example!
Mark moved forward yard when doing a back flip. Daisy moved forward 3\(\frac{1}{6}\) feet. How much more did Daisy move forward than Mark? One yard is 3 times as long as a foot.

Guided Practice
Do You Understand?
Question 1.
Does it take more inches or feet to equal a given length? Explain.
Answer:
Converting Between Units of Length:
There are many more inches for a measurement than there are feet for the same measurement, as feet is a longer unit of measurement. You could use the conversion factor.

Question 2.
Which is a greater distance, 9 yards or 9 miles?
Answer:
9 miles is a greater distance between 9 yards or 9 miles.

Explanation:
1 miles = 1760 yards.
9 miles = ??? yards.
=> 9 × 1760
=> 15840 yards.

Do You Know How?
For 3-4, convert each unit.
Question 3.
2 miles = _________ yards
Answer:
2 miles = __3520 _______ yards.

Explanation:
1 miles = 1760 yards.
2 miles = 2 × 1760
=> 3520 yards.

Question 4.
\(\frac{2}{3}\) yard = _____feet
Answer:
\(\frac{2}{3}\) yard = __2___feet.

Explanation:
1 yard = 3 feet.
\(\frac{2}{3}\) yard = \(\frac{2}{3}\) × 3
=> 2 feet.

Independent Practice
In 5-7, write > or < in each to compare the measures.
Question 5.
6 inches 6 feet
Answer:
6 inches <  6 feet.

Explanation:
1 feet = 12 inches.
6 feet = 6 × 12
=> 72 inches.

Question 6.
2 yards 7 feet
Answer:
2 yards < 7 feet.

Explanation:
1 yard = 3 feet.
2 yards = 2 × 3
=> 6 feet.

Question 7.
4 yards 100 inches
Answer:
4 yards > 100 inches.

Explanation:
1 yard = 36 inches.
4 yards = 4 × 36
=> 144 inches.

For 8-11, convert each unit.
Question 8.
8 yards = _______ inches
Answer:
8 yards = __288_____ inches.

Explanation:
1 yard = 36 inches.
8 yards = 8 × 36
=> 288 inches.

Question 9.
28 yards = ______ feet
Answer:
28 yards = __84____ feet.

Explanation:
1 yard = 3 feet.
28 yards = 3 × 28
=> 84 feet.

Question 10.
18 feet = ________ inches
Answer:
18 feet = ___216_____ inches.

Explanation:
1 feet = 12 inches.
18 feet = 12 × 18
=> 216 inches.

Question 11.
7 miles = ______ yards
Answer:
7 miles = __12320____ yards.

Explanation:
1 mile = 1760 yards.
7 miles = 1760 × 7
=> 12320 yards.

Problem Solving
Question 12.
Be Precise Lou cuts 3 yards from a 9-yard roll of fabric. Then he cuts 4 feet from the roll. How many feet of fabric are left on the roll?
Answer:
Remaining feet of fabric are left on the roll = 14.

Explanation:
Length of fabric Lou cuts = 3 yards.
Length of roll of fabric = 9 yards.
Remaining length of roll of fabric = Length of roll of fabric – Length of fabric Lou cuts
= 9 – 3
= 6 yards.
Conversion: 1 yard = 3 feet.
= 6 yards = ??? feet
=> 6 × 3 feet
= 18 feet.
Length of fabric later cut = 4 feet.
Remaining feet of fabric are left on the roll = Remaining length of roll of fabric – Length of fabric later cut
= 18 – 4
= 14 .

Question 13.
What customary units would you use to measure the length of a praying mantis? Explain.
Answer:
The customary system of measurement is inches used to measure the length of a praying mantis.

Explanation:
The customary system of measurement is defined as a set of weights and measures used for measuring length, weight, capacity, and temperature. Most praying mantis are no more than 5 inches in length. The smaller species measure around 2 to 3 inches while the bigger specimens reach the overall length of 6 to 7 inches.

Question 14.
Algebra On the field trip, Toni collected 4 times as many bugs as Kaylie. Kaylie collected 14 bugs. Draw a bar diagram, and write and solve an equation to find b, how many bugs Toni collected.
Answer:
Number of bugs Toni collected = 56.

Explanation:
Number of bugs Kaylie collected = 14.
Toni collected 4 times as many bugs as Kaylie.
Number of bugs Toni collected = 4 × Number of bugs Kaylie collected
= 4 × 14
=> 56.

Question 15.
Which is greater, 3 miles or 5,000 yards? How much greater? Explain.
Answer:
3 miles is greater by 280 yards than 5,000 yards.

Explanation:
3 miles,5000 yards.
Conversion: 1 mile = 1760 yards.
3 miles = ??? yards
=> 3 × 1760
=> 5280 yards.
Difference:
5280 yards – 5000 yards
=> 280 yards.

Question 16.
Higher Order Thinking Jenna uses \(\frac{1}{2}\) yard of ribbon for each box she wraps. How many inches of ribbon does she need to wrap 4 boxes? Use the linear model to help solve.

Answer:
Number of inches of ribbon she needs to wrap 4 boxes = 72 inches.

Explanation:
Length of ribbon Jenna uses for each box she wraps = \(\frac{1}{2}\) yard.
Total Length of ribbon she needs to wrap 4 boxes = 4 × Length of ribbon Jenna uses for each box she wraps
= 4 × \(\frac{1}{2}\) yard
= 2 yards.
Conversion: 1 yard = 36 inches.
Number of inches of ribbon she needs to wrap 4 boxes = Total Length of ribbon she needs to wrap 4 boxes × 36 inches
= 2  × 36
=> 72 inches.

Assessment Practice
Question 17.
Connor has 3\(\frac{3}{4}\) feet of brown fabric and \(\frac{3}{4}\) yard of green to make a costume for the school play. How many more feet of brown than green fabric does Connor have? Show both measures with points on the number line.

Answer:
1 \(\frac{2}{4}\) feet more feet of brown than green fabric Connor have.

Explanation:
Length of brown fabric Connor has = 3\(\frac{3}{4}\) feet.
Length of green fabric Connor has = \(\frac{3}{4}\) yard
Conversion: 1 yard = 3 feet.
\(\frac{3}{4}\) yard = ?? feet
=> 3 × \(\frac{3}{4}\)
=> 2 \(\frac{1}{4}\)  feet.
Difference:
Length of brown fabric Connor has  – Length of green fabric Connor has
= 3\(\frac{3}{4}\) feet – 2 \(\frac{1}{4}\) feet
= 1 \(\frac{2}{4}\) feet.

Question 18.
Charlotte made \(\frac{11}{2}\) yard of a paper chain for the school dance. Josh made 4\(\frac{1}{12}\) feet, and Mika made 3\(\frac{4}{12}\) feet. How many feet of chain did they make in all?
A. 8\(\frac{4}{12}\) feet
B. 9\(\frac{4}{12}\) feet
C. 10\(\frac{2}{12}\) feet
D. 10\(\frac{4}{12}\) feet
Answer:
Total length of feet of chain they make in all = 9\(\frac{4}{12}\) feet.
B. 9\(\frac{4}{12}\) feet.

Explanation:
Length of a paper chain Charlotte made = \(\frac{11}{2}\) yard.
Conversion:
1 yard = 3 feet.
\(\frac{11}{2}\) yard = \(\frac{11}{2}\) × 3
= 16 \(\frac{1}{2}\) feet.
Length of a paper chain Josh made = 4\(\frac{1}{12}\) feet.
Length of a paper chain Mika made = 3\(\frac{4}{12}\) feet.
Total length of feet of chain they make in all = Length of a paper chain Charlotte made + Length of a paper chain Josh made + Length of a paper chain Mika made
= 16 \(\frac{1}{2}\) feet + 4\(\frac{1}{12}\) feet + 3\(\frac{4}{12}\) feet
= 9\(\frac{4}{12}\) feet.

Lesson 13.2 Equivalence with Customary Units of Capacity

Solve & Share
Casey has \(\frac{1}{2}\) gallon of juice. How many 1-pint containers can he fill? Solve this problem any way you choose.
I can … convert customary units of capacity from one unit to another and recognize the relative size of different units.

Look Back! Generalize How did you convert from a larger unit of capacity to a smaller unit of capacity? Did you use the same process you used to convert from a larger unit of length to a smaller unit of length? Explain.

Answer:
When converting a larger unit of capacity to a smaller one of capacity, you multiply; when you convert a smaller unit of capacity to a larger one of capacity, you divide.
Yes, I used the same process you used to convert from a larger unit of length to a smaller unit of length.

Essential Question
How Can You Convert from One Unit of Capacity to Another?
Answer:
We can convert from One Unit of Capacity to Another by converting a larger unit of capacity to a smaller one of capacity, you multiply; when you convert a smaller unit of capacity to a larger one of capacity, you divide.

Visual Learning Bridge
Ms. Nealy’s class needs 5 gallons of punch for family math night. How much of each ingredient is needed to make enough punch with the recipe shown?

Units of capacity include gallons, quarts, pints, cups, and fluid Ounces.
Capacity is how much liquid a container can hold. This diagram shows the relative sizes of customary units of capacity. 1 gallon is 4 times as much as 1 quart

Step 1
Convert 5 gallons to pints.

5 gallons = 40 pints

Step 2
Add the number of pints in the recipe to find how many batches the class needs to make.
5 + 4 +1 = 10
10 × n = 40
n = 4
The class needs to make 4 batches of the recipe.

Step 3
Find how much of each ingredient is in 4 batches.
4 × 5 = 20 pints
4 × 4 = 16 pints
4 × 1 = 4 pints
20 pints of apple juice, 16 pints of lemon/lime soda, and 4 pints of frozen orange juice are needed.

Convince Me! Reasoning Complete the sentence below.
One gallon equals _______ quarts, _______ pints, or _______ cups.
Answer:
One gallon equals ___4____ quarts, ____8___ pints, or ___16____ cups.

Explanation:
1 gallon = 8 pints.
1 gallon = 4 quarts.
1 gallon = 16 cups.

Guided Practice
Do You Understand?
Question 1.
How many cups of punch does 5 gallons of the punch from the previous page make?
Answer:
Number of cups of punch 5 gallons of the punch from the previous page makes = 80 cups.

Explanation:

Number of cups of punch 5 gallons of the punch from the previous page makes =
5 gallons = ??? cups
Conversion:
1 gallon = 16 cups.
5 gallons = 5 × 16
= 80 cups.

Question 2.
Which size container holds more, 3 pints or 3 quarts?
Answer:
3 quarts size container holds more.

Explanation:
3 pints and 3 quarts.
1 quarts = 2 pints.
3 quarts = 3 × 2
= 6 pints.

Do You Know How?
For 3-5, convert each unit.
Question 3.
2 cups = _______ fluid ounces
Answer:
2 cups = ___16____ fluid ounces.

Explanation:
Conversion: 1 cup = 8 fluid ounces.
2 cups = 8 × 2
= 16 fluid ounces.

Question 4.
\(\frac{1}{2}\) gallon = _______ pints
Answer:
\(\frac{1}{2}\) gallon = ___4____ pints.

Explanation:
Conversion: 1 gallon = 8 pints.
\(\frac{1}{2}\) gallon = 8 × \(\frac{1}{2}\)
= 4 pints.

Question 5.
5 pints = ______ cups
Answer:
5 pints = __10____ cups.

Explanation:
Conversion: 1 pint = 2 cups.
5 pints = 2 × 5
= 10 cups.

Independent Practice
In 6-8, write > or < in each to compare the measures.
Question 16.
2 pints 2 gallons
Answer:
2 pints < 2 gallons.

Explanation:
2 pints and 2 gallons.
Conversion: 1 gallon = 8 pints.
2 gallons = 8 × 2
= 16 pints.

Question 7.
5 quarts 8 pints
Answer:
5 quarts  >  8 pints.

Explanation:
5 quarts and 8 pints.
Conversion: 1 quart = 2 pints.
5 quarts = 2 × 5
= 10 pints.

Question 8.
10 cups 2 quarts
Answer:
10 cups > 2 quarts.

Explanation:
10 cups and 2 quarts.
Conversion: 1 quart = 4 cups.
2 quarts = 4 × 2
= 8 cups.

For 9-12, convert each unit.
Question 9.
7 quarts = ________ cups
Answer:
7 quarts = ____28____ cups.

Explanation:
Conversion:  1 quart = 4 cups.
7 quarts = 4 × 7
= 28 cups.

Question 10.
12 gallons = ______ quarts
Answer:
12 gallons = ___48___ quarts.

Explanation:
Conversion: 1 gallon = 4 quarts.
12 gallons = 4 × 12
= 48 quarts.

Question 11.
7 pints = _______ fluid ounces
Answer:
7 pints = __112_____ fluid ounces.

Explanation:
Conversion: 1 pint = 16 fluid ounces.
7 pints = 16 × 7
= 112 fluid ounces.

Question 12.
\(\frac{3}{4}\) gallon = ______ pints
Answer:
\(\frac{3}{4}\) gallon = ___6___ pints.

Explanation:
Conversion: 1 gallon = 8 pints.
\(\frac{3}{4}\) gallon = 8 × \(\frac{3}{4}\)
= 6 pints.

For 13-14, convert each unit.
Question 13.

Answer:

Explanation:
Conversion: 1 pint = 16 fluid ounces.
\(\frac{2}{4}\) = 16 × \(\frac{2}{4}\)
= 8 fluid ounces.
1 pint = 16 fluid ounces.
2 pints = 16 × 2
= 32 fluid ounces.
4 pints = 16 × 4
= 64 fluid ounces.

Question 14.

Answer:

Explanation:
Conversion: 1 gallon = 16 cups.
2 gallon = 16 × 2 = 32 cups.
3 gallon = 16 × 3 = 48 cups.
4 gallon = 16 × 4 = 64 cups.

Problem Solving
Question 15.
en Vision® STEM Scientists measure how much water and debris flow past a river station at different times of the year. The water and debris are called discharge. The table shows the average discharge at the Camp Verde station on the Verde River in two months. How many more quarts of discharge per second are there in December than November?

Answer:
2664 more quarts of discharge per second are there in December than November .

Explanation:
Average discharge at the Camp Verde station on the Verde River for November month = 1619 gallons per second.
Average discharge at the Camp Verde station on the Verde River for December month = 2285 gallons per second.
Conversion: 1 gallon = 4 quarts.
Number of quarts of discharge per second  in November = Average discharge at the Camp Verde station on the Verde River for November month × 4
= 1619 × 4
= 6476 quarts.
Number of quarts of discharge per second  in December = Average discharge at the Camp Verde station on the Verde River for December month × 4
= 2285 × 4
= 9140 quarts.
Difference:
Number of quarts of discharge per second  in December – Number of quarts of discharge per second  in November
= 9140 – 6476
= 2664 .

Question 16.
How many quarts of discharge per second were recorded in November and December?
Answer:
Number of quarts of discharge per second  in November = 6476 quarts.
Number of quarts of discharge per second  in December = 9140 quarts.

Explanation:
Conversion: 1 gallon = 4 quarts.
Number of quarts of discharge per second  in November = Average discharge at the Camp Verde station on the Verde River for November month × 4
= 1619 × 4
= 6476 quarts.
Number of quarts of discharge per second  in December = Average discharge at the Camp Verde station on the Verde River for December month × 4
= 2285 × 4
= 9140 quarts.

Question 17.
Make Sense and Persevere Annabelle had the following containers of paint left over: \(\frac{1}{2}\) gallon, \(\frac{3}{4}\) quart, and \(\frac{1}{4}\) gallon. How many quarts of paint does Annabelle have left over? Explain.
Answer:
Total quarts of paint does Annabelle have left over = 3 \(\frac{3}{4}\) quarts.

Explanation:
Quantity of containers of paint left over:
First container = \(\frac{1}{2}\) gallon.
Second container = \(\frac{3}{4}\) quart.
Third container = \(\frac{1}{4}\) gallon.

Conversion: 1 gallon = 4 quarts.
First container = \(\frac{1}{2}\) gallon.
= \(\frac{1}{2}\)  × 4
= 2 quarts.
Third container = \(\frac{1}{4}\) gallon.
= \(\frac{1}{4}\)  × 4
= 1 quarts.
Total quarts of paint does Annabelle have left over = First container + Second container + Third container
= 2 quarts + \(\frac{3}{4}\)  + 1 quarts
= 3 \(\frac{3}{4}\) quarts.

Question 18.
Higher Order Thinking A caterer combines 3 quarts of orange juice, 5 pints of milk, and 5 cups of pineapple juice to make smoothies. How many cups can be filled with smoothies? Explain.
Answer:
Number of cups can be filled with smoothies = 27 cups.

Explanation:
Quantity of orange juice = 3 quarts.
Quantity of pints of milk = 5 pints.
Quantity of cups of pineapple juice = 5 cups.
Conversion: 1 pint = 2 cups.
Quantity of pints of milk = 5 pints.
=> 5 pints = 2 × 5 = 10 cups.

Conversion: 1 quarts = 4 cups.
Quantity of orange juice = 3 quarts.
=> 3 quarts = 4 × 3
= 12 cups.
Number of cups can be filled with smoothies = Quantity of orange juice + Quantity of pints of milk + Quantity of cups of pineapple juice
= 12 cups + 10 cups + 5 cups
= 27 cups.

Assessment Practice
Question 19.
Which equals 3 quarts?
A. 6 cups
B. 12 cups
C. 12 pints
D. 3 gallons
Answer:
3 quarts = 12 cups.
B. 12 cups

Explanation:
1 quarts = 4 cups.
3 quarts = 4 × 3 = 12 cups.
1 quart = 2 pint.
3 quarts = 2 × 3 = 6 pints.
1 quart = 0.25 gallon.
3 quarts = 3 × 0.25 = 0.75 gallon.

Question 20.
Select all the comparisons that are true.
☐ 4 cups < 4 pints
☐ 7 pints > 7 fluid ounces
☐ 2 gallons > 9 quarts
☐ 3 quarts < 14 cups
☐ 3 gallons < 18 pints
Answer:
All the comparisons that are true:
4 cups < 4 pints (TRUE)
7 pints > 7 fluid ounces (TRUE)
3 quarts < 14 cups (TRUE)
3 gallons < 18 pints (TRUE)

Explanation:
All the comparisons that are true:
☐ 4 cups < 4 pints (TRUE)
☐ 7 pints > 7 fluid ounces (TRUE)
☐ 2 gallons > 9 quarts (FALSE)
☐ 3 quarts < 14 cups (TRUE)
☐ 3 gallons < 18 pints (TRUE)

☐ 4 cups < 4 pints
1 pint = 2 cups.
4 cups < 4 pints
=> 4 × 2 = 8 cups < 4 pints.

☐ 7 pints > 7 fluid ounces
1 pint = 16 fluid ounces
=> 7 × 16 = 112 > 7 fluid ounces.

1 gallon = 4 quarts.
☐ 2 gallons > 9 quarts
=> 2 × 4 = 8 quarts > 9 quarts.

1 quarts = 4 cups.
☐ 3 quarts < 14 cups
=> 3 × 4 = 12 < 14 cups.

1 gallon = 8 pints.
3 gallons < 18 pints
=> 3 × 8 = 24 < 18 pints.

Lesson 13.3 Equivalence with Customary Units of Weight

Solve & Share
When Lori’s puppy, Bay, was born she weighed \(\frac{3}{8}\) pound. What was Bay’s weight in ounces? Solve this problem any way you choose.
I can … convert customary units of weight from one unit to another and recognize the relative size of different units.

Look Back! Be Precise How did you know you needed to convert units to solve the problem above?
Answer:
Well, we need to know the units given in the problem to convert. Next we should find the units value into which, the value should be converted into and later convert into the required units to solve the problem asked above.

Essential Question
How Can You Convert from One Unit of Weight to Another?
Answer:
We have also learnt conversion of one unit to another. We can convert from One Unit of Weight to Another by knowing the value of the conversion unit and multiplying it.

For example:
We can convert kilogram into grams by multiplying the number of kilograms by 1000. To convert grams into kilograms, we divide the number of grams by 1000.

Visual Learning Bridge
Mark made dinner for his family using the ingredients shown. How many 6-ounce servings did Mark make?
Weight is how heavy an object is. Units of weight include ounces, pounds, and tons.
This table shows the relative sizes of customary units of weight. 1 pound is 16 times as heavy as 1 ounce.

To convert the weight of the pasta and the meatballs to ounces, multiply each weight by 16.
Pasta:
2 × 16 = 32
= 6\(\frac{2}{5}\) ounces
Meatballs:
\(\frac{3}{5}\) × 16 = \(\frac{48}{5}\)
= 9\(\frac{3}{5}\) ounces

Add the weights of all the ingredients to find the total ounces.

The weight of all the ingredients is 24 ounces.

Divide to find s, the number of servings.

24 = 6 = s
s = 4
Mark made four 6-ounce servings.

Convince Me! Generalize How do you convert a larger unit of weight to a smaller unit of weight?
Answer:
We can convert a larger unit of weight to a smaller unit of weight by multiplying. To convert from a smaller unit to a larger one, divide.

Guided Practice
Do You Understand?
Question 1.
Would it make sense to describe the total weight of Mark’s dinner in tons? Why or why not?
Answer:
No, it does not makes sense to describe the total weight of Mark’s dinner in tons because it is not asked in the problem to find.

Do You Know How?
For 2-4, convert each unit.
Question 2.
9 tons = ________ pounds
Answer:
9 tons = ________ pounds.

Explanation:
Conversion: 1 ton = 2000 pounds.
9 tons = 2000 × 9
= 18000 pounds

Question 3.
\(\frac{3}{4}\) pound = _______ ounces
Answer:
\(\frac{3}{4}\) pound = ___12____ ounces

Explanation:
Conversion: 1 pound = 16 ounces.
\(\frac{3}{4}\) pound = 16 × \(\frac{3}{4}\)
= 12 ounces.

Question 4.
17 pounds = _________ ounces
Answer:
17 pounds = ___272______ ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
17 pounds = 16 × 17
= 272 ounces.

Independent Practice
In 5-7, write > or < in each to compare the measures.
Question 5.
6 ounces 6 pounds
Answer:
6 ounces < 6 pounds.

Explanation:
6 ounces and 6 pounds.
Conversion: 1 pound = 16 ounces.
6 pounds = 16 × 6
= 96 ounces.

Question 6.
3 pounds 40 ounces
Answer:
3 pounds > 40 ounces.

Explanation:
3 pounds  and 40 ounces.
Conversion: 1 pound = 16 ounces.
3 pounds = 16 × 3
= 48 ounces.

Question 7.
5,000 pounds 2 tons
Answer:
5,000 pounds > 2 tons.

Explanation:
5,000 pounds and 2 tons.
Conversion: 1 ton = 2000 pounds.
2 tons = 2000 × 2
= 4000 pounds.

For 8-13, convert each unit.
Question 8.
15 pounds = ________ ounces
Answer:
15 pounds = ___240_____ ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
15 pounds = 16 × 15
= 240 ounces.

Question 9.
7 tons = _______ pounds
Answer:
7 tons = _14000______ pounds.

Explanation:
Conversion: 1 ton = 2000 pounds.
7 tons = 2000 × 7
= 14000 pounds.

Question 10.
46 pounds = ________ounces
Answer:
46 pounds = __736______ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
46 pounds = 16 × 46
= 736 ounces.

Question 11.
\(\frac{1}{8}\) pound = ________ ounces
Answer:
\(\frac{1}{8}\) pound = ____2____ ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
\(\frac{1}{8}\) pound = 16 × \(\frac{1}{8}\)
= 2 ounces.

Question 12.
6 tons = _______ pounds
Answer:
6 tons = ___12000______ pounds.

Explanation:
Conversion: 1 ton = 2000 pounds.
6 tons = 2000 × 6
= 12000 pounds.

Question 13.
3 pounds = _______ ounces
Answer:
3 pounds = __48_____ ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
3 pounds = 16 × 3
= 48 ounces.

For 14-15, complete each table.
Question 14.

Answer:

Explanation:
Conversion: 1 ton = 2000 pounds.
2 tons = 2000 × 2 = 4000 pounds.
3 tons = 2000 × 3 = 6000 pounds.

Question 15.

Answer:

Explanation:
Conversion: 1 pound = 16 ounces.
\(\frac{2}{4}\) pound = 16 × \(\frac{2}{4}\)
= 8 ounces.
1 pound = 16 ounces.
2 pounds = 16 × 2 = 32 ounces.

Problem Solving
For 16-19, use the line plot at the right.

Question 16.
Be Precise What is the total weight in ounces of the three kittens that weight the least?
Answer:
Total weight in ounces of the three kittens that weight the least = 40 ounces.

Explanation:
Weight of Three kittens that weight the least = \(\frac{3}{4}\) pound + \(\frac{3}{4}\) pound + 1 pound.
= 2\(\frac{2}{4}\) pound.
Conversion: 1 pound = 16 ounces.
Total weight in ounces of the three kittens that weight the least = 2\(\frac{2}{4}\) pound = 16 × 2\(\frac{2}{4}\)
= 40 ounces.

Question 17.
Higher Order Thinking Two kittens had a total weight of 3\(\frac{1}{4}\) pounds. What could their individual weights have been?
Answer:
Their individual weights could be = 1\(\frac{2}{4}\) pounds + 1\(\frac{3}{4}\) pounds.

Explanation:
Weight of two kitten had a total weight of 3\(\frac{1}{4}\) pounds:
Their individual weights could be = 1\(\frac{2}{4}\) pounds + 1\(\frac{3}{4}\) pounds.
= 3\(\frac{1}{4}\) pounds.

Question 18.
Algebra How many more pounds did the heaviest kitten weigh than the lightest kitten?
Answer:
1\(\frac{2}{4}\) more pounds the heaviest kitten weights than the lightest kitten,

Explanation:
Weight of the heaviest kitten = 2\(\frac{1}{4}\) pounds.
Weight of the lightest kitten = \(\frac{3}{4}\) pounds.
Difference:
Weight of the heaviest kitten – Weight of the lightest kitten
= 2\(\frac{1}{4}\) pounds – \(\frac{3}{4}\) pounds
= 1\(\frac{2}{4}\) pounds.

Question 19.
Each of the greatest number of kittens weighed how many pounds?
Answer:
1\(\frac{1}{4}\) pounds is the greatest number of kittens weighed of 3\(\frac{3}{4}\) pounds.

Explanation:
Greatest number of kittens weighed = 3 × 1\(\frac{1}{4}\) pounds
= 3\(\frac{3}{4}\) pounds.

Question 20.
About how many pounds does this African elephant weigh? Complete the table to solve.

Answer:
This African elephant weights = 10000 pounds.

Explanation:
This African elephant weights = 5 tons.
Conversion: 1 ton = 2000 pounds.
=> 5 tons = 2000 × 5
= 10000 pounds.
Table :
\(\frac{2}{4}\) ton = 2000 × \(\frac{2}{4}\) = 1000 pounds.
1 ton = 2000 pounds.
2 ton = 2000 × 2 = 4000 pounds.
3 ton = 2000 × 3 = 6000 pounds.
4 ton = 2000 × 4 = 8000 pounds.
5 ton = 2000 × 5 = 10000 pounds.

Assessment Practice
Question 21.
Which is most likely to weigh 3 ounces?
A. A shoe
B. A large spider
C. A box of cerea!
D. A loaded pick-up truck
Answer:
A shoe is most likely to weigh 3 ounces.
A. A shoe

Explanation:
A. A shoe    – 9.5 ounces.
B. A large spider    – 5300 ounces.
C. A box of cereal    – 12 ounces to 18 ounces.
D. A loaded pick-up truck   – 64000 ounces.

Question 22.
Which comparison is true?
A. 7,000 pounds < 3 tons
B. 5 pounds > 85 ounces
C. 50 ounces > 3 pounds
D. 4 pounds < 60 ounces
Answer:
The following below comparison is true:
C. 50 ounces > 3 pounds.

Explanation:
A. 7,000 pounds < 3 tons (False)
Conversion: 1 ton = 2000 pounds.
=> 3 tons = 2000 × 3 = 6000 pounds.
B. 5 pounds > 85 ounces (False)
Conversion: 1 pound = 16 ounces.
=> 5 pounds = 16 × 5 = 80 ounces.
C. 50 ounces > 3 pounds (True)
=> 3 pounds = 16 × 3 = 48 ounces.
D. 4 pounds < 60 ounces (False)
=> 4 pounds = 16 × 4 = 64 ounces.

Lesson 13.4 Equivalence with Metric Units of Length

Solve & Share
Find the length of the marker shown in both centimeters and millimeters. Describe the relationship between the two units.
I can …convert metric units of length from one unit to another and recognize the relative size of different units.

Look Back! The length of Toby’s giant pencil is 25 centimeters. How could you find the length of his pencil in millimeters?
Answer:
We can find the length of his pencil in millimeter by using conversion of units into another required unit.
Length of his pencil in millimeters = 250 millimeters.

Explanation:
Length of Toby’s giant pencil = 25 centimeters.
Conversion: 1 centimeter =  10 millimeters.
Length of his pencil in millimeters = 25 centimeters = 10 × 25
= 250 millimeters.

Essential Question
How Can You Convert from One Metric Unit of Length to Another?
Answer:
To convert from one unit to another within the metric system usually means moving a decimal point. If you can remember what the prefixes mean, you can convert within the metric system relatively easily by simply multiplying or dividing the number by the value of the prefix

Visual Learning Bridge
For the standing long jump, Corey jumped 2 meters and Gary jumped 175 centimeters. Who jumped farther?

Step 1
Convert 2 meters to centimeters.
1 meter = 100 centimeters

Corey jumped 200 centimeters.

Step 2
Compare the lengths jumped.
200 centimeters is greater than 175 centimeters.
Corey jumped farther than Gary

Convince Me! Critique Reasoning Shayla says 5 kilometers are equal to 500 meters. Do you agree? Explain.
Answer:
Yes, I agree with Shayla saying ” 5 kilometers are equal to 500 meters.”

Explanation:
Conversion: 1 kilometer = 1000 meters.
5 kilometers = 1000 × 5 = 5000 meters.

Another Example!
Kendra and Lili measured the length of several rosebuds. The longest one Kendra measured was 2.4 centimeters long. The longest one Lili measured was 1.8 centimeters. Who measured the longest rosebud? Use a linear model to help explain.

Since 2.4 cm > 1.8 cm, Kendra measured the longest rosebud.

Guided Practice
Do You Understand?
Question 1.
What metric unit would you use to measure the length of a field?
Answer:
The most common units that we use to measure length of a field in the metric system are the millimeter, centimeter, meter, and kilometer.

Do You Know How?
For 2-3, convert each unit.
Question 2.
5 kilometers = _______ meters
Answer:
5 kilometers = __5000_____ meters.

Explanation:
Conversion: 1 kilometer = 1000 meters.
5 kilometers = 1000 × 5
= 5000 meters.

Question 3.
75 centimeters = ________ millimeters
Answer:
75 centimeters = _____750_______ millimeters.

Explanation:
Conversion: 1 centimeters  = 10 millimeters.
75 centimeters = 10 × 75
= 750 millimeters.

Independent Practice
In 4-6, tell what metric unit you would use to measure each.
Question 4.
The length of your math book
Answer:
Metric unit used to measure the length of your math book centimeter (cm).

Question 5.
The distance between cities
Answer:
Metric unit used to measure the distance between cities is  Kilometers per hour.

Question 6.
The length of a fly
Answer:
Metric unit used to measure the length of a fly is meter.

For 7-8, complete each table.
Question 7.

Answer:

Explanation:
Conversion: 1 meter = 1000 millimeter.
2 meter = 2 × 1000 = 2000 millimeter.
3 meter = 3 × 1000 = 3000 millimeter.

Question 8.

Answer:

Explanation:
Conversion: 1 centimeter = 10 millimeter.
2 centimeter  = 10 × 2 = 20 millimeter.
3 centimeter  = 10 × 3 = 30 millimeter.

Problem Solving
For 9-10, use the table at the right.

Question 9.
Be Precise The table shows the amount of rainfall students measured for a week. What was the total rainfall for the week, in millimeters?
Answer:
Total rainfall for the week, in millimeters = 110 millimeters.

Explanation:
Amount of rainfall on Monday = 3 cm.
Amount of rainfall on Tuesday = 0 cm.
Amount of rainfall on Wednesday = 1 cm.
Amount of rainfall on Thursday = 5 cm.
Amount of rainfall on Friday = 2 cm.
Total rainfall for the week = Amount of rainfall on Monday  + Amount of rainfall on Tuesday + Amount of rainfall on Wednesday + Amount of rainfall on Thursday + Amount of rainfall on Friday
= 3 cm + 0 cm + 1 cm  + 5 cm + 2 cm
= 11 cm.
Conversion: 1 cm = 10 mm.
Total rainfall for the week, in millimeters = Total rainfall for the week × 10
=> 11 × 10 = 110 millimeters.

Question 10.
How many more millimeters of rain fell on Thursday than on Monday and Wednesday combined?
Answer:
10 more millimeters of rain fell on Thursday than on Monday and Wednesday combined.

Explanation:
Amount of rainfall on Monday = 3 cm.
Amount of rainfall on Wednesday = 1 cm.
Amount of rainfall on Thursday = 5 cm.
Combine Rain fell on Monday and Wednesday = Amount of rainfall on Monday + Amount of rainfall on Wednesday
= 3 cm + 1 cm
= 4 cm.
Difference:
Amount of rainfall on Thursday – Combine Rain fell on Monday and Wednesday
= 5 cm – 4 cm
= 1 cm.
Conversion: 1 centimeter = 10 millimeter.
Difference in  millimeter of rain fell on Thursday than on Monday and Wednesday combined = 1 centimeter = 10 millimeter.

Question 11.
Which is greater, 2,670 meters or 2 kilometers? Explain.
Answer:
2,670 meters is greater.

Explanation:
2,670 meters or 2 kilometers.
Conversion: 1 kilometer = 1000 meters.
2 kilometers = 1000 × 2 = 2000 meters.

Question 12.
Critique Reasoning Milo thinks 8 hours is greater than 520 minutes. Is Milo correct? Remember 1 hour is equal to 60 minutes.
Answer:
No, Milo  is incorrect because 8 hours = 480 minutes less than 520 minutes.

Explanation:
Conversion: 1 Hour = 60 minutes.
8 hours = 60 × 8 = 480 minutes.

Question 13.
Algebra Leah ran around the track 8 times. She ran a total of 2,000 meters. How many meters equal 1 lap? Use the bar diagram to write an equation which can be used to find m, the meters in one lap.

Answer:
1 Lap = 400 meters.

Explanation:
Number of meters She ran = 2000m.
Number of times Algebra Leah ran around the track = 8.
Number of meters equal 1 lap = Number of meters She ran ÷ Number of times Algebra Leah ran around the track
= 2000 ÷ 8
= 400 meters.
1 Lap = 400 meters

Question 14.
Higher Order Thinking Signs are placed at the beginning and at the end of a 3-kilometer hiking trail. Signs are also placed every 500 meters along the trail. How many signs are along the trail? Explain.
Answer:
Total signs along the trail = 7.

Explanation:
Distance of Signs are placed at the beginning and at the end of a hiking trail = 3 kilometer.
Signs  placed along the trail = 500 meters.
Conversion: 1 km = 1000 meters.
3 km = 1000 × 3 = 3000 meters.
Total signs along the trail = Distance of Signs are placed at the beginning and at the end of a hiking trail ÷ Signs  placed along the trail + 1
= 3000 ÷ 500 + 1
= 6 + 1
= 7.

Assessment Practice
Question 15.
Select all the true statements.
☐ 14 meters = 1,400 centimeters
☐ 10 centimeters = 1,000 millimeters
☐ 55 kilometers = 5,500 meters
☐ 3 meters = 3,000 millimeters
☐ 5 meters = 500 centimeters
Answer:
All the true statements:
14 meters = 1,400 centimeters
55 kilometers = 5,500 meters
3 meters = 3,000 millimeters
5 meters = 500 centimeters

Explanation:
☐ 14 meters = 1,400 centimeters. (True)
Conversion: 1 meters = 100 centimeters.
14 meters = 10 × 14 = 1400 centimeters.

☐ 10 centimeters = 1,000 millimeters. (False)
Conversion: 1 centimeters = 10 millimeters.
10 centimeters = 10 × 10 = 100 millimeters.

☐ 55 kilometers = 5,500 meters. (True)
Conversion: 1 kilometers  =  1000 meters.
55 kilometers  = 1000 × 55 = 5500 meters.

☐ 3 meters = 3,000 millimeters. (True)
Conversion: 1 meter = 1000 millimeters.
3 meters = 1000 × 3 = 3000 millimeters.

☐ 5 meters = 500 centimeters. (True)
Conversion: 1 meter = 100 centimeters.
5 meters = 100 × 5 = 500 centimeters.

Question 16.
Select all the true statements.
☐ 3 meters > 3,000 centimeters
☐ 2 kilometers < 2,500 meters
☐ 4 centimeters > 38 millimeters
☐ 3.5 meters < 3.2 meters
☐ 5 kilometers < 5,200 meters
Answer:
All the true statements:
2 kilometers < 2,500 meters.
4 centimeters > 38 millimeters.
5 kilometers < 5,200 meters.

Explanation:
☐ 3 meters > 3,000 centimeters. (False)
Conversion: 1 meter = 100 centimeters.
3 meters = 100 × 3 = 300 centimeters.

☐ 2 kilometers < 2,500 meters . (True)
Conversion: 1 kilometers  =  1000 meters.
2 kilometers = 1000 × 2 = 2000 meters.

☐ 4 centimeters > 38 millimeters. (True)
Conversion: 1 centimeters = 10 millimeters.
4 centimeters = 10 × 4 = 40 millimeters.

☐ 3.5 meters < 3.2 meters. ( False)

☐ 5 kilometers < 5,200 meters. (True)
Conversion: 1 kilometers  =  1000 meters.
5 kilometers  = 1000 × 5 = 5000 meters.

Lesson 13.5 Equivalence with Metric Units of Capacity and Mass

Solve & Share
Jenny has 3 liters of water. How many milliliters of water does she have, and what is the mass of the water in grams? Solve this problem any way you choose.
I can… convert metric units of capacity and mass from one unit to another and recognize the relative size of different units.

Look Back! Why did you need to convert units to solve the problem above?
Answer:
Well, it is the conversion between an amount in one unit to the corresponding amount in a desired unit using various conversion factors. This is valuable because certain measurements are more accurate or easier to find than others.

Essential Question
How Can You Convert from One Metric Unit of Capacity or Mass to Another?
Answer:
We convert from One Metric Unit of Capacity or Mass to Another, larger unit multiply, smaller unit divide.

Visual Learning Bridge
Louis needs 8 liters of apple juice. He has 5,000 milliliters of juice. Does Louis have enough apple juice?

Step 1
Find how many milliliters of apple juice Louis needs.
1 liter = 1,000 milliliters

Louis needs 8,000 milliliters of juice.

Step 2
Compare to find if Louis has enough apple juice.
8,000 milliliters > 5,000 milliliters
Louis does not have enough apple juice. How much more does he need?
8,000 – 5,000 = 3,000
Louis needs 3,000 milliliters more.

Convince Me! Be Precise Why did you need to convert liters to milliliters?
Answer:
We need to convert liters to milliliters because Louis needs milliliters of juice not liters.

Another Example!
How many grams of apples are needed to make 1 liter of apple juice?

1 kilogram = 1,000 grams
2 kilograms = 2 × 1,000 grams
= 2,000 grams
2,000 grams of apples make 1 liter of apple juice.

Guided Practice
Do You Understand?
Question 1.
What metric unit would you use to measure your mass? the amount of blood in your body? Explain.
Answer:
The gram and kilogram are two units used to measure mass in the metric system. the amount of blood in your body is measured in units of millimeters of mercury (mmHg).

Do You Know How?
For 2-3, convert each unit.
Question 2.
6 grams = _______ milligrams
Answer:
6 grams = ___6000____ milligrams.

Explanation:
Conversion: 1 gram = 1000 milligrams.
6 grams = 1000 × 6
= 6000 milligrams.

Question 3.
9 liters = _________ milliliters
Answer:
9 liters = ___9000______ milliliters.

Explanation:
Conversion: 1 gram = 1000 milligrams.
9 liters = 1000 × 9
= 9000 milliliters.

Independent Practice
In 4-6, tell what metric unit you would use to measure each.
Question 4.
Medicine in a pill
Answer:
Orally administered liquid medications should be dosed exclusively by using metric-based dosing with milliliters (ie, mL) to avoid confusion and dosing errors associated with common kitchen spoons