Go through the enVision Math Common Core Grade 1 Answer Key Topic 8 Understand Place Value regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 8 Understand Place Value

enVision STEM Project: Daylight Throughout the Year
Find Out Talk to friends and relatives about why there is more daylight in summer than in winter.
Ask them to help you find information about the changes in daylight each season.

Journal: Make a Book Draw pictures of the tilting globe and the sun at different times of the year. In your book, also:

• Add labels to show summer and winter.
• Write a sentence to describe the pattern of the seasons in your own words.

Review What You Know

Vocabulary

Question 1.
Circle the tens digit.

Answer:

Explanation:
Given 2 digit number 48.
Two digit number have tens place and ones place.
4 is in tens place and 8 in ones place
4 is circled as tens digit.

Question 2.
Circle the ones digit.

Answer:

Explanation:
Given 2 digit number 76.
Two digit number have tens place and ones place.
7 is in tens place and 6 in ones place
6 is circled as ones digit.

Question 3.
Use the ten-frames to find the sum.
7 + 9 = ___

Answer:

Counting to 120

Question 4.
Write the number that comes next when counting forward by Is. Use a hundred chart to help you.
110, 111, 112, ____
Answer:
110, 111, 112, 113
Explanation:
Given
A sequence of  3 digit numbers
110, 111, 112, ____ and asked to find the 4th digit by counting forward by Is
3 digit number have hundreds place  tens place and ones place
Since counting forward by 1s
we add the 1 to the ones place of 3rd digit to get the 4th digit keeping the tens place and hundreds place constant.
112 + 001 = 113.
Missing number is 113.

Question 5.
Maria counts by 10s. She starts at 30. Write the missing numbers.
30, ___, ___
60, ___
Answer:
30, _40__, _50__
60, _70__
Explanation:
Maria counts by 10s
Given
30, ___, ___ and 2 number missing to find the missing number we add 1 to the tens place keeping ones place constant.
given
30 = 3 is tens digit and 0 ones digit.
Adding tens digit with 1
3 + 1 = 4, 4 + 1 = 5.
30, _40__,_50__
60 = 6 tens digit and 0 ones digit
60 + 10 = 70
60, _70__

Hundred Chart

Question 6.
Write the missing numbers in this part of the hundred chart.

Answer:

pick a Project

PROJECT 8A
What do you put on your hot dog?
Project: Act Out Serving Up Hot Dogs

Answer:
Topping on the Hot dog
1. Hot dog bun.
2. Veg- dog or Non- Veg dog
3. Onion
4. Jalapenos
5. Lattice
6. Herbs
7. Sauces.

PROJECT 8B
What is your favorite color?
Project: Make a Color Poster

PROJECT 8C
Can you eat a tiger?
Project: Play a Cracker Stack Game

PROJECT 8D
Which sea creatures have 10 legs?
Project: Make a Finger Painting

Answer:

Lesson 8.1 Make Numbers 11 to 19

Solve & Share

Use counters and ten-frames to show 12, then 15, and then 18. Draw your counters in the ten-frames below. Tell what is the same and different about each number you show.

Visual Learning Bridge

Answer:

Convince Me!
How could you use ten-frames to show 13 counters?
Answer:

Explanation:
one group of 10 ones = 1 ten
13 is made up of one group of 10 ones and 3 ones
13 is 1 ten and  3 ones.

Guided Practice

Use counters to make each number. Then write each number as I ten and some ones.

Question 1.
twelve
is 1 ten and ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
12 is made up of one group of 10 ones and 2 ones
12 = 10 + 2
12 is 1 ten and  2 ones.

Question 2.
fourteen
is 1 ten and ___ ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
14 is made up of one group of 10 ones and 4 ones
14 = 10 + 4
14 is 1 ten and  4 ones.

Question 3.
fifteen
is 1 ten and __ ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
15 is made up of one group of 10 ones and 5 ones
15 = 10 + 5
15 is 1 ten and  5 ones.

Independent Practice

Use counters to make each number. Then write the word or number.

Question 4.
sixteen
is ___ ten and 6 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
16 is made up of one group of 10 ones and 6 ones
16 = 10 + 6
16 is 1 ten and  6 ones.

Question 5.
____
is 1 ten and 8 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
18 is made up of one group of 10 ones and 8 ones
18 = 10 + 8
18 is 1 ten and  8 ones.

Question 6.
thirteen
is 1 ten and __ ones.
Answer:

is 1 ten and __ ones.
Explanation:
one group of 10 ones = 1 ten
13 is made up of one group of 10 ones and 3 ones
13 = 10 + 3
13 is 1 ten and 3 ones.

Question 7.
eleven
is ___ ten and 1 one.
Answer:

Explanation:
one group of 10 ones = 1 ten
11 is made up of one group of 10 ones and 1 ones
11 = 10 + 1
11 is 1 ten and  1 ones.

Question 8.
_____
is 1 and 7 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
17 is made up of one group of 10 ones and  7 ones
17 = 10 + 7
17 is 1 ten and  7 ones.

Question 9.
nineteen
is 1 ten and 9 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
19 is made up of one group of 10 ones and 9 ones
19 = 10 + 9
19 is 1 ten and  9 ones.

Question 10.
Vocabulary Circle the tens and ones that match the words shown.

Answer:

Explanation:
one group of 10 ones = 1 ten
12 is made up of one group of 10 ones and 2 ones
12 = 10 + 2
12 is 1 ten and 2  ones.
Explanation:
one group of 10 ones = 1 ten
15 is made up of one group of 10 ones and 5 ones
15 = 10 + 5
15 is 1 ten and  5 ones.

Problem Solving

Solve each problem below.

Question 11.
Use Tools Jill has 14 buttons and 2 boxes. She puts 10 buttons in one box. How many buttons does Jill put in the other box? Draw counters to solve. Write the numbers.
___ buttons
__ is ___ ten and __ ones.

Answer:

Question 12.
Higher Order Thinking Choose a number between 11 and 14. Draw a picture to show how to make the number with ten-frames. Write the number and the number word.

Answer:

Question 13.
Assessment Practice Match the groups or numbers on the left with the number word on the right.

Answer:

Lesson 8.2 Numbers Made with Tens

Solve & Share

How are 2 tens and 20 ones alike and different?
Use cubes to show your answer. Then draw your cubes.

Visual Learning Bridge

Answer:

Convince Me!
How many tens are in 90? How do you know?
Answer:

Explanation:
10 cubes make 1 ten.
To count the number of tens in 90
we count by 10’s as  10,20,30,40,50,60,70,80,90.
we count by tens as 1 ten, 2 tens, 3 tens, 4 tens, 5 tens, 6 tens, 7 tens, 8 tens, 9 tens.
There are 90 cubes
90 is 9 tens and 0 ones.

Guided Practice

Use cubes. Count by 10s. Write the numbers.

Question 1

Answer:

Explanation:
10 cubes make 1 ten.
Here are 3 ten.
Count by 10’s to
10, 20, 30.
There are 30 cubes in all.
3 tens and 0 ones is 30.

Question 2.

___ tens and ___ ones is ____.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 5 ten.
Count by 10’s to
10, 20, 30, 40, 50.
There are 50 cubes in all.
5 tens and 0 ones is 50.

Independent Practice

Use cubes. Count by 10s. Draw the cubes. Write the numbers.

Question 3.

6 tens and 0 ones is ___.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 6 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60.
There are 60 cubes in all.
6 × 10 = 60.
6 tens and 0 ones is Sixty.

Question 4.

___ tens and ___ ones is 90.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 9 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60, 70, 80, 90.
There are 90 cubes in all.
9 × 10 = 90.
9 tens and 0 ones is Ninety.

Question 5.

8 tens and 0 ones is ___.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 8 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60, 70, 80.
There are 80 cubes in all.
8 × 10 = 80.
8 tens and 0 ones is Eighty.

Question 6.

__ tens and ___ ones is 70.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 7 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60, 70.
There are 70 cubes in all.
7 × 10 = 70.
7 tens and 0 ones is Seventy

Question 7.
Number Sense Joey has 2 tens. He wants to trade the tens for ones. How many ones should Joey get?
____ ones

Answer:
Number of tens Joey has = 2 tens
Joey wants to trade tens for ones.
1 ten = 10 ones
So, 2 tens  = 2 × 10 = 20 ones.
Joel gets 20 ones foe 2 tens.

Problem Solving

Solve the problems below.

Question 8.
Reasoning There are 2 buses. 10 people are in each bus. How many people ride in the buses? Count by 10s. Draw a picture to solve.

Answer:

Question 9.
Reasoning George has 3 boxes of pens. 10 pens are in each box. How many pens does George have?
___ pens
Answer:

Question 10.
Higher Order Thinking Brian has a book. He reads 10 pages every day. Show how many pages Brian reads in 5 days. Use pictures, numbers, or words.

Answer:

Question 11.
Assessment Practice
Beth has 4 jars. Each jar has 10 bouncy balls in it. How many bouncy balls does Beth have in all?


Answer:
Number of Jars Beth has = 4
Number of bouncy balls in each jar = 10
Total number of bouncy balls in the 4  jars = 10 + 10 + 10 + 10 = 40
4 × 10 = 40.
C)40 is the answer.
There are 40 bouncy balls in the jars.

Lesson 8.3 Count with Groups of Tens and Ones

Solve & Share

Tara has 34 cubes. How many groups of 10 can she make with the cubes? Show your work in the space below.

Answer:

Visual Learning Bridge

Convince Me!
Why does 37 have 3 groups of 10 and not 4 groups of 10?
Answer:
37 = 10 + 10 + 10 + 7
= 3 tens and 7 ones
= 3 groups of 10 and 7 ones.
4 groups of 10 = 10 + 10 + 10 + 10  = 40
So, 37 has 3 groups of 10 and 7 ones.

Guided Practice
Circle groups of 10. Write the numbers.

Question 1.

Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 5 sets of 5 cubes and 2 cubes
out of 5 set of 5 cubes 4 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
2 group of  10’s are formed.
The left over cubes are ones  = 5 + 2 = 7 ones.
2 groups of 10’s and 7 ones = 27 .

Question 2.

Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 7 sets of 5 cubes and 9 cubes
out of 7 set of 5 cubes 6 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
3 group of  10’s are formed.
The left over cubes are ones  = 5 + 4 = 9 ones.
3 groups of 10’s and 9 ones = 39.

Independent Practice

Circle the groups of 10. Write the numbers.

Question 3.

___ groups of 10 and ___ ones is ___.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 8 sets of 5 cubes and 3 cubes
8 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
4 group of  10’s are formed.
The left over cubes are ones  = 3 = 3 ones.
4 groups of 10’s and 3 ones = 43.

Question 4.

___ groups of 10 and __ ones is ____.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 7 sets of 5 cubes
out of 7 set of 5 cubes 6 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
3 group of  10’s are formed.
The left over cubes are ones  = 5 = 5 ones.
3 groups of 10’s and 5 ones = 35.

Question 5.

___ group of 10 and ___ ones is ___.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 3 sets of 5 cubes and 1 cubes
out of 3 set of 5 cubes 2 sets of 5 cubes make a
5 + 5 = 10
1 group of  10’s are formed.
The left over cubes are ones  = 5 + 1 = 6 ones.
1 groups of 10’s and 6 ones = 16.

Question 6.

___ groups of 10 and ___ ones is ___.

Write the number of groups of 10 and the number of ones. Then write the total.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 9 sets of 5 cubes and 3 cubes
out of 9 set of 5 cubes 8 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
4 group of  10’s are formed.
The left over cubes are ones  = 5 +3 = 8 ones.
4 groups of 10’s and 8 ones = 48.

Question 7.

___ groups of 10 and ___ ones is ___.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 5 sets of 5 cubes
out of 5 set of 5 cubes 4 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
2 group of  10’s are formed.
The left over cubes are ones  = 5  = 5 ones.
2 groups of 10’s and 5 ones = 25.

Question 8.

__ groups of 10 and ___ ones is __.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 4 sets of 5 cubes
4 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
2 group of  10’s are formed.
The left over cubes are ones  = 2  = 2 ones.
2 groups of 10’s and 2 ones = 22.

Problem Solving

Draw a picture and write the numbers to solve each Solving problem below.

Question 9.
Model A monkey has 32 bananas. 10 bananas are in each bunch.

How many bunches are there? ____
How many bananas are left over? ___
Answer:

Question 10.
Model The dogs have 21 bones. 10 bones are in each bowl.

How many bowls are there? ____
How many bones are left over? ____
Answer:

Question 11.
Higher Order Thinking
Amil writes a number. His number has 5 groups of 10. His number has less than 9 ones. What number could Amil have written? ____
Answer:
Number of groups of 10’s Amil number has = 5
10 + 10 + 10 + 10 + 10 = 50
Number of ones Amil number has = less than 9
less than 9 may be = 1,2, 3, 4, 5, 6, 7, 8.
The number may be
5 groups of 10’s and 1 ones = 51
5 groups of 10’s and 2 ones = 52
5 groups of 10’s and 3 ones = 53
5 groups of 10’s and 4 ones = 54
5 groups of 10’s and 5 ones = 55
5 groups of 10’s and 6 ones = 56
5 groups of 10’s and 7 ones = 57
5 groups of 10’s and 8 ones = 58.
Amil number may be 51, 52, 53, 54, 55, 56, 57, 58.

Question 12.
Assessment Practice
A store has 5 bunches of grapes and 3 left over. Each bunch has 10 grapes. How many grapes are there in all? Explain.
Answer:
Number of bunches of grapes in the store = 5
Number of grapes in each bunch = 10 grapes
Number of left over = 3
Number of grapes in 5 bunches = 10 + 10 + 10 + 10 + 10 = 50 grapes.
Total number of grapes = 50 grapes and 3 left over is 53 grapes.

Lesson 8.4 Tens and Ones

Solve & Share

Estimate how many cubes are in your bag. Then empty the bag in the space below. Without counting each cube, estimate how many cubes there are. Write each estimate.

Now count the cubes and write the total number of cubes.

Estimate 1: ___ cubes
Estimate 2: ___ cubes
Actual amount: ___ cubes
Answer:

Visual Learning Bridge

Convince Me!
How are these numbers alike? How are they different?

Answer:
46 and 64 are two digit numbers
Two digit number have tens and ones.
Both the number have tens and ones digits only.
They are different as the place values of the number are different.
46 has 4 in tens place and 6 in ones place
64 has 6 in tens place and 4 in ones place .

Guided Practice
Use cubes. Count the tens and ones. Then write the numbers.

Question 1.

Answer:

Explanation:
Given
3 sets of 10 cubes in tens place
5 + 3 = 8 cubes in ones place
30 + 8 = 38.
3 tens and 8 ones  is 38.
3 in  38 is the tens digit
8 in 38 is the ones digit.

Question 2.

Answer:

Explanation:
Given
4 sets of 10 cubes in tens place
1 cubes in ones place
40 + 1 = 41
4 tens and 1 ones  is 41.
4 in  41 is the tens digit
1 in 41 is the ones digit.

Independent Practice

Use cubes. Count the tens and ones. Then write the numbers.

Question 3.

___ Ten and ___ ones is ___.
Answer:

Explanation:
Given
1 sets of 10 cubes in tens place
5 + 4 = 9 cubes in ones place
10 + 9 = 19
1 ten and 9 ones  is 19.
1 in  19 is the tens digit
9 in 19 is the ones digit.

Question 4.

___ tens and ___ ones is ___.
Answer:

Explanation:
Given
2 sets of 10 cubes in tens place
3 cubes in ones place
20 + 3 = 23
2 tens and 3 ones  is 23.
2 in  23 is the tens digit
3 in 23 is the ones digit.

Question 5.

___ tens and ___ ones is ___.
Answer:

Explanation:
Given
4 sets of 10 cubes in tens place
5 + 3 = 8 cubes in ones place
40 + 8 = 48
4 tens and 8 ones  is 48.
4 in  48 is the tens digit
8 in 48 is the ones digit.

Solve the problem below any way you choose.

Question 6.
Number Sense Bill writes a number. It has the same number of tens and ones. What could Bill’s number be?
Answer:
The number Bill wrote has same number of tens and ones.
Bills number may be any of these numbers.
1 ten and 1 one is 11
2 tens and 2 ones is 22
3 tens and 3 ones is 33
4 tens and 4 ones is 44
5 tens and 5 ones is 55
6 tens and  6 ones is 66
7 tens and  7 ones is 77
8 tens and 8 ones is 88
9 tens and 9 ones is 99.
Bill number may be 11, 22, 33, 44, 55, 66, 77, 88, 99.

Problem Solving

Solve each problem below.

Answer:

Question 7.
Reasoning Luz has juice boxes at her party. There are 3 packages of 10 and 7 extra juice boxes.
How many juice boxes are there in all?
Write the number of tens and ones. Then write the total number of juice boxes.

Answer:

Question 8.
Higher Order Thinking Draw a picture to show a number greater than 25 and less than 75. Then write the number.

Answer:

Question 9.
Assessment Practice Kai brought 2 packages of 10 juice boxes and 5 extra juice boxes. How many juice boxes did Kai bring? Write the number of tens and ones. Then write the total number of juice boxes.

Answer:

Lesson 8.5 Continue with Tens and Ones

Solve & Share

Laylani has 28 buttons. Draw her buttons so that a friend can see that there are 28 buttons without counting them one by one.

Answer:

Visual Learning Bridge

Convince Me!
When you draw to model a number, which digit tells you how many lines to draw? Which digit tells you how many dots to draw?
Answer:
When we draw a model a number
Tens place digit tells us to draw the number of lines.
Ones place digit tells us to draw the number of dots.

Guided Practice

Write the numbers and draw a model to show each number. Count by tens and ones to check.

Question 1.

Answer:

Explanation:
Given number 17
17 is 1 ten and 7 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
17 is represented with 1 line and 7 dots.

Question 2.
29 is ___ tens and ___ ones.

Answer:

Explanation:
Given number 29
29 is 2 ten and 9 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
29 is represented with 2 line and 9 dots.

Independent Practice

Write the numbers and draw a model to show each number. Count by tens and ones to check.

Question 3.
There are ___ tens and ___ ones in 43.
Answer:

There are 4 tens and 3 ones.
Explanation:
Given number 43
43 is 4 ten and 3 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
43 is represented with 4 line and 3 dots.

Question 4.
There are ___ tens and ___ ones in 86.
Answer:

Explanation:
Given number 86
86 is 8 ten and 6 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
86 is represented with 8 line and 6 dots.

Question 5.
There are ___ ten and __ ones in 15.
Answer:

Explanation:
Given number 15
15 is 1 ten and 5 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
15 is represented with 1 line and 5 dots.

Question 6.
There are ___ tens and ___ ones in 37.
Answer:

Explanation:
Given number 37
37 is 3 ten and 7 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
37 is represented with 3 line and 7 dots.

Question 7.
There are ___ tens and ___ ones in 62.
Answer:

Explanation:
Given number 62
62 is 6 ten and 2 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
62 is represented with 6 line and 2 dots.

Question 8.
There are ___ tens and __ ones in 24.
Answer:

Explanation:
Given number 24
24 is 2 ten and 4 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
24 is represented with 2 line and 4 dots.

Problem Solving

Solve the problems below.

Question 9.
Model Kevin draws the model below to show a number. What number is Kevin showing?

Answer:

Question 10.
enVision® STEM Gina is collecting
data on the number of hours of daylight in the fall and winter. She records data for 68 days. Draw a model to show 68.
Answer:

Question 11.
Higher Order Thinking Peyton starts drawing a model for the number 48, but she is interrupted. Help her finish her model.

Answer:

Question 12.
Assessment Practice Which number is represented here?

Answer:
Given
2 lines and 3 dots
Line represent Tens
Dot represents Ones.
2 lines = 10 + 10 = 20
3 dots  = 3
The number which is represented is 20 + 3 = 23.
Answer is C)23.

Lesson 8.6 Different Names for the Same Number

Solve & Share

Use cubes. Show two different ways to make 28. Draw each way in the spaces below.

Visual Learning Bridge

Convince Me!
How could you break apart 24 using only I ten? Explain.
Answer:
24 is 2 tens and 4 left over
24 is 2 tens and 4 ones
breaking 24 using only 1 ten
Breaking other  ten to make 10 more ones
24 is 1 ten and 14 ones.

Guided Practice

Count the tens and ones. Write different Practice ways to show the number.

Question 1.
Write two ways to break apart 34.

Answer:

Explanation:
Given a model of number 34 in two different ways
34 is represented as
34 is 3 tens and 4 ones in 1st case.
In 2nd case
out of 3 tens. 1 ten is broken down to make 10 more ones.
34 is 2 tens and 14 ones.

Independent Practice

Count the tens and ones. Write different ways to show each number.

Question 2.
Write two ways to break apart 21.

21 is ___ ten and __ one.
Answer:

Explanation:
Given to break apart 21 in two way
Case 1.
21 is represented as
21 is 2 tens and 1 ones
21 = 20 + 1
In 2nd case
out of 2 tens. 1 ten is broken down to make 10 more ones.
21 is 1 tens and 11 ones.
21 = 10 + 11.

Question 3.
Draw models and write two ways to break apart 59.

59 is ___ tens and ___ ones.

59 is __ tens and ___ ones.
Answer:

Explanation:
Given to break apart 59 in two way
Case 1.
59 is represented as
59 is 5 tens and 9 ones
59 = 50 + 9
In 2nd case
out of 5 tens. 1 ten is broken down to make 10 more ones.
59 is 4 tens and 19 ones.
59 = 40 + 19 .

Write each number in two different ways. Use cubes to help if needed.

Question 4.
Show two ways to break apart 44.
44 is __ tens and ___ ones.
Answer:

Explanation:
Given to break apart 44 in two way
Case 1.
44 is represented as
44 is 4 tens and 4 ones
44 = 40 + 4
In 2nd case
out of 4 tens. 1 ten is broken down to make 10 more ones.
44 is 3 tens and 14 ones.
44 = 30 + 14.

Question 5.
Show two ways to break apart 25.
25 is __ tens and __ones.
25 is __ tens and ___ ones.
Answer:

Explanation:
Given to break apart 25 in two way
Case 1.
25 is represented as
25 is 2 tens and 5 ones
25 = 20 + 5
In 2nd case
out of 2 tens. 1 ten is broken down to make 10 more ones.
25 is 1 tens and 15 ones.
25 = 10 + 15.

Problem Solving

Solve the problems below.

Question 6.
Explain Nate says 5 tens and 3 ones shows the same number as 3 tens and 13 ones. Do you agree? Explain.
Answer:

5 tens and 3 ones shows
50 + 3 = 53
3 tens and 13 ones shows
30 + 13 = 43
No, they both don’t show the same number.
To show the same number as
5 tens and 3 ones = 50 + 3 = 53
It should be 4 tens and 13 ones = 40 + 13 = 53 or
as given 3 tens and 13 ones add 10 more ones
3 tens and 23 ones = 30 + 23 = 53.

Question 7.
Number Sense Nancy shows a number as 4 tens and 16 ones. What number does she show?
Answer:
Nancy’s number shows 4 tens and 16 ones
4 tens and 16 ones = 40 + 16 = 56.
Nancy’s number is 56

Question 8.
What number is shown on the mat?

Answer:

Question 9.
Jeff picks 36 apples. He puts some of the apples in bags. Each bag holds 10 apples. Show two ways Jeff can put the apples in bags.

___ bags and __ apples left over
__ bags and __ apples left over
Answer:

Question 10.
Higher Order Thinking Meg breaks apart the number 80 three ways. What could be those ways?
___ tens and ___ ones
___ tens and ___ ones
___ tens and ___ ones
Answer:
Three ways Meg breaks apart the number 80 are
_80__ tens and _0__ ones
80 + 0 = 80
_70__ tens and _10__ ones
70 + 10 = 80
_60__ tens and _20__ ones
60 + 20 = 80.

Question 11.
Assessment Practice which is a way to break apart 38? Choose two that apply.
2 tens and 18 ones
2 tens and 8 ones
1 ten and 28 ones
8 tens and 3 ones
Answer:
The ways to break 38 are
3 tens and 8 ones
2 tens and 18 ones
1 ten and 28 ones
0 tens and 38 ones
In the above option given
2 tens and 18 ones is 38
1 ten and 28 ones is 38 make 38 other 2 options make
2 tens and 8 ones is 28
8 tens and 3 ones is 83.

Lesson 8.7 Look For and Use Structure

Solve & Share

Barry showed the number 42 with cubes. What are some of the ways he could have shown 42? Write the tens and ones to show the ways. Describe any patterns you see in the table.

Thinking Habits

Is there a pattern to the answers? How does the pattern help me? What do the answers have in common?

Visual Learning Bridge

Convince Me!
How can you help you. Talk to a partner about patterns use patterns to show all the ways to break apart a number into tens and ones?

Guided Practice

Make a list to solve. You can use cubes to help you. Talk to partner about patterns you see in your list.

Question 1.
Carly lists all the ways to 25 as tens and ones. What ways does she list?

Answer:

Explanation:
Here different way of 25 are represented
as you look at the ways you can notice a pattern
Ten decrease by 1 and Ones increase by 10.

Question 2.
Andy wants to show 31 as tens and ones. What are all the ways?

Answer:

Explanation:
Here different way of 31 are represented
as you look at the ways you can notice a pattern
Ten decrease by 1 and Ones increase by 10.

Independent Practice

Question 3.
Alma lists all the ways to show 46 as tens and ones. What ways does she list?

Answer:

Question 4.
Seth wants to show 33 as tens and ones. What are all the ways?

Answer:

Question 5.
Higher Order Thinking Dana says there are 4 ways to show 25 using tens and ones. Is she right? How do you know?

Answer:

Problem Solving

Performance Task

Bake Sale Rose brings 48 muffins to a bake sale. She only uses trays for groups of 10 muffins. Each plate holds only I muffin. How many trays and plates could Rose use to display the muffins?

Question 6.
Look For Patterns Fill in the table to show how many trays and plates Rose could use to display the muffins. Describe a pattern you see in the table.
Answer:

Question 7.
Reasoning Is there any way Rose can display her muffins using only trays? Explain how you know.
Answer:
No, Rose can not display her muffins using only trays.
Number of muffins Rose brought = 48
As she used trays for group of 10 muffins.
48 is 4 tens and 8 ones.
If she only uses trays then their will be 8 muffins left over. As she can only display 40 muffins in trays.

Topic 8 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 I and Partner 2 each point to a black number at the same time. Both partners add those numbers.

If the answer is on your color, you get a tally mark. Work until one partner gets twelve tally marks.

TOPIC 8 Vocabulary Review

Understand Vocabulary

Question 1.
Write the number word that is one more than fourteen.
Answer:
one more than fourteen is fifteen
1 + 14 = 15.

Question 2.
Write the number word that is one fewer than eighteen.
Answer:
Seventeen is one fewer than eighteen.
18 – 1 = 17.

Question 3.
Circle the cubes that make 2 tens.

Answer:

Explanation:
Given a set of 5 cubes.
There are 7 sets of 5 cubes.
To make 2 tens
2 sets of 5 cubes make 1 ten
So, to make 2 tens we need 4 sets of 5 cubes.
4 sets of 5 cubes make 2 tens.

Question 4.
Circle the cubes that make 1 ten and 5 ones.

Answer:

Explanation:
Given a set of 5 cubes.
There are 7 sets of 5 cubes.
To make 1 tens  and 5 ones
2 sets of 5 cubes make 1 ten
So, to make 1 tens we need 2 sets of 5 cubes.
2 sets of 5 cubes make 1 tens.
1 set of 5 cubes make 5 ones.

Question 5.
Circle the cubes that make 3 tens and 3 ones.

Answer:

Explanation:
Given a set of 5 cubes.
There are 7 sets of 5 cubes.
To make 3 tens  and 3 ones
2 sets of 5 cubes make 1 ten
So, to make 3 tens we need 6 sets of 5 cubes.
6 sets of 5 cubes make 3 tens.
3 cubes make 3 ones.

Use Vocabulary in Writing

Question 6.
Ben shows 33 as 3 tens and 3 ones. Show 33 a different way. Use tens and ones. Explain using a word from the Word List.
Answer:

33 is 2 tens and 13 ones
33 is 2 groups of 10 and 13 ones left overs.

TOPIC 8 Reteaching

Set A

You can group objects by 10 to count.

Answer:

Circle groups of 10. Write the numbers.

Question 1.

___ is ___ groups of 10 and __ ones left over.
Answer:

Explanation:
Given a set of 5 cubes.
There are 5 sets of 5 cubes.
To make groups of 10
2 sets of 5 cubes make 10
So, to make 10 we join 2 sets 5 cubes.
We get 2 groups of 10 and 5 more cubes left over.
2 tens and 5 ones is 25.

Question 2.

___ is ___ groups of 10 and __ ones left over.
Answer:

Set B

You can show a two-digit number as tens and ones.

Count the tens and ones. Then write the number.
Answer:

Explanation:
Given a two digit number.
Two digit number has Tens and Ones.
Here given 4 tens cubes in tens place and 3 one cubes is the table.
4 tens = 40
3 ones = 3
4 tens and 3 one is 43.

Question 3.

Answer:

Explanation:
Given a two digit number.
Two digit number has Tens and Ones.
Here given 5 tens cubes in tens place and 4 one cubes is the table.
5 tens = 50
4 ones = 4
5 tens and 4 one is 54.

Set C

You can draw a model to show tens and ones.

Answer:

Draw a model to show tens and ones.

Question 4.
There are __ tens and __ ones in 78.
Answer:

Explanation:
Given number 78
78 is 7 ten and 8 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
78 is represented with 7 line and 8 dots.

Set D

Thinking Habits
Look For and Use Structure

Is there a pattern to the answers? How does the pattern help me? What do the answers have in common?

Use patterns and make a list to solve.

Question 5.
Lupita wants to show all the ways to break apart 54 as tens and ones. What are all the ways?

Answer:

Topic 8 Assessment Practice

Question 1.
A. Which of these is a way to show 16?
A. 1 ten and 11 ones
B. 1 ten and 6 ones
C. 16 tens and 0 ones
D. 9 tens and 5 ones
Answer:

A. 1 ten and 11 ones is 10 + 11 = 21
B. 1 ten and 6 ones is 10 + 6 = 16
C. 16 tens and 0 ones is 160 + 0 = 160
D. 9 tens and 5 ones is 90 + 5 = 95
way to show 16 is B.

B. Which equation shows why your answer for A is correct?
A. 10+ 11 = 21
B 10+ 6 = 16
C 16 + 2 = 18
D 9 +5 = 14
Answer:

way to show 16
16 is 1 ten and 6 ones
16 is 0 tens and 16 ones.
16 = 10 + 6
So, B 10 + 6 = 16 is correct.

Question 2.
A. Write a way to show 42.
__ groups of ten and __ ones.
Answer:

42 is 4 groups of 10 and 2 ones.

B. Write another way to show 42.
___ groups of ten and ___ ones
Answer:
42 is 3 groups of ten and 12 ones.

Question 3.

___ Tens and ___ Ones is ___.
Answer:

Question 4.
Write two ways to show 1 1.
Answer:

Ways to show 11
11 is 1 ten and 1 one
11 is 0 tens and 11 ones.
These are the ways to show 11.

Question 5.
A. What number does 5 groups of ten represent?
Answer:

5 groups of ten represents
10 + 10+ 10+10+10 = 50.
5 groups of 10 represents 50.
B. What is another way to write 5 groups of ten?
___ groups of ten and ___ ones
Answer:

Another way to represent 5 group of ten
5 group of ten  is 50
50 is 4 tens and 10 ones
4 groups of 10 and 10 ones is 50.

Question 6.
A. Which of these is another way to show 4 groups of ten and 9 ones?
A 3 tens and 19 ones
B 5 tens and 0 ones
C 3 tens and 9 ones
D 5 tens and 8 ones
Answer:
A 3 tens and 19 ones is 30 + 19 = 49
B 5 tens and 0 ones is 50 + 0 = 50
C 3 tens and 9 ones is 30 + 9 = 39
D 5 tens and 8 ones is  50 + 8 = 58
Way to show 4 groups of tens and 9 ones is
4 groups of tens and 9 ones = 40 + 9 = 49.
A. 3 tens and 19 ones. is another way to represent 4 groups of tens and 9 ones.

Question 7.
Nicole found 2 ways to make 41. Complete the list to show all of the ways. Then draw a model to show one of the ways.

Answer:

TOPIC 8 Performance Task

Snack Time

Manuel’s class has a snack every day.

Question 1.
On Monday, Manuel and Ryan share 19 crackers. 10 crackers are in one bag. How many crackers are in the other bag?
Explain your answer. Use pictures, numbers, or words. Draw counters to solve. Write the word and numbers.

Answer:

Explanation:
one group of 10 ones = 1 ten
19 is made up of one group of 10 ones and  9 ones
19 = 10 + 9
19 is 1 ten and  9 ones.

Question 2.
On Tuesday, Manuel’s class has 3 packages of juice boxes. There are 10 juice boxes in each package.
How many juice boxes does his class have?
___ juice boxes
Explain your answer. Use pictures, numbers, and words.
Answer:

Explanation:
Given
3 packages of juice boxes
1 package has 10 juice boxes
3 packages of 10 juice boxes each
10 + 10 + 10 = 30
3 tens and 0 ones  is 30.
3 in  30 is the tens digit
0 in 30 is the ones digit.

Question 3.
On Wednesday, Manuel’s class has 28 bottles of water.
Manuel starts drawing a model for the bottles. Use lines and dots to finish his drawing.

Explain what the drawing shows.
Answer:

Explanation:
Given number 28
28 is 2 ten and 8 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
Manuel drew 1 line and 3 dots
To complete the 28 number model
we need to draw more 1 line and 5 dots.
2 line – 1 line = 1 line
8 dots – 3 dots = 5 dots.
28 is represented with 2 line and 8 dots.

Question 4.
On Thursday, Manuel’s class had 34 packages of raisins. How many ways could the packages of raisins be grouped as tens and ones? Make a list to show all of the ways.

Answer:

Question 5.
On Friday, Manuel’s class had 26 bags of grapes. Manuel said that there are 2 ways to group the 26 bags as tens and ones. Do you agree? Circle Yes or No. Explain your answer. Use numbers, pictures, or words.
Answer:

Go through the enVision Math Common Core Grade 2 Answer Key Topic 15 Graphs and Data regularly and improve your accuracy in solving questions.

enVision Math Common Core 2nd Grade Answers Key Topic 15 Graphs and Data

Essential Question:
How can line plots, bar graphs, and picture graphs be used to show data and answer questions?

enVision STEM Project: Comparing Objects and Data
Find Out Work with a partner. Compare two backpacks. Which one holds more? Which one has more parts? Which one is easier to put on? Think of other ways to compare.
Journal: Make a Book Show what you learn in a book. In your book, also:

• Tell one good thing and one bad thing about each backpack.
• Draw line plots, picture graphs, and bar graphs to show and compare data.

Review What You Know

Vocabulary
Question 1.
Circle the number that has a 6 in the tens place.

Answer:
6 in the ten’s place is 160. so circle the 169.

Question 2.
Circle the tally marks that show 6.

Answer: tally marks that show 6 is is a doll.

Question 3.
Circle the difference.
22 – 9 = 13
34 + 61 = 95
Answer:
From the given 22 – 9 = 13 is the difference. So circle the difference.

Comparing Numbers
Question 4.
A zoo has 405 snakes. It has 375 monkeys. Compare the number of snakes to the number of monkeys.
Write > or <.
405 375
Answer:
Given that,
Zoo has 405 snakes and 357 monkeys.
405 > 375

Interpret Data

Question 5.

Who sold the most picnic tickets?
Answer:
Given that,
Picnic tickets sold by Jean = 16
Picnic tickets sold by Paulo = 18
Picnic tickets sold by Fatima = 12
Therefore Paulo sold the most picnic tickets.

Addition and Subtraction

Question 6.
Byron scores 24 points in a game. Ava scores 16 points in the same game. How many more points does Byron score than Ανα?
________ more points
Answer:
Given that,
Byron scores in a game = 24 points
Ava scores in a game = 16 points
Byron scores than Ava = 24 – 16 = 8
Byron scores 8 points more than Ava.

Pick a Project

PROJECT 15A
What types of flowers grow in your neighborhood?
Project: Graph Data About Flowers

PROJECT 15B
How many birds do you see every day?
Project: Create a Bird-Watching Poster

PROJECT 15C
Why should you plan a Florida vacation?
Project: Make a Florida Travel Brochure

3-ACT MATH PREVIEW

Before watching the video, think: How do you know what size clothing you should wear? Is there a way you can find out without trying the clothes on?

I can … model with math to solve a problem that involves making graphs to study data.

Lesson 15.1 Line Plots

Solve & Share
Find four objects that are each shorter than 9 inches. Measure the length of each object to the nearest inch. Record the measurements in the table. Then plot the data on the number line. Which object is longest? Which is shortest?
I can … measure the lengths of objects, then make a line plot to organize the data.

Visual Learning Bridge

Convince Me! Measure the length of your pencil to the nearest inch. Record your measurement on the line plot above. How does it change the data?

Guided Practice

Use a ruler to measure each object in inches. Record each length in the table. Then make a line plot. Show each length on the line plot.
Question 1.

Answer: 3 inches long.

Question 2.

Answer:

Independent Practice

Use a ruler to measure each object in inches. Record each + Practice length in the table. Show each length on the line plot.
Question 3.
The paintbrush is ________ inches long.

Answer: the paintbrush is 7 inches long.

Question 4.
The chalk is _______ inches long.

Answer: the chalk is 3 inches long.

Question 5.
The straw is ________ inches long.

Answer: the straw is 8 inches long.

Question 6.
The feather is ________ inches long.

Answer:
The feather is 6 inches long.

Question 7.

Answer:

Problem Solving

Solve each problem. Use the line plot.
Question 8.
Be Precise Sophia measured the lengths of her colored pencils and made a table. Use the data to make a line plot.

Answer:

Question 9.
What is the length of the shortest pencil? Explain.
Answer:
Blue pencil is the shortest length in pencils.

Question 10.
Higher Order Thinking What are the lengths of the two pencils have a total length of 16 inches? Explain.
Answer:
Given that,
The length of the green pencil = 7 inches
The length of the yellow pencil = 9 inches
Adding of green pencil and yellow pencil = 16 inches

Question 11.
Assessment Practice Measure the length of the purple pencil in inches. Write the length below. Record your measurement on the line plot above in Item 8.

_________ inches
Answer: the length of the purple pencil is 4 inches long.

Lesson 15.2 More Line Plots

Solve & Share
Measure the length of your shoe to the nearest inch. Then use your data and data from your class to make a line plot. Tell one thing you learn from the data.

I can … measure the lengths of objects, then make a line plot to organize the data.

Visual Learning Bridge

Convince Me! In the example above, how many students measured their height? Tell how you know.

Guided Practice

Use the table to make a line plot. Then use the line plot to answer each question.
Question 1.

Question 2.
What is the most common feather length? _______ xm
Answer:
6 cm

Question 3.
Why does the number line use the numbers 4 through 9?
Answer:

Independent Practice

Collect data and use the data to complete the line plot. Then use the line plot to solve the problems.

Question 4.
Measure the length of your pencil in centimeters. Collect pencil-length data from your classmates. Make a line plot with the data.
Title: __________

Label: ________
Answer: length of the pencil date from classmates is 4, 6, 7, 8.

Question 5.

What is the length of the longest pencil?
Answer: The length of the longest pencil is 8 inches.

Question 6.
What is the sum of the lengths of the shortest and longest pencils?
Answer:
Given that;
The length of the shortest pencil is 4 inches
length of the longest pencil is 8 inches
The sum of the longest and shortest pencil is 8 + 4 = 12.

Question 7.
What is the difference in lengths between the shortest and longest pencils?
Answer:
Given that;
The length of the shortest pencil is 4 inches.
The length of the longest pencil is 8
The difference between the shortest and longest pencil is 8 – 4 = 4.

Question 8.
What is the most common pencil length?
Answer: The most common pencil length is 6 inches.

Question 9.
Vocabulary Use these words to complete the sentences.
longest
line plot
order
A ________ can help you see the data in __________.
A line plot can show the lengths of the shortest and _________ objects.
Answer:
A line plot can help you see the data in order.
A line plot can show the lengths of the shortest and longest objects.

Problem Solving

Model Use the data in the table to complete the line plot. Then use the line plot to solve the problems.
Question 10.

Answer:

Question 11.
Higher Order Thinking Measure the length of one of your crayons in centimeters, 5 different times. Make a line plot of the data on a separate sheet of paper. Did you get the same measurement each time? Explain.
Answer:

Question 12.
Assessment Practice Measure the length of the blue crayon to the nearest centimeter. Write the length below.

_______________
Then record your measurement on the line plot above that you made in Item 10.
Answer:

Lesson 15.3 Bar Graphs

Solve & Share
The graph shows the number of birthdays in each season for a class. Use the graph to write the number of birthdays in the table. How many more birthdays are celebrated during spring, fall, and winter than during summer? Be ready to explain how you know.
I can … draw bar graphs and use them to solve problems.

Visual Learning Bridge

Convince Me! Which activity did the most students choose? Explain how you know.

Guided Practice

Use the table to complete the bar graph. Then use the bar graph to solve the problems.

Question 1.
How many students chose cat? ________
Answer:
4 students choose a cat.

Question 2.
How many students chose bird or dog? _______
Answer:
6 students choose a dog.
2 students choose a bird.

Independent Practice

Use the bar graph to solve the problems.

Question 3.
How many students write after school?
Answer:
8 students write after school.

Question 4.
How many fewer students draw than write after school?
________ fewer students
Answer:
Students draw after school = 3
Students write after school = 8
Fewer students draw than write after school = 8 – 3 = 5

Question 5.
Which activity do the fewest students do after school?
Answer:
The fewest students do after school is writing activity.

Question 6.
How many students read or draw after school?
Answer:
Students read after school = 5
Students write after school = 8
Students read and write after school = 13

Question 7.
Which activity do the most students do after school?
Answer:
Most students do school in play activities.

Question 8.
How many more students play than read after school?
__________ more students
Answer:
Students play activity after the school = 11
Students read activity after the school = 5
Students play than read after school = 11 – 5 = 6 students

Question 9.
Higher Order Thinking How would the graph be different if 2 students changed their after-school activity from play to read?
Answer:

Problem Solving

Solve the problems below.
Question 10.
Model Wanda goes to the farm. She buys 8 pears, 5 oranges, 2 apples, and 9 peaches.
Use this data to make a bar graph.

Answer:

Question 11.
Higher Order Thinking Look at the graph you made in Item 10. How would the graph change if Wanda returns 3 of the pears that she buys?
Answer:

Question 12.
Assessment Practice Look at the bar graph you made in Item 10. Which are correct? Choose all that apply.
☐ Wanda buys the same number of pears and peaches.
☐ Wanda buys 3 more oranges than apples.
☐ Wanda buys 24 pieces of fruit in all.
☐ Wanda buys 3 fewer oranges than pears.
Answer:

Lesson 15.4 Picture Graphs

Solve & Share
The picture graph shows the favorite subjects of a class. Draw a smiley face on the graph to show your favorite subject. Then interview two classmates and add their data. How many students responded to the survey? Which subject do most students like best? How many students like math or science best?
I can … draw picture graphs and use them to solve problems.

Visual Learning Bridge

Convince Me! How are the tally chart and the picture graph for the favorite ball games of Ms. Green’s class alike?

Guided Practice

Use the tally chart to complete the picture graph. Then use the picture graph to solve the problems.

Question 1.
How many students like blue or red best? _______
Answer:
11

Question 2.
Which color is the favorite of most students? ________
Answer:
The blue color is the favorite of most students.

Independent Practice

Use the tally chart to complete the picture graph. Then use the picture graph to solve the problems.
Question 3.

Answer:

Question 4.
How many students like fall best?
Answer:
6 students like fall best.

Question 5.
Which season do exactly 4 students like best?
Answer:
Spring season do exactly 4 students like best.

Question 6.
Which season do the fewest students like?
Answer:
Winter season do the fewest students like.

Question 7.
How many fewer students voted for winter than for summer?
Answer:
Students voted for winter is 2
Students voted for summer is 10
Fewer students voted for winter than summer is 10 – 2 = 8.

Question 8.
How many more students voted for summer than for spring and winter combined?
__________ more students
Answer:
Students voted for summer is 10
Students voted for spring  is 4
Students voted for winter is 2
Students voted for winter and spring combined is 4 + 2 = 6
Students voted for summer more than winter and spring is 10 – 6 = 4

Question 9.

How many students like the season with the most votes?
Answer:
Students like the season with the most votes are the summer season.

Question 10.
Higher Order Thinking Look at the picture graph above. How would the graph change if 2 students changed their votes from summer to fall?
Answer:

Problem Solving

Use the tally chart to complete the picture graph. Use the picture graph to solve the problems.
Question 11.
Model Bob made a tally chart to show the trees in a park.

Answer:

Question 12.
en Vision® STEM Birch, oak, maple, and pine trees are common in North America. Which type of tree is most common in the park?
Answer:

Question 13.
Higher Order Thinking How many birch and maple trees are there in all?
Answer:
Birch trees in the park = 3
Maple tree in the park = 4
Birch and maple trees in all are 7.

Question 14.
Assessment Practice Draw a picture graph to show the data in the table.

Answer:

Lesson 15.5 Draw Conclusions from Graphs

Solve & Share
7 students voted for Turtle as their favorite pond animal. 10 students voted for Frog. 4 students voted for Fish. Make a picture graph to show the data. Write two things you notice about the data.
I can .. draw conclusions from graphs.

1. __________________
2. __________________

Visual Learning Bridge

Convince Me! Look at the graph above. How many tickets did Kim and Neil sell in all? How do you know?

Guided Practice

Use the bar graph to solve the problems.

Question 1.
How many pennies does Jake have? ________
Answer:
Jake has 5 pennies.

Question 2.
Jake spends 3 of his quarters. How many does he have left?
Answer:
Total quarters at Jake = 7
Jake spends 3 of his quarters
He have left = 7 – 3 = 4

Independent Practice

Use the bar graph to solve the problems.

Question 3.
How many absences were there in all on Tuesday and Thursday?
Answer:
Total students absences in Tuesday = 2
Total students absences in Thursday = 4
Total students absences in Tuesday and Thursday = 2 + 4 = 6 students.

Question 4.
Were fewer students absent on Monday or Friday? How many fewer?
Answer:
Total students absent on Monday = 5
Total students absent on Friday = 6
1 Fewer student is absent on Monday

Question 5.

Three of the students absent on Friday were boys. How many girls were absent on Friday?
Answer:
Given that,
Total students absent on Friday = 6
From 6 students 3 are boys = 6 – 3 = 3
3 girls are absent on Friday.

Question 6.
On which two days were the same number of students absent?
Answer:
No two days were the same number of students absent.

Question 7.
Were more students absent on Wednesday or Thursday? How many more?
Answer:
Given that,
Total number of students absent on Wednesday = 5
Total number of students absent on Thursday = 4
More students are absent on Wednesday than Thursday
1 student is more absent on Wednesday.

Question 8.
Higher Order Thinking The graph shows the number of absences last week. This week, there are 19 absences. Compare the number of absences this week to the number of absences last week.
Answer:

Problem Solving

Use the bar graph to solve each problem.

Question 9.
Make Sense Complete each sentence.
The farm has ________ Cows and ________ horses.
The farm has ________ goats and ________ sheep.
Answer:
The farm has 5 cows and 3 horses
The farm has 8 goats and 2 sheeps

Question 10.
The sheep and goats are kept in the same pen. How many farm animals are in that pen?
Answer:
Given that,
Sheep and goats are kept in the same pen.
Total number of sheep = 2
Total number of goats = 8
Total number of farm animals are in that pen = 8 + 2 = 10

Question 11.
Suppose 3 new baby goats are born. Then how many goats will the farmer have?
Answer:
Total number of goats = 8
3 new baby goats are born
Total number of goats at the farmer = 8 + 3 = 11 goats

Question 12.
How many fewer horses than cows are on the farm?
_________ fewer horses
Answer:
Total number of horses = 3
Total number of cows = 5
2 fewer horses than cows are on the farm.

Question 13.
Write the order of animals on the farm from the greatest number to the least number.
Answer:
Number of goats = 8
Number of cows = 5
Number of horses = 3
Number of sheep = 2

Question 14.

Higher Order Thinking Do you think the bars on a bar graph should all be the same color? Explain.
Answer:
No, the bars on a bar graph have different colours because to show the difference between the given data.

Question 15.
Assessment Practice The farmer wants to buy some sheep. He wants to have as many sheep as cows. How many more sheep should the farmer buy?
_________ more sheep
Answer:

Lesson 15.6 Problem Solving

Reasoning
Solve & Share

Make a picture graph to show how many connecting cubes, counters, and ones cubes you have. Then write and solve a problem about your data.
I can … reason about data in bar graphs and picture graphs to write and solve problems.

Each = 1 math tool

Thinking Habits What do the symbols mean? How are the numbers in the problem related?

Visual Learning Bridge

Convince Me! Use reasoning to write your own problem about the data in the graph. Then solve it.

Guided Practice

Use the bar graph to write and solve problems.

Question 1.

Answer:

Question 2.
_____________
_____________
________ _________ = ________
Answer:

Independent Practice

Use the bar graph to write and solve problems.

Question 3.
_____________
_____________
________ _________ = ________
_____________
_____________
Answer:

Question 4.
_____________
_____________
________ _________ = ________
_____________
_____________
Answer:

Problem Solving

Performance Task
Vacation Time! The picture graph shows votes for favorite vacation spots. Each student voted only once. Which vacation spot has the same number of votes as two other vacation spots combined?

Question 5.
Explain Solve the problem above and explain your reasoning.
Answer:

Question 6.
Make Sense How many students voted in all? Tell how you know.
Answer:

Question 7.
Reasoning Write your own problem about the data in the graph. Then solve it.
_____________
_____________
________ _________ = ________
_____________
_____________
Answer:

Topic 15 Fluency Practice

Find a Match
Find a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box next to the match. Find a match for every clue.
I can … add and subtract within 100.

Clues
A. The difference is less than 16.
B. The sum equals 43 + 25.
F The sum equals 75.
C. The difference equals 75 – 46.
D. The sum equals 53 + 20.
E. The difference equals 96 – 19.
G. The sum is between 60 and 65.
H. The difference is between 25 and 28.

Topic 15 Vocabulary Review

Understand Vocabulary

Label each data display. Write line plot, bar graph, or picture graph.
Word List
• bar graph
• data
• line plot
• picture graph
• symbol

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Use Vocabulary in Writing
Question 4.
Look at the graph in Item 2. Use words to tell how to find which ball game is the most popular. Use terms from the Word List.
Answer:

Topic 15 Reteaching

Set A

Line plots show and organize data. Use an inch ruler. Measure the length of the toy car. Then record the measurement in the table.

Place a dot over the number that shows the length of each toy.

Complete the table and show the data on a line plot.
Question 1.
Use an inch ruler. Measure the length of the pencil. Then record the measurement in the table.

Answer:

Question 2.
Make a line plot to show each length in the table.

Answer:

Set B

You can make a bar graph to show the data in a table.
Students voted for their favorite nut. The table shows the number of votes.

Color one space for each vote in the bar graph. Then use the graph to solve the problem.

How many students voted?
16

Use the table to complete the bar graph. Then solve each problem.
Question 3.

Answer:

Question 4.
How many more students voted for vanilla than banana? ________
Answer:
Given that,
Students voted for vanilla = 7
Students voted for banana = 6
Students voted for vanilla than banana is 1.

Question 5.
How many fewer students voted for lemon than vanilla? _________
Answer:
Given that,
Students voted for lemon = 3
Students voted for vanilla = 7
Fewer students voted for lemon than Vanilla is 7 – 3 = 4
4 students voted for lemon than Vanilla.

Set C

A picture graph uses pictures or symbols to show data.
The tally chart shows votes for favorite sea animals.

Which sea animal has the fewest votes?

Use the tally chart to complete the picture graph. Then solve each problem.
Question 6.

Answer:

Question 7.
How many votes did seagull get?
Answer:
10 votes did seagull get.

Question 8.
Which bird had the fewest votes?
Answer:
Blue Jay bird had the fewest votes.

Set D

Thinking Habits
Reasoning
What do the symbols mean?
How are the numbers in the problem related? How can I write a word problem using the information that is given? How do the numbers in my problem relate to each other? How can I use a word problem to show what an equation means?

Use the picture graph to solve each problem. Each student voted once.

Question 9.
How many fewer students chose ice fishing than snowboarding?
Answer:
given that;
students who chose ice fishing is 4
students who chose snowboarding is 10
students chose ice fishing than snowboarding is 10 – 4 = 6

Question 10.
Write and solve your own problem about the data.
______________
______________
____ ______ = _________
______________
Answer:

Topic 15 Assessment Practice

Question 1.
Pam has 5 pennies, 2 nickels, 8 dimes, and 9 quarters. Show this data in the bar graph below. Draw the bars.

Answer:

Question 2.
Use the bar graph you made above. Pam spends 5 of her dimes to buy an apple. Now how many dimes does Pam have left?
A. 13
B. 5
C. 3
D. 0
Answer:

Question 3.
Is each sentence about the picture graph correct? Choose Yes or No.

Answer:

Question 4.
How many more tickets did Kendra sell than Leon?

A. 5
B. 6
C. 11
D. 17
Answer:
5 more tickets did kendra band concert

Question 5
Complete the table and the line plot.
A. Use a centimeter ruler. Measure the length of the crayon to the nearest centimeter. Write the length in the table below.

Answer:

B. Use the data in the table to complete the line plot.

What is the difference in length between the shortest and longest crayon?
Answer:
The shortest length of the crayon is 4
The longest length of the crayon is 8
The difference between the shortest and longest crayon is 8 – 4 = 4.

Question 6.
Scott is making a picture graph from the data in the tally chart.
How many symbols should he draw in the bottom row?

A. 3
B. 4
C. 5
D. 6
Answer:

Question 7.
Mary gets new stamps every month. The bar graph shows the number of stamps she collects each month.

Which statements are true? Choose all that apply.
☐ Mary collects I more stamp in May than she does in April.
☐ Mary collects 2 fewer stamps in June than she does in July.
☐ Mary collects a total of |stamps in May and June.
☐ Mary collects one additional stamp each month from May to July.
☐ Mary collects the most stamps in June.
Answer:
the true statements are
Mary collects I more stamp in May than she does in April.
Mary collects one additional stamp each month from May to July.
Mary collects one additional stamp each month from May to July.

Question 8.
Use the tally chart to complete the picture graph. Then use the picture graph to solve the problems.

How many students voted for Lily? _________
Which flower is the least favorite? _________
Answer:
8 students voted for Lily.
Daisy is the least favorite flower.

Question 9.
Use the line plot and the numbers on the cards to complete each sentence.

3 pencils are ________ inches long.
The longest pencil is ________ inches long.
The shortest pencil is ________ inches long.
The difference between the shortest and longest pencil is _________ inches.
Answer:3 pencils are 1 inch long.
The longest pencil is 3 inches long.
The shortest pencil is 1 inch long.
The difference between the shortest and longest pencil is 2 inches

Topic 15 Performance Task

School Surveys Some students asked their classmates different questions.
George asked his classmates to vote for their favorite lunch. This table shows the results.

Question 1.
Use the table to complete the bar graph.

Answer:

Question 2.
Use the Favorite Lunch table to complete the picture graph.

Answer:

Question 3.
Use the graphs you made to answer these questions.
How many students chose salad as their favorite lunch? _________
How many fewer students chose taco than hamburger? __________ fewer students
How would the bar graph change if two more students chose taco?
Answer:

Question 4.
Write and solve a math story about the Favorite Lunch graphs you made.
Part A
Use the bar graph or the picture graph about favorite lunches to write a math story problem. The problem should include addition or subtraction.
Answer:

Part B
Solve your math story problem. Explain how you solved the problem.
Answer:

Question 5.
Gina asked her classmates to measure the length of their favorite storybook in inches. She recorded their measurements in this table.

Part A
Use the table to make a line plot.
Answer:

Part B What is the difference in length between the longest and shortest books?
________ inches
Answer:
Given that,
The length of the longest pencil is 12 inches
The length of the shortest book is 7 inches
The difference between longest book and shortest book = 12 – 7 = 5 inches

Go through the enVision Math Common Core Grade 1 Answer Key Topic 9 Compare Two-Digit Numbers regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 9 Compare Two-Digit Numbers

enVision STEM Project: Light and Objects

Find Out Talk to friends and relatives about light. Discuss how light changes when it shines on different kinds of objects.

Journal: Make a Book Show what you found out. In your book, also:

• Draw pictures showing light shining on objects that are see-through and not see-through.
• Make up and solve number stories about shining light on different objects.

Review What You Know

Vocabulary

Question 1.
Circle the group of cubes that has more.

Answer:

Explanation :
The orange cubes are 3
The Green cubes are 5
3 < 5 . so Green cubes are circled .

Question 2.
Circle the group of cubes that has less.

Answer:

Explanation :
The orange cubes are 3
The Green cubes are 5
3 < 5 . so orange cubes are circled .

Question 3.
How many tens are in the number?
50
___ tens
Answer:
50 = 5 tens
Explanation :
counting

Number Lines

Question 4.
Use the number line to count by 10s. Write the missing numbers.

Answer:

Explanation :
Count on Tens 10, 20, 30 and 40 .

Question 5.
Pat sees 5 bugs. Erin sees 6 bugs. How many bugs did they see in all?
Use the number line to count.

___ bags
Answer:
Number of bugs seen by Pat = 5 bugs
Number of bugs seen by Erin = 6 bugs
Total Number of bugs = 5 + 6 = 11 bugs  .

Hundred Chart

Question 6.
Use the part of the hundred chart to count.

Answer:
18, 19 , 20, 21, 22
Explanation:
Count by ones from 18 to 22 .

Pick a Project

PROJECT 9A

How hot can it get?
Project: Create a Temperature Drawing

Answer :

The climate is too hot as the camel cannot take the weight of the person so, walking in the Sand .

PROJECT 9B
Where did they all come from?
Project: Make a Shorebird Comparison Model

Answer :
Instructions used to make a Shoe bird

PROJECT 9C
How was that made?
Project: Make a Sponge Stamp Picture

Answer :

Explanation :
Take the sponge .
Cut the sponge into required shape like star, Moon , Heart and aetc into different shapes .
Then later , Put the required shape sponge in water colors or ink .
Then Press the sponge imprint on the paper . then required drawing can be made with the required shape .

Math Modeling

Digit Flip

3-ACT MATH PREVIEW
Before watching the video, think: Have you ever played a card game? What were some of the rules? How did someone win the game?

Lesson 9.1 1 More, 1 Less; 10 More, 10 Less

Solve & Share

Sarah has 12 marbles. Chris has one more marble than Sarah. Lucia has 10 more marbles than Sarah. How many marbles does Chris have? How many marbles does Lucia have? Show how you know.

Answer :
Number of Marbles with Sarah = 12
Number of Marbles with Chris = one more marble than Sarah = 12 + 1 = 13
Number of Marbles with Lucia = ten more marble than Sarah = 12 + 10 = 23

Visual Learning Bridge

Convince Me!
How can you find 10 more than a number? Explain.
Answer :
To find 10 more than a number, add 1 to the digit at the tens place.

Guided Practice

Use place-value blocks to show each number and to help you complete each sentence.

Question 1.

Answer:
1 more than 45 is 46
1 less than 45 is 44
10 more than 45 is 55
10 less than 45 is 35

Question 2.

1 more than 17 is ___
1 less than 17 is ___
10 more than 17 is ___
10 less than 17 is ___
Answer:
1 more than 17 is 18
1 less than 17 is 16
10 more than 17 is 27
10 less than 17 is 7

Independent Practice

Use place-value blocks to show each number and to help you
complete each sentence.

Question 3.

1 more than 11 is ___
1 less than 11 is ___
10 more than 11 is ___
10 less than 11 is ___
Answer:
1 more than 11 is 12
1 less than 11 is 10
10 more than 11 is 21
10 less than 11 is 1

Question 4.

1 more than 40 is ___
1 less than 40 is ___
10 more than 40 is __
10 less than 40 is ___
Answer:
1 more than 40 is 41
1 less than 40 is 39
10 more than 40 is 50
10 less than 40 is 30

Question 5.

1 more than 81 is ___
1 less than 81 is ___
10 more than 81 is ___
10 less than 81 is ___
Answer:
1 more than 81 is 82
1 less than 81 is 80
10 more than 81 is 91
10 less than 81 is 71

Question 6.

1 more than 19 is ___
1 less than 19 is ____
10 more than 19 is ___
10 less than 19 is ___
Answer:
1 more than 19 is 20
1 less than 19 is 18
10 more than 19 is 29
10 less than 19 is 9

Question 7.

1 more than 65 is ___
1 less than 65 is ___
10 more than 65 is ___
10 less than 65 is ___
Answer:
1 more than 65 is 66
1 less than 65 is 64
10 more than 65 is 75
10 less than 65 is 55

Question 8.

1 more than 43 is ___
1 less than 43 is ___
10 more than 43 is ___
10 less than 43 is ___
Answer:
1 more than 43 is 44
1 less than 43 is 42
10 more than 43 is 53
10 less than 43 is 33

Question 9.
Higher Order Thinking Circle the picture that shows 10 more than 24. Explain how you know.

Answer:

Explanation :
To find 10 more than a number, add 1 to the digit at the tens place.
24 + 10 = 34 .

Problem Solving
Solve each problem below.

Question 10.
Generalize Sheila wants to write instructions to tell her friend how to find 10 more than any number. What instructions should Sheila write?
Answer:
Instructions are :
To find 10 more than a number, add 1 to the digit at the tens place.
When we add 10 the ones always stay the same.

Question 11.
Number Sense Fill in the missing numbers. Use place-value blocks to help you.

Answer:

Question 12.
Higher Order Thinking Write and solve a riddle for a number greater than 40 and less than 60. Use “I more than” and “I less than” or “10 more than” and “10 less than” as clues.
Clues: __________
_______________
_______________
My number is ____.
Answer:
My number is 44

Question 13.
Assessment Practice Match each number with its description.

Answer:

Lesson 9.2 Find Numbers on a Hundred Chart

Solve & Share

How can you use a hundred chart to help you find I more than 36? What about I less, 10 more, and 10 less than 36? Write the numbers.

1 more than 36 is ___.
10 more than 36 is ___
1 less than 36 is ___
10 less than 36 is ____
Answer :
1 more than 36 is 37
10 more than 36 is 46
1 less than 36 is 35
10 less than 36 is 26 .
Explanation :
1 more than 36 means the next number to its right as per hundred chart .
10 more than 36 means the number below 36 as per hundred chart .
1 less than 36 means before number to its left as per hundred chart .
10 less than 36 means the Number above 36 as per hundred chart .

Visual Learning Bridge

Convince Me!
How could you use a hundred chart to find what number is 10 more than 86? What number is that?
Answer :

Explanation :
1 more than 86 means the next number to its right as per hundred chart .
10 more than 86 means the number below 86 as per hundred chart .
1 less than 86 means before number to its left as per hundred chart .
10 less than 86 means the Number above 86 as per hundred chart .

Guided Practice
Complete the part of the hundred chart. Practice Use place-value blocks if needed.

Question 1.

Answer:

Explanation :
1 more than 33 means the next number to its right as per hundred chart .
10 more than 33 means the number below 33 as per hundred chart .
1 less than 33 means before number to its left as per hundred chart .
10 less than 33 means the Number above 33 as per hundred chart .

Question 2.

Answer:

Explanation :
1 more than 46 means the next number to its right as per hundred chart .
10 more than 46 means the number below 46 as per hundred chart .
1 less than 46 means before number to its left as per hundred chart .
10 less than 46 means the Number above 46 as per hundred chart .

Independent Practice

Use a hundred chart to complete each sentence. Use place-value blocks if needed.

Question 3.
1 more than 37 is ___.
1 less than 37 is ____.
10 more than 37 is ___.
10 less than 37 is ____.
Answer:
1 more than 37 is 38.
1 less than 37 is  36.
10 more than 37 is 47.
10 less than 37 is 27

Explanation :
1 more than 37 means the next number to its right as per hundred chart .
10 more than 37 means the number below 37 as per hundred chart .
1 less than 37 means before number to its left as per hundred chart .
10 less than 37 means the Number above 37 as per hundred chart .

Question 4.
1 more than 22 is ___.
1 less than 22 is ___.
10 more than 22 is ___.
10 less than 22 is ___.
Answer:
1 more than 22 is 23.
1 less than 22 is 21.
10 more than 22 is 32.
10 less than 22 is 12

Explanation :
1 more than 22 means the next number to its right as per hundred chart .
10 more than 22 means the number below 22 as per hundred chart .
1 less than 22 means before number to its left as per hundred chart .
10 less than 22 means the Number above 33 as per hundred chart .

Question 5.
1 more than 54 is ___
1 less than 54 is ____
10 more than 54 is ___
10 less than 54 is ___
Answer:
1 more than 54 is 55
1 less than 54 is 53
10 more than 54 is 64
10 less than 54 is 44

Explanation :
1 more than 54 means the next number to its right as per hundred chart .
10 more than 54 means the number below 54 as per hundred chart .
1 less than 54 means before number to its left as per hundred chart .
10 less than 54 means the Number above 33 as per hundred chart .

Question 6.
1 more than 78 is ___.
1 less than 78 is ___.
10 more than 78 is ___.
10 less than 78 is ___.
Answer:
1 more than 78 is 79.
1 less than 78 is . 77
10 more than 78 is  88.
10 less than 78 is 68

Explanation :
1 more than 78 means the next number to its right as per hundred chart .
10 more than 78 means the number below 78 as per hundred chart .
1 less than 78 means before number to its left as per hundred chart .
10 less than 78 means the Number above 78 as per hundred chart .

Question 7.
1 more than 82 is ___
1 less than 82 is ____
10 more than 82 is ___.
10 less than 82 is ___.
Answer:
1 more than 82 is 83
1 less than 82 is 81
10 more than 82 is 92.
10 less than 82 is 72

Explanation :
1 more than 82 means the next number to its right as per hundred chart .
10 more than 82 means the number below 82 as per hundred chart .
1 less than 82 means before number to its left as per hundred chart .
10 less than 82 means the Number above 82 as per hundred chart .

Question 8.
1 more than 16 is ___
1 less than 16 is ___
10 more than 16 is ___
10 less than 16 is ___
Answer :
1 more than 16 is 17
1 less than 16 is 15
10 more than 16 is 26
10 less than 16 is 6

Explanation :
1 more than 16 means the next number to its right as per hundred chart .
10 more than 16 means the number below 16 as per hundred chart .
1 less than 16 means before number to its left as per hundred chart .
10 less than 16 means the Number above 16 as per hundred chart .

Algebra Use a hundred chart to find each student’s number.

Question 9.
Alex’s number is 27. Kendra’s number is 1 less than Alex’s number. Devon’s number is 10 more than Kendra’s number. Finish the equations to find each friend’s number.

Answer:

Explanation :
Alex Number = 27
Kendra’s number is 1 less than Alex’s number = 27 -1 = 26
Devon’s number is 10 more than Kendra’s number =  26 + 10 = 36

Problem Solving

Solve the problems below.

Question 10.
Look for Patterns Use the clues to find the missing number of marbles in each bag. Write the number. Ben has more than 54 marbles.
Anna has 10 more marbles than Ben.
Todd has a number that is 1 less than the number Anna has.

Answer:
Ben has more than 54 marbles. so, take 55 marbles .
Number of Marbles with Anna =10 more marbles than Ben = 10 + 55 = 65 Marbles .
Number of Marbles with Todd = has a number that is 1 less than the number Anna has = 65 – 1 = 64 marbles

Question 11.
Higher Order Thinking Write a clue a partner could use to find how many marbles are in a bag. Then use the clue to tell how many marbles are in the bag.

Answer:

Number of marbles in the bag = 10 less than 60 = 60 – 10 = 50 .

Question 12.
Assessment Practice

Which are true? Choose two.
10 more than 23 is 32.
1 more than 23 is 24.
10 less than 23 is 13.
1 less than 23 is 20.
Answer:
Option
Explanation :
10 more than 23 = 10 + 23 = 33 Option 1 is wrong .
1 more than 23 = 1 + 23 = 24 . Option 2 is right .
10 less than 23 = 23 – 10 = 13 Option 3 is right .
1 less than 23 = 23 – 1 = 22 Option 4 is right .

Lesson 9.3 Compare Numbers

Solve & Share
How can place-value blocks help you decide which number is larger? Circle the number that is larger.

Answer :

73 > 37
Explanation :
First Compare the Tens of 7 tens and 3 tens . 7 > 3 . so, 73 is greater than 37 .

Visual Learning Bridge

Convince Me!
Which number is greater, 38 or 26? How do you know?
Answer :
38 > 26
Explanation :
First Compare the Tens of 3 tens and 2 tens . 3 > 2 . so, 38 is greater than 26 .

Guided Practice
Write a number to match each model. Then circle is greater than or is less than.

Question 1.

Answer:

Explanation :
First Compare the Tens of 7 tens and 5tens . 7 > 5 .
so, 78 is greater than 53 .

Question 2.

Answer:

Explanation :
First Compare the Tens, Both have 2 tens
Then compare the ones , 4 < 9 . so, 24 < 29 .
24 less than 29 .

Independent Practice

Write a number to match each model. Then circle is greater than or is less than.

Question 3.

Answer:

Explanation :
First Compare the Tens of 4 tens and 2tens . 4 > 2 .
so, 43 is greater than 27 .

Question 4.

Answer:

Explanation :
First Compare the Tens, Both have 2 tens
Then compare the ones , 8 ones and 2 ones 8 > 2 . so, 28 > 22 .
28 is Greater than 22 .

Question 5.

Answer:

Explanation :
First Compare the Tens, Both have 3 tens
Then compare the ones , 1 ones and 9 ones 1 < 9 . so, 31 < 39 .
31 is less than 39

Question 6.

Answer:

Explanation :
First Compare the Tens of 6 tens and 5 tens . 6 > 5 .
so, 60 is greater than 55 .

Question 7.

Answer:

Explanation :
First Compare the Tens, Both have 9 tens
Then compare the ones , 3 ones and 7 ones 3 < 7 . so, 93 < 97 .
93 is less than 97

Question 8.

Answer:

Explanation :
First Compare the Tens, of 2 tens and 7 tens . 2 > 7 .
so, 79 is greater than 22.

Question 9.
Number Sense Laura counts 36 stars. Andy counts 7 more stars than Laura. Write the number of stars Andy counted. Then complete the sentence.
___ stars
___ is less than ___.
Answer :
Number of stars Laura counted = 36 stars
Number of stars Andy counted = counts 7 more stars than Laura = 36 + 7 = 43 stars .
43 stars
36 is less than 43.

Problem Solving

Solve each problem below. Then complete each sentence.

Question 10.
Make Sense Ming sees 28 girls at the park. She sees 32 boys at the park. Does Ming see more girls or more boys?
She sees more ___
___ is less than
Answer:
Number of girls = 28 .
Number of boys = 32 .
She sees more boys
28 is less than 32 .

Question 11.

Make Sense Julio counts 81 pennies. He counts 76 dimes.
Does Julio count more pennies or more dimes?
He counts more ___
___ is greater than ___
Answer:
Number of pennies = 81
Number of Dimes = 76
he counts more Pennies
81 is greater than 76 .

Question 12.
Higher Order Thinking Choose
2 numbers between 40 and 99. Write a sentence that compares the numbers.
My numbers are ___ and ___

Answer:
My numbers are 60 and 55

Explanation :
First Compare the Tens of 6 tens and 5 tens . 6 > 5 .
so, 60 is greater than 55 .

Question 13.
Assessment Practice Ann has 46 shells. Ben has 43 shells.
Compare the numbers. Circle is greater than or is less than.

Answer:
Number of shells Ann have = 46
Number of shells Ben have = 43

Explanation :
First Compare the Tens, Both have 4 tens
Then compare the ones , 6 ones and 3 ones 6 > 3 . so, 46 > 43 .
46 is Greater than 43 .

Lesson 9.4 Compare Numbers with Symbols (>, <, =)

Solve & Share

Write a two-digit number inside the TV. Write a different two-digit number inside the radio. Then write the numbers and circle the words to complete the sentence below. Explain how you know.

Answer :

Visual Learning Bridge

Convince Me!
How do you know that 48 is greater than 40?
Answer :

Guided Practice
Complete each sentence. Write greater than, less than, or equal to. Then write >, <, or =.

Question 1.

Answer:

Explanation :
Notice the blocks of 28 and 41. compare the tens first .
41 have more tens than 28.
so, 28 < 41.

Question 2.

Answer:

Explanation :
Notice the blocks of 53 and 35. compare the tens first .
53 have more tens than 35.
so, 53 > 35.

Independent Practice

Complete each sentence. Write greater than, less than, or equal to. Then write >, <, or =.

Question 3.

Answer:

Explanation :
The Tens are same
The Ones are same .

Question 4.

Answer:

Explanation :
Notice the blocks of 62 and 37. compare the tens first .
62 have more tens than 37.
so, 62 > 37.

Question 5.

Answer:

Explanation :
Notice the blocks of 86 and 89. compare the ones when they have same tens .
86 have less ones than 89.
so, 86 < 89 .

Question 6.
34 43
Answer:

Explanation :
Notice the blocks of 34 and 43. compare the tens first .
43 have more tens than 34.
so, 34 < 43.

Question 7.
95 90
Answer:

Explanation :
Notice the blocks of 95 and 90. compare the ones when they have same tens .
90 have no ones than 95.
so, 95 > 90 .

Question 8.
74 74
Answer:

Explanation :
The Tens are same
The Ones are same .

Higher Order Thinking Choose 2 number cards for each problem. Compare the numbers. Write >, <, or = in the circle. Use each number card one time.

Question 9.

Answer:

Explanation :
The Tens are same
The Ones are same .

Question 10.

Answer:

Explanation :
Notice the blocks of 99 and 72. compare the tens first .
99 have more tens than 72.
so, 99 > 72.

Question 11.

Answer:

Explanation :
Notice the blocks of 42 and 56. compare the tens first .
42 have less tens than 56.
so, 42 < 56.

Problem Solving
Solve each problem below.

Question 12.
Be Precise Mary has 21 red ribbons. She has 12 yellow ribbons. Does Mary have more red ribbons or yellow ribbons? Write >, <, or = to compare the numbers.
21 12
She has more ___ ribbons.
Answer:
Number of Red Ribbons  = 21
Number of Yellow Ribbons = 12
21 > 12 .
She has more Red Ribbons .
Explanation :
Compare the tens first .
21 have more tens than 12.
so, 21 > 12.

Question 13.
Vocabulary Write a sentence using greater than (>).

Answer:
75   > 74
Explanation :
Notice 75 and 74.
Compare the Ones when we have same tens .
75 have more ones than 74.
so, 75 > 74.

Question 14.
Higher Order Thinking Write a story that compares 2 numbers. Then complete the sentence to compare the numbers.

Answer:

Explanation :
Number of pink balls = 20
Number of blue balls = 25 .
20 < 25 .
She has more blue balls .

Question 15.
Assessment Practice Jake has 92 stickers. Brian has 97 stickers.
Which sentences show the correct way to compare Jake’s stickers and Brian’s stickers? Choose two that apply.
92 = 97
97 > 92
92 > 97
92 < 97
Answer:
Number of stickers Jake have = 92
Number of stickers Brian have = 97 .
92 is less than 97
97 is greater than 92 .

Lesson 9.5 Compare Numbers on a Number Line

Solve & Share

Nick skipped rope 24 times. Look at the number line below. Find a number that is greater than 24 and a number that is less than 24. Show your numbers on the number line and explain how you know.

____ is greater than 24.
____ is less than 24.
Answer :

25, 26, 27, 28, 29 and so on are greater than 24.
23, 22, 21 and so on are lesser than 24.
Explanation :
The numbers to the right of 24 on a number line are greater than 24 .
The numbers to the left of 24 on a number line are lesser than 24 .

Visual Learning Bridge

Convince Me!
Using a number line, how do you know if 70 is greater than or less than 53?

Explanation :
53 is left of 70 on a number line so, 70 is greater than 53 .

Guided Practice

Write a number to make each correct. Use the number line to help if needed.

Question 1.
31 < 32
Answer:

Explanation :
The numbers to the left of 32 on a number line are lesser than 32 .
31 is left of 32 .
so, 31 < 32 .

Question 2.
40 > ___
Answer:

Explanation :
Any number to the left of 40 on a number line is lesser than 40 .
38 is left of 40 so, 40 > 38 .

Question 3.
35 > __
Answer:

Explanation :
Any number to the left of 35 on a number line is lesser than 35 .
30 is left of 35 so, 35 > 30 .

Question 4.
___ < 37
Answer:

Explanation :
The numbers to the left of 37 on a number line are lesser than 37.
31 is left of 37 .
so, 31 < 37 .

Question 5.
___ < 40
Answer:

Explanation :
The numbers to the left of 40 on a number line are lesser than 40 .
38 is left of 40 .
so, 38 < 40 .

Question 6.
50 > __
Answer:

Explanation :
Any number to the left of 50 on a number line is lesser than 40 .
40 is left of 50 so, 40 < 50 .

Independent Practice
Write the number or symbol > or < to make each correct. Draw a number line to help if needed.

Question 7.
___ < 26
Answer:
22 < 26 .

Explanation :
Any number to the left of 26 on a number line is lesser than 26 .
22 is left of 26 so, 22 < 26 .

Question 8.
75 > __
Answer:
75 > 70 .
Explanation :
Any number to the left of 75 on a number line is lesser than 75 .
70 is left of 75 so, 75 > 70 .

Question 9.
33 > ___
Answer:
33 > 30
Explanation :
Any number to the left of 33 on a number line is lesser than 33 .
30 is left of 33 so, 33 > 30 .

Question 10.
___ < 95
Answer:
80 < 95
Explanation :
Any number to the Left of 95 on a number line is lesser than 95 .
80 is left of 95 so, 80 < 95 .

Question 11.
__ > 50
Answer:
52 > 50
Explanation :
Any number to the Right of 50 on a number line is Greater than 50 .
52 is Right of 50 so, 52 > 50 .

Question 12.
90 < ___
Answer:
90 < 100
Explanation :
Any number to the Right of 90 on a number line is Greater than 90 .
100 is Right of 90 so, 90 < 100 .

Question 13.
39 48
Answer:
39 < 48
39 is less than 48
Explanation :
Check the numbers.
Compare the tens First .
in 39 we have 3 tens
in 48 we have 4 tens.
48 have more tens than 39
so, 39 is lesser than 48 .

Question 14.
47 35
Answer:
47 > 35 .
Explanation :
Check the numbers.
Compare the tens First .
in 47 we have 4 tens
in 35 we have 3 tens.
47 have more tens than 35
so, 47 is greater than 35 .

Question 15.
29 72
Answer:
29 < 72 .
Explanation :
Check the numbers.
Compare the tens First .
in 29 we have 2 tens
in 72 we have 7 tens.
72 have more tens than 29
so, 29 is lesser than 72 .

Higher Order Thinking Write numbers to make each correct. Place the numbers on the number lines.

Question 16.

Answer:

Explanation :
Numbers to the left of 70 are lesser than numbers .
Number to the Right of 70 are greater numbers .

Question 17.

Answer:

Explanation :
Numbers to the left of 64 are lesser than numbers .
Number to the Right of 64 are greater numbers .

Problem Solving

Solve each problem below. Solving Model You can use a number line to help you.

Question 18.
3 friends wrote a number on paper. Paul wrote a number that is greater than Nicole’s number and less than Tina’s number. Nicole’s number is 42. Tina’s number is 44.
What is Paul’s number? __
Answer:
Tina’s Number = 44
Nicole’s Number = 42 .
Paul’s Number = number that is greater than Nicole’s number and less than Tina’s number = 42 < 43 < 44.
Therefore, Paul’s Number = 43 .

Question 19.
enVision® STEM Jay covers some windows with cardboard to block the sunlight from shining through. The number of windows he covers is less than 28 and more than 26. How many windows does Jay cover?
___ windows
Answer:
Number of Windows Covered = Less than 28 and more than 26. = 28 > 27 > 26 .
Therefore, Number of Windows Covered = 27 Windows .

Question 20.
Higher Order Thinking How can you find a number that is greater than 90? Explain.

Answer:

Numbers greater than 90 are on the Right side of the number line of number 90 .
90 < 91< 92< 93< 94 < 95 < 96  are numbers greater than 90 .

Question 21.
Assessment Practice The number on Taylor’s mailbox is less than (<) 70. Which numbers could be on Taylor’s mailbox? Choose two.

60
69
70
71
Answer :
The number on Taylor’s mailbox is less than (<) 70 are 60 and 69 .

Lesson 9.6 Make Sense and Persevere

I am thinking of a secret number. The number is greater than 20 and less than 30. The number is inside a shape with 4 sides. What is the secret number ? What strategy did you use to find it?

The secret number is ____.
Answer :
The secret number is 27 .
Explanation :
The numbers which are greater than 20 and less than 30 as per above figure .
22 , 25 , and 27 .
22 is written in a Triangle with three sides.
25 is written in a circle with no sides.
27 is written in a Rhombus with 4 sides .
in 4 sides we have 27.
so, the secret number = 27 .

Thinking Habits
What am I asked to find? What is a good plan for solving this problem?

Visual Learning Bridge

Convince Me!
How does making a list help you make sense of a problem?
Answer :
Making a list will help you understand the problem clearly with step by step and helps to know the answer clearly without any confusions .

Guided Practice
Use the numbers above to solve each riddle. Write the secret number. Explain your work.

Question 1.
I am a green number. I am greater than 45 and less than 60. Which number am I?
57
Answer :
Green Numbers : 22, 45 and 57 .
Number greater than 45 and less than 60 is 57.
I am number 57 .

Question 2.
I am a blue number. You say my name when you count by 10s. Which number am I?
___
Answer:
Blue Number  :  50, 24, 41.
Count by tens means it is 10 multiple .
so, the number is 50 .

Independent Practice

Make sense of each riddle to find the secret number. Show and explain your work.

Question 3.
The number of pages in my book is less than 96 and greater than 90.
Who could I be?
I have 3 letters in my name. Who am I?
___ ___
Answer:
Jay
Explanation :
Books with pages less than 96 and greater than 90 are
Carla – 92 pages
Jay – 95 pages
I have 3 letters in my name. that is Jay .

Question 4.
The number of pages in my book is greater than 92.
Who could I be?
__ ___ ___
I have the greatest number of pages. Who am I?
___
Answer:
my book is greater than 92.
Carla – 92 pages
Molly – 95 pages
Lisa – 96 pages 
Peg – 98 Pages .
Greatest number of pages  – peg have 98 that is greatest number of pages .

Question 5.

The number of pages in my book is less than 65.
Who could I be?
__ __ ___
I have 10 more than 54 pages. Who am I?
___
Answer:
The number of pages in my book is less than 65 are :
Greg – 55 pages
Yao- 96 pages 
Katie – 98 Pages .
I could be – Greg – 55 pages .
I have 10 more than 54 pages = 54 + 10 = 64 pages – Katie .

Problem Solving

Performance Task

Missing Numbers Akayla has to find a secret number missing from the chart. She gets some clues to help her.

Akayla’s Clues:
– The secret number is greater than 75.
– The number does NOT have an 8 in the ones place.
What is the secret number?

Question 6.
Make Sense What is your plan for solving this problem? Explain.

Answer:
Greater than 75 .
Missing Numbers – 78, 83 and 88 .
which doesn’t have 8 in ones place = 83 as 78 and 88 have 8 in one’s place .
Therefore, The missing number is 83 .
Explanation :
Write the missing numbers for given Condition one by one and sort them .

Question 7.
Explain What is the secret number? How do you know your answer is correct?
Secret number: ___
Answer:
The Secret number is 83 .
As per the conditions given the secret number satisfices them .

Topic 9 Fluency Practice Activity

Find a Match

Find a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box next to the match. Find a match for every clue.

Clues
A 6+ 2
B 5 + 5
C 9 – 3
D 5 – 1
E 8 – 6
F 5 + 4
G 7 – 2
H 1 + 2

10 – 0
2 + 2
10 – 1
9 – 7
2 + 3
7 – 4
4 + 4
3 + 3
Answer :

Explanation :
A= 6+ 2= 4+4 =8
B= 5 + 5=10- 0 =10
C= 9 – 3= 3 +3 = 6
D=5 – 1=2 + 2 =4
E= 8 – 6=9 – 7 = 2
F =5 + 4=10 – 1= 9
G= 7 – 2=2 + 3 =5
H= 1 + 2=7 – 4 = 3

Topic 9 Vocabulary Review

Understand Vocabulary

Question 1.
Compare the numbers. Circle the number that is more.
26 29
Answer:

Explanation :
Check the numbers
Compare Ones when they have same Tens .
we have more ones in 29 than 26 .
So, 29 is more than 26 .

Question 2.
Compare the numbers. Circle the number that is less.
58 68
Answer:

Explanation :
Check the numbers
Compare Tens they have5 tens in 58 and 6 tens in 68 .
we have more tens in 68 than 58 .
So, 68 is more than 58 .

Question 3.
Choose a term from the Word List. Fill in the blank to make it true.

Answer:

Use Vocabulary in Writing

Question 4.
Write a problem using the terms from the Word List. Use place-value blocks to help solve your problem.

Answer:

Topic 9 Reteaching

Set A

You can use blocks to show 1 more, 1 less, 10 more, and 10 less than a number.

Use blocks. Write the numbers to complete each sentence.

Question 1.

1 more than 87 is ___
1 less than 87 is ___
10 more than 87 is ___
10 less than 87 is ___
Answer:

1 more than 87 is 88
1 less than 87 is 86
10 more than 87 is 97
10 less than 87 is 77

Set B

You can use a hundred chart to find the number that is I more than, I less than, 10 more than, and 10 less than.

Write the number that is I more, I less, 10 more, or 10 less. You can use a hundred chart to help you.

Question 2.
1 less than 37
___, 37
Answer :
1 less than 37 is 36 .
36, 37
Explanation :
10 more than 37 means the number below 37 as per hundred chart .

Question 3.
1 more than 37
37, ___
Answer:
1 more than 37 is 38
37, 38
Explanation :
1 more than 37 means the next number to its right as per hundred chart .

Question 4.
10 less than 55
__, 55
Answer:
10 less than 55 is 45 .
45, 55
Explanation :
10 less than 55 means the Number above 45 as per hundred chart .

Question 5.
10 more than 55
55, ___
Answer:
10 more than 55 is 65 .
55, 65 .
Explanation :
10 more than 55 means the number below 65 as per hundred chart .

Set C

You can compare numbers using >, <, or =
> means greater than. 33 is greater than 24.

< means less than. 24 is less than 33.

Answer:

Write greater than, less than, or equal to. Then write >, <, or =

Question 6.
46 is ____ 26.
46 26
Answer :
46 is greater than 26.
46 > 26
Explanation :
Check the numbers .
Compare the tens place vales first
we have more tens in 46 than 26 .
so, 46 > 26 .

Question 7.
25 is ___ 52.
24 33
Answer:
25 is less than  52.
24 < 33
Explanation :
check the numbers .
Compare the tens place vales first
we have more tens in 33 than 24 .
so, 24 < 33 .

Set D

Thinking Habits
Make Sense and Persevere

What am I asked to find?
What is a good plan for solving this problem?
How can I check that my solution makes sense?

Look at the numbers below. Find the secret number.

Question 8.
I am a number greater than 65. What numbers could I be? ___
Answer:
Numbers below 65 are 42, 7, 13, 63 and 50 .
Therefore numbers could be 42, 7, 13, 63 and 50 .

Question 9.
I am 10 less than 83. What number am I? __
Answer:
10 less than 83 = 83 – 10 = 73 .
i am 73 .

Topic 9 Assessment Practice

Question 1.
Trina’s house number is 54. Frank’s house number is greater than Trina’s house number. Which is Frank’s house number? How do you know?
A. 52; because 52 > 50
B. 53; because 53 < 54
C. 54; because 54 > 50
D. 55; because 55 > 54

Answer:

D. 55; because 55 > 54
Numbers Right of 54 of a number line are the greater numbers .
Explanation :
House Number of Trina’s = 54 .
House Number of Frank’s = greater than 54 that means more than 54
As per options Only Option D is having house number as 55 which is greater than 54 .

Question 2.
Choose two ways to compare the place-value blocks. Explain.

82 < 87; 82 has fewer ones than 87.
87 = 82; 87 and 82 have the same number of tens.
87 < 82; 82 has more ones than 87.
87 > 82; 87 has more ones than 82.
82 > 87; 82 has more ones than 87.
Answer:

Question 3.
Find 10 more than 37 without having to count. Explain how you know.
A. 36; 36 has one fewer one than 37.
B. 47; 47 has one more ten than 37.
C. 38; 38 has one more one than 37.
D. 27; 27 has one fewer ten than 37.
Answer:
Option B. 47; 47 has one more ten than 37.
Explanation :
10 more than 37 means add 1 to the tens place of value 37 that gives 10 more than 37 = 47 .

Question 4.
Use the clues to find the secret number from the choices on the right.

I am less than 48. What numbers could I be? ___
I have a 0 in the ones place. What number am I? __
Answer:
I am less than 48 means 42 , 37 and 40 .
I have a 0 in the ones place is 40 as 42 and 37 have 2 and 7 in ones place .
The Number is 40 .

Question 5.
Write the number to complete the part of the hundred chart. Explain how you know.

Answer:

Explanation :
1 more than 43 means the next number to its right as per hundred chart .
10 more than 43 means the number below 43 as per hundred chart .
1 less than 43 means before number to its left as per hundred chart .
10 less than 43 means the Number above 43 as per hundred chart .

Question 6.
What number is 10 more than 74?
What number is 10 less than 74?
10 more than 74 is ___
10 less than 74 is ___
Answer:
10 more than 74 is 84
10 less than 74 is 64
Explanation :
10 more than 74 means add 1tens to the tens place of value of 74 that gives 84 .
10 less than 74 means subtract 1 tens from the tens place value of 74 that gives 64 .

Question 7.
Look at the place-value blocks. Write the numbers to make the sentences true. Explain how you know which number is greater.

___ is greater than ___.
___ is less than ___.
Answer:

27 is greater than 22 .
22 is less than 27 .
Explanation :
Check the numbers 27 and 22.
Compare the ones value if both have same tens .
27 have more ones than 22 .
so, 27 is greater than 22
22 is less than 27 .

Topic 9 Performance Task

Mailbox Mysteries
Meg sees these mailboxes in her neighborhood. Each mailbox has a different number.

Question 1.
Write the mailbox number for each clue. You can use the hundred chart to help you.

1 more than 59 __
1 less than 26 ___
10 more than 7 ___
10 less than 83 ___
Answer:
1 more than 59 is 60
1 less than 26 is 25
10 more than 7 is 17
10 less than 83 is 73

Question 2.
Use these clues to figure out each student’s mailbox number.
Show your work on the hundred chart.

Answer :
Bill’s Number = 34
Sue’s Number = 1 more than Bill’s Number = 34 + 1 = 35
Larry’s Number = 10 less than Sue’s Number = 35 – 10 = 25 .

Question 3.
Fill in the missing numbers. You can use the number lines to help you.
Write a mailbox number that is greater than 50.

Write a mailbox number that is less than 30.

Answer:

Question 4.
Meg describes her mailbox number.
She uses these clues.
What is her mailbox number? ___
Explain how you know.

Clues

• The number is greater than 40.
• The number is NOT on a red mailbox.
• The number has more ones than tens.

Answer:

• The numbers greater than 40 are :
  60 – Green Mail box
  58 – Red Mail Box .
  89 – Blue Mail Box .
  73 – Red Mail Box  .
• The number is NOT on a red mailbox :
  60 – Green Mail box
  89 – Blue Mail Box .
• The number has more ones than tens.
  89 – Blue Mail Box .
  ones are 9
  Tens are 8
  ones are more than tens .
  Therefore, The Mail Box number is 89/

Go through the enVision Math Common Core Grade 5 Answer Key Topic 13 Write and Interpret Numerical Expressions regularly and improve your accuracy in solving questions.

enVision Math Common Core 5th Grade Answers Key Topic 13 Write and Interpret Numerical Expressions

enVision STEM Project: Food Chains and Food Webs
Do Research Use the Internet or other sources to find out more about food chains and food webs. Investigate the roles of producers, consumers, and decomposers. Explain how energy from sunlight is transferred to consumers.

Journal: Write a Report Include what you found. Also in your report:
• Draw a food web from an ecosystem near your home.
• Draw arrows on your food web to show how energy moves. Explain why the order is important.
• On one food chain of your food web, label each organism as a producer, consumer, or decomposer.

Review What You Know

Vocabulary

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

• difference
• equation
• product
• sum
• quotient

Question 1.
The answer to a division problem is the ____.
Answer:

The answer to a division problem is the  Quotient

Question 2.
The ____ of 5 and 7 is 12.
Answer:

The sum of 5 and 7 is 12

Question 3.
To find the ___ between 16 and 4, you subtract.
Answer:

To find the difference between 16 and 4, you subtract

Question 4.
A number sentence that shows two equivalent values is a(n) ____.
Answer:

A number sentence that shows two equivalent values is an Equation

Mixed Review
Find each answer.

Question 5.
648 ÷ 18
Answer:

Question 6.
35 × 100
Answer:

3500

Question 7.
47.15 + 92.9
Answer:

140.05

Question 8.
\(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)
Answer:

1/4 + 1/4 + 1/4

1/2 + 1/4

3/4

Question 9.
3.4 – 2.7
Answer:

0.7

Question 10.
1.9 + 7
Answer:

8.9

Question 11.
3\(\frac{2}{5}\) + \(\frac{1}{2}\)
Answer:

3 2/5 + 1/2

17/5 + 1/2

39/10

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

75 ÷ 1/5

75 / 1/5

75 x 5

= 375

Question 13.
$3.75 + $2.49
Answer:

$6.24

Question 14.
8\(\frac{5}{8}\) – 1\(\frac{2}{8}\)
Answer:

8 5/8 – 1 2/8

69/8 – 10/8

59/8

Question 15.
31.8 × 2.3
Answer:

73.14

Question 16.
9 – 4.6
Answer:

4.4

Question 17.
Jackson bought 2 tickets to the state fair. Each ticket cost $12. He spent $15 on rides and $8.50 on food. How much did Jackson spend in all?
Answer:

Total cost of tickets = $12 x 2 = $24

Total money after spending $15 on rides = $24 + $15 =$39

Total money after spending $8.50 on food = $39 + $8.50 = $47.50

Total money spent =  $47.50

Question 18.
A baker has 3 pounds of dried fruit. Each batch of a recipe she is making uses \(\frac{1}{2}\) pound of the fruit. How many batches can she make?
A. 9 batches
B. 6 batches
C. 2 batches
D. 1\(\frac{1}{2}\) batches
Answer:

B. 6 batches

Multiplication

Question 19.
What equation comes next in the pattern below? Explain.
7 × 10 = 70
7 × 100 = 700
7 × 1,000 = 7,000
Answer:

7 × 10,000 = 70,000

pick a Project

PROJECT 13A
What’s been recovered from the wreck of the Atocha?
Project: Write a Treasure Adventure Mystery Story

PROJECT 13B
Do you like to play games?
Project: Design a Game Using Dominos

PROJECT 13C
What happens when a calculation is incorrect?
Project: Program a Robot

3-ACT MATH PREVIEW

Math Modeling

Video

Before watching the video, think:
A conjecture is a statement someone believes is true based on observations. You can usually either prove or disprove a conjecture. Keep an eye out for the conjecture in this video.

Lesson 13.1 Evaluate Expressions

Activity

Solve&Share

Jordan and Annika are working on 15 + 12 ÷ 3 + 5. Jordan says the answer is 14 and Annika says the answer is 24. Who is right?

Solve this problem any way you choose.

Look Back! Construct Arguments Do you think two students, who made no computation errors, would get different values for this numerical expression? Explain.
(4 × 35) + (36 × 8)

Visual Learning Bridge

Essential Question What Order Should You Use When You Evaluate an Expression?

A.
Jack evaluated [(7 × 2) – 3] ÷ 8 = 2 × 3.
To avoid getting more than one answer, he used the order of operations given at the right.

Parentheses, brackets, and braces are all used to group numbers in numerical expressions.

Order of Operations
1. Evaluate inside parentheses (), brackets [ ], and braces {}.
2. Multiply and divide from left to right.
3. Add and subtract from left to right,

B.
Step 1
First, do the operations inside the parentheses.

Then, evaluate the terms inside the brackets.

C.
Step 2
Next, multiply and divide in order from left to right.

D.
Step 3
Finally, add and subtract in order from left to right.
11 + 12 = 23
So, the value of the expression is 23.

Convince Me! Construct Arguments Would the value of {2+[(15 – 3) – 6]} ÷ 2 change if the braces were removed? Explain.

Guided Practice

Do You Understand?

Question 1.
Explain the steps involved in evaluating the expression [(4 + 2) – 1] × 3.
Answer:

[(4 + 2) – 1] × 3

[(6) – 1] × 3

[5] × 3

15.

Question 2.
Would the value of (12 – 4) ÷ 4 + 1 change if the parentheses were removed? Explain.
Answer:

(12 – 4) ÷ 4 + 1

(8) ÷ 4 + 1

2 + 1

3.

Do You Know How?

In 3-6, use the order of operations to evaluate the expression.

Question 3.
[7 × (6 – 1)] + 100
Answer:

[7 × (6 – 1)] + 100

[7 × (5)] + 100

[35] + 100

135

Question 4.
17 + 4 × 3
Answer:

17 + 4 × 3

17 + 12

29

Question 5.
(8 + 1) + 9 × 7
Answer:

(8 + 1) + 9 × 7

(9) + 9 × 7

(9) + 63

72

Question 6.
{[(4 × 3) ÷ 2] + 3} × 6
Answer:

{[(4 × 3) ÷ 2] + 3} × 6

{[(12) ÷ 2] + 3} × 6

{6 + 3} × 6

{9} × 6

54.

Independent Practice

Remember to evaluate inside parentheses, brackets, and braces first.

Leveled Practice In 7-21, use the order of operations to evaluate the expression.

Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

Question 10.
5 ÷ 5 + 4 × 12
Answer:

5 ÷ 5 + 4 × 12

1 + 4 × 12

1 + 48

49

Question 11.
[6 – (3 × 2)] + 4
Answer:

[6 – (3 × 2)] + 4

[6 – (6)] + 4

[0] + 4

4

Question 12.
(4 × 8) ÷ 2 + 8
Answer:

(4 × 8) ÷ 2 + 8

(32) ÷ 2 + 8

16 + 8

24

Question 13.
(18 + 7) × (11 – 7)
Answer:

(18 + 7) × (11 – 7)

(25) × (4)

100

Question 14.
2 + [4 + (5 × 6)]
Answer:

2 + [4 + (5 × 6)]

2 + [4 + (30)]

2 + [34]

36

Question 15.
(9 + 11) ÷ (5 + 4 + 1)
Answer:

(9 + 11) ÷ (5 + 4 + 1)

(20) ÷ (10)

2

Question 16.
90 – 5 × 5 × 2
Answer:

90 – 5 × 5 × 2

90 – 50

40

Question 17.
120 – 40 ÷ 4 × 6
Answer:

120 – 40 ÷ 4 × 6

120 – 10 × 6

120 – 60

60

Question 18.
22 + (96 – 40) ÷ 8
Answer:

22 + (96 – 40) ÷ 8

22 + (56) ÷ 8

22 + 7

29

Question 19.
(7.7 + 0.3) ÷ 0.1 × 4
Answer:

(7.7 + 0.3) ÷ 0.1 × 4

(8) ÷ 0.1 × 4

80 x 4

320

Question 20.
32 ÷ (12 – 4) + 7
Answer:

32 ÷ (12 – 4) + 7

32 ÷ (8) + 7

4 + 7

11

Question 21.
{8 × [1 + (20 – 6)} ÷ \(\frac{1}{2}\)
Answer:

{8 × [1 + (20 – 6)} ÷ \(\frac{1}{2}\)

{8 × [1 + (20 – 6)} ÷ 1/2

{8 × [1 + (14)} ÷ 1/2

{8 × 15} ÷ 1/2

{120} ÷ 1/2

240.

Problem Solving

Question 22.
Dan and his 4 friends want to share the cost of a meal equally. They order 2 large pizzas and 5 small drinks. If they leave a tip of $6.30, how much does each person pay?

Answer:

Given,

They order 2 large pizzas and 5 small drinks.

They leave a tip of $6.30

So,

(2 x 12) + (5 x 1.50) + 6.30

(24) + (7.50) + 6.30

$37.8

Total Number of friends = 5

Each person have to pay = 37.8 ÷ 5

= $7.56

Question 23.
Higher Order Thinking Use the operation signs +, -, ×, and ÷ once each in the expression below to make the number sentence true.

Answer:

Question 24.
Be Precise Carlotta needs 12\(\frac{1}{2}\) yards of ribbon for a project. She has 5\(\frac{1}{4}\) yards of ribbon on one spool and 2\(\frac{1}{2}\) yards on another spool. How much more ribbon does she need?
Answer:

Question 25.
Theresa bought three containers of tennis balls at $2.98 each. She had a coupon for $1 off. Her mom paid for half of the remaining cost. How much did Theresa pay? Evaluate the expression [(3 × 2.98) – 1] ÷ 2.
Answer:

[(3 × 2.98) – 1] ÷ 2

[8.94 – 1] ÷ 2

[7.94] ÷ 2

3.97

Question 26.
enVision®STEM Giraffes are herbivores, or plant eaters. A giraffe can eat up to 75 pounds of leaves each day. Write and evaluate an expression to find how many pounds of leaves 5 giraffes can eat in a week.

Evaluate the expression in the parentheses first. Then subtract inside the brackets.

Assessment Practice

Question 27.
Which expression has a value of 8?
A. 11 – 6 – 3
B. 4 + 30 ÷ 6
C. (9 + 7) ÷ 2
D. 1 + 1 × (2 + 2)
Answer:

C. (9 + 7) ÷ 2
D. 1 + 1 × (2 + 2)

Question 28.
Using the order of operations, which operation should you perform last to evaluate this expression?
(1 × 2.5) + (52 ÷ 13) +(6.7 – 5) – (98 + 8)
A. Addition
B. Subtraction
C. Multiplication
D. Division
Answer:

B. Subtraction

Lesson 13.2 Write Numerical Expressions

Activity

Solve & Share
A baker packages 12 cupcakes to a box. Sean orders 5 boxes for his sister’s graduation party and 3.5 boxes for the Variety Show party. Write an expression that shows the calculations you could use to find the number of cupcakes Sean orders.

Model with Math
You can write a numerical expression to model this situation.

Look Back! Write a different expression to model Sean’s order. Evaluate both expressions to check that they are equivalent. How many cupcakes does Sean order?

Visual Learning Bridge

Essential Question How Can You Write a Numerical Expression to Record Calculations?

A.
The school auditorium has 546 seats on the main floor and 102 in the balcony. Every seat is filled for all of the Variety Show performances. Write an expression that shows the calculations you could use to determine how many tickets were sold.

B.
Think about how you would calculate the total number of tickets.
Add 546 + 102 to find the total number of seats.
Then multiply by the number of performances, 4.
So, you need to write a numerical expression that represents:
“Find 4 times the sum of 546 and 102.”

C.
Use numbers and symbols to write the numerical expression.
The sum of 546 and 102: 546 + 102
4 times the sum: 4 × (546 + 102)

Remember, parentheses show which calculation to do first.

The expression 4 × (546 + 102) shows the calculations for the number of tickets sold.

Convince Me! Reasoning Two students wrote different expressions to find the total number of tickets sold. Is their work correct? Explain.

Guided Practice

Do You Understand?

Question 1.
Why do some numerical expressions contain parentheses?
Answer:

Parentheses are symbols that group things together. This becomes very important in numerical expressions because operations inside parentheses are always completed first when evaluating the expression.

Question 2.
Show how to use a property to write an equivalent expression for 9 × (7 + 44). Can you use a different property to write another equivalent expression? Explain.
Answer:

Do You Know How?

In 3-6, write a numerical expression for each calculation.

Question 3.
Add 8 and 7, and then multiply by 2.
Answer:

(8 + 7) x 2

Question 4.
Find triple the difference between 44.75 and 22.8.
Answer:

3 x (44.75 – 22.8)

Question 5.
Multiply 4 times \(\frac{7}{8}\) and then add 12.
Answer:

(4 x 7/8) + 12

Question 6.
Add 49 to the quotient of 125 and 5.
Answer:

49 + (125 ÷ 5)

Independent Practice

In 7-11, write a numerical expression for each calculation.

Question 7.
Add 91, 129, and 16, and then divide by 44.
Answer:

(91 + 129 + 16) ÷ 44

Question 8.
Find 8.5 times the difference between 77 and 13.
Answer:

8.5 x (77 – 13)

Question 9.
Subtract 55 from the sum of 234 and 8.
Answer:

(234 + 8) – 55

Question 10.
Multiply \(\frac{2}{3}\) by 42, and then multiply that product by 10.
Answer:

( 2/3 x 42 ) x 10

Question 11.
Write an expression to show the calculations you could use to determine the total area of the rectangles at the right.

Answer:

3 x ( 18 x 22 )

Problem Solving

Question 12.
Model with Math Ronnie’s Rentals charges $25 plus $15 per hour to rent a chain saw. David rented a chain saw for 5 hours. Write an expression to show how you could calculate the total amount David paid.
Answer:

5 x (25 + 15)

Question 13.
Fourteen students bought their art teacher a new easel for $129 and a set of blank canvases for $46. Sales tax was $10.50. They shared the cost equally. Write an expression to show how you could calculate the amount each student paid.
Answer:

[(129 + 46) + 10.50] ÷ 14

Question 14.
A-Z Vocabulary When evaluating an expression, why is it important to use the order of operations?
Answer:

When evaluating an expression, it is important to use the order of operations. The order of operations is a set of rules for how to evaluate expressions. They make sure everyone gets the same answer.

Question 15.
A storage shed is shaped like a rectangular prism. The width is 8 yards, the height is 4 yards, and the volume is 288 cubic yards. Explain how to find the length of the storage shed.
Answer:

Volume = Length x Breadth x Height

Length = Volume ÷ (Breadth x Height)

Length = 288 ÷ (8 x 4)

Length = 288 ÷ 32

Length = 9 yards

Question 16.
Higher Order Thinking Danielle has a third of the amount needed to pay for her choir trip expenses. Does the expression (77 + 106 +34) ÷ 3 show how you could calculate the amount of money Danielle has? Explain.

Answer:

Yes.

The expression (77 + 106 +34) ÷ 3 show how I could calculate the amount of money Danielle has

(77 + 106 +34) ÷ 3

(217) ÷ 3

$72.3

Assessment Practice

Question 17.
Which expression represents the following phrase?
Subtract 214 from 721 and then divide by 5.
A. (721 ÷ 214) – 5
B. 721 – 214 ÷ 5
C. (721 ÷ 5) – 214
D. (721 – 214) ÷ 5
Answer:

D. (721 – 214) ÷ 5

Question 18.
What is the first step in evaluating this expression?
2 × (47 + 122) – 16
A. Multiply 2 and 47
B. Multiply 2 and 16
C. Add 47 and 122
D. Add 2 and 47
Answer:

C. Add 47 and 122

Lesson 13.3 Interpret Numerical Expressions

Solve & Share
Mrs. Katz is planning her family’s trip to the museum. She made a list of the expenses. Then she wrote the following expression to show how she can calculate the total cost.
6 × (4.20 + 8 + 12 + 3.50)
How many people do you think are in the family? How can you tell?

Use Structure You can interpret the relationships in numerical expressions without doing any calculations.

Look Back! While they are at the museum, the family decides to watch a movie about earthquakes for $2.75 per person. Jana and Kay disagree as to how they should adjust Mrs. Katz’s expression to find the total expenses for the trip. Jana says the expression should be 6 × (4.20 + 8 + 12 + 3.50) + 2.75. Kay says the expression should be 6 × (4.20 + 8 + 12 + 3.50 + 2.75). Who is correct? Explain.

Visual Learning Bridge

Essential Question
How Can You Interpret Numerical Expressions Without Evaluating Them?

A.
Jimmy’s clown costume requires \(\frac{7}{8}\) + \(\frac{1}{2}\) + 1\(\frac{3}{4}\) yards of fabric.
His dad’s matching clown costume requires 3 × (\(\frac{7}{8}\) + \(\frac{1}{2}\) + 1\(\frac{3}{4}\))) yards. How does the amount of fabric needed for the dad’s costume compare to the amount needed for Jimmy’s costume?

You can compare the expressions and solve the problem without doing any calculations.

B.
Interpret the part of each expression that is the same.
\(\frac{7}{8}\) + \(\frac{1}{2}\) + 1\(\frac{3}{4}\)

Both expressions contain the sum \(\frac{7}{8}\) + \(\frac{1}{2}\) + 1\(\frac{3}{4}\). This is the amount of fabric needed for Jimmy’s costume.

C.
Interpret the part of each expression that is different.

Remember, multiplying by 3 means “3 times as much.”

The second expression shows that the sum is multiplied by 3. So, the dad’s costume requires 3 times as much fabric as Jimmy’s costume.

Convince Me! Reasoning The 7 students in a sewing class equally share the cost of fabric and other supplies. Last month, each student paid ($167.94 + $21.41) ÷ 7. This month, each student paid ($77.23 + $6.49) ÷ 7. Without doing any calculations, in which month did each student pay more? Explain.

Answer:

In the last month each student paid more. Because the value is more compared to this month.

Guided Practice

Do You Understand?

Question 1.
The number of yards of fabric needed for Rob’s costume is . How does the amount of fabric needed for Rob’s costume compare to the amount needed for Jimmy’s costume? Explain.
Answer:

Question 2.
Without doing any calculations, explain why the following number sentence is true.
14 + (413 × 7) > 6+ (413 × 7)
Answer:

Do You Know How?

Without doing any calculations, describe how Expression A compares to Expression B.

Question 3.
A 8 × (41,516 – 987)
B 41,516 – 987
Answer:

In 4 and 5, without doing any calculations, write >, <, or =.

Question 4.

Answer:

Question 5.

Answer:

Independent Practice

In 6 and 7, without doing any calculations, describe how Expression A compares to Expression B.

Question 6.
A (613 + 15,090) ÷ 4
B 613 + 15,090
Answer:

Question 7.
A (418 × \(\frac{1}{4}\)1) + (418 × \(\frac{1}{2}\))
B 418 × \(\frac{3}{4}\)
Answer:

In 8-11, without doing any calculations, write >, <, or =.

Question 8.
(284 + 910) ÷ 30 img 73 (284 + 7,816) ÷ 30
Answer:

(284 + 910) ÷ 30 < 73 (284 + 7,816) ÷ 30

Question 9.
\(\frac{1}{3}\) × (5,366 – 117) img 735,366 – 117
Answer:

\(\frac{1}{3}\) × (5,366 – 117) < 735,366 – 117

Question 10.
71 +(13,888 – 4,296) img 73 70 + (13,888 – 4,296)
Answer:

71 +(13,888 – 4,296) < 73 70 + (13,888 – 4,296)

Question 11.
15 × (3.6 + 9.44) img 73 (15 × 3.6) + (15 × 9.44)
Answer:

15 × (3.6 + 9.44) < 73 (15 × 3.6) + (15 × 9.44)

Problem Solving

Question 12.
A four-story parking garage has spaces for 240 + 285 + 250 + 267 cars. While one floor is closed for repairs, the garage has spaces for 240 +250 + 267 cars. How many spaces are there on the floor that is closed? Explain.
Answer:

240 + 285 + 250 + 267 > 240 +250 + 267

By comparing,

285 spaces are there on the floor that is closed

Question 13.
Use Structure Peter bought yards of ribbon. Marilyn bought yards of ribbon. Without doing any calculations, determine who bought more ribbon. Explain.
Answer:

Marilyn bought more ribbon.

Question 14.
Brook’s score in a card game is 713 + 102 + 516. On her next turn, she draws one of the cards shown. Now her score is (713 + 102 + 516) ÷ 2. Which card did Brook draw? Explain.

Answer:

Question 15.
Marta bought a 0.25-kilogram box of fish food. She uses 80 grams a week. Is one box of fish food enough for 4 weeks? Explain.
Answer:

No. For 4 weeks, she needs 4 x 80 = 320 grams

But, she bought only 250 grams.

Question 16.
Higher Order Thinking How can you tell that (496 + 77 + 189) × 10 is twice as large as (496 + 77 + 189) × 5 without doing complicated calculations?
Answer:

10 is twice 5. Hence, (496 + 77 + 189) × 10 is twice as large as (496 + 77 + 189) × 5

Assessment Practice

Question 17.
Which statement describes the expression (21 + 1.5) × 12 – 5?
A. The sum of 21 and 1.5 times the difference of 12 and 5
B. Five less than the sum of 21 and 1.5 multiplied by 12
C. Five less than the product of 12 and 1.5 added to 21
D. Subtract the product of 12 and 5 from the sum of 21. and 1.5
Answer:

A. The sum of 21 and 1.5 times the difference of 12 and 5

Lesson 13.4 Reasoning

Activity

Problem Solving

Solve & Share
The camp cook has 6 dozen eggs. He uses 18 eggs to bake some brownies. Then he uses twice as many eggs to make pancakes. How many eggs does the cook have left? Use reasoning to write and evaluate an expression that represents the problem.

Thinking Habits
Be a good thinker! These questions can help you.
• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Look Back! Reasoning Explain how the numbers, symbols, and operations in your expression represent this problem.

Visual Learning Bridge

Essential Question How Can You Use Reasoning to Solve Problems?

A.
Rose has 3 albums for her soccer cards. She gets 7 more cards for each of her albums for her birthday. How many cards does Rose have in all?

What do I need to do to solve the problem?
I need to find how many cards, including Rose’s new cards, will be in each album. Then I need to multiply to find the number of cards in 3 albums.

You can use tools or draw a diagram to help solve the problem.

B.
How can I use reasoning to solve this problem?
I can
• identify the quantities I know.
• use mathematical properties, symbols, and operations to show relationships.
• use diagrams to help.

Here’s my thinking…

C.
I need to find how many cards Rose has in all.
I can use a diagram to show how the quantities in the problem are related. Then I can write an expression.
There are 22 cards in each of her 3 albums. She gets 7 more cards for each of her 3 albums.

3 × (22 + 7) = 3 × 29
= 87
Rose has 87 cards.

Convince Me! Reasoning How can you use the Distributive Property to write an expression equivalent to the one given above? Use reasoning to explain how you know the expressions are equivalent.

Guided Practice

Reasoning Todd has 4 baseball card albums like the one pictured. He lets his best friend Franco choose 5 cards from each album. How many cards does Todd have now?

Question 1.
Write an expression to represent the total number of cards in Todd’s albums before he gives some cards to Franco. Explain how your expression represents the quantities and the relationship between the quantities.

Answer:

(4 x 42)

4 represents the number of card albums

42 represents the number of cards in each album

multiplication or ‘x’ gives the total number of cards in 4 albums.

Question 2.
Write an expression to represent the total number of cards in Todd’s albums after he gives some cards to Franco.
Answer:

(4 x 42) – (4 x 5)

Question 3.
How many cards does Todd have after he gives some cards to Franco? Explain how you solved the problem.
Answer:

(4 x 42) – (4 x 5)

168 – 20 = 148

Todd have 148 cards.

Independent Practice

Remember to think about the meaning of each number before solving the problem.

Reasoning
Brandon is filling a flower order for a banquet. He needs 3 large arrangements and 12 small arrangements. The large arrangements each contain 28 roses. The small arrangements each contain 16 roses. How many roses does Brandon need in all?

Question 4.
Write an expression to represent the total number of roses Brandon needs. You can use a diagram to help.
Answer:

(3 x 28) + (12 x 16)

Question 5.
Explain how the numbers, symbols, and operations in your expression represent the problem.
Answer: