Download Thank you for participating in Teach It First!

Thank you for participating
in Teach It First!
This Teach It First Kit contains a Crosswalk Plus student lesson and teacher answer
key. Also included is a teacher mini-lesson and worksheet. The mini-lesson was
designed as an introduction to each chapter. Use the student lesson as your
instructional tool or begin with the mini lesson if you feel your students need a
refresher on the topic—you decide!
Are you transitioning to the Common Core State Standards? If you are getting
ready for change, or have already begun your shift to the new standards,
Crosswalk Coach PLUS for the Common Core State Standards has you covered!
This series is newly revised and better than ever—it now includes:
•Two Common Core Practice Tests
•Lots of additional practice
•New item types that reflect the rigor of the new CCSS assessments
Each lesson targets a single skill, promoting achievement through instruction
and practice, and allowing you to assess mastery of discrete skills. You’ll get
maximum flexibility in addressing areas of need. Plus, Coached Examples
throughout strengthen comprehension. Everything you need to transition to the
new standards is right here!
We are happy to provide you this complimentary sample and would love to know
what you think. Once you have read through this lesson, do what you do best—
present it to your students. Then, don’t forget to complete a quick survey by
going to www.triumphlearning.com/teach-it-first. By doing so, you will be
entered into our quarterly raffle for one of five American Express $100 gift cards.
Regards,
Triumph Learning
Join the conversation about Common Core today by visiting commoncore.com, the place
where teachers, parents, and experts come together to share best practices and practical
information for successfully implementing Common Core standards in the classroom.
Learn it Today, Use it tomorrow.
136 Madison Avenue • New York, NY 10016 • p: 212.652.0215 • f : 212.857.8499 • www.triumphlearning.com
Cr
os
s
wa
l
kPl
us
,
Ma
t
h,
T
e
a
c
he
rE
di
t
i
on,
Gr
a
de8
Mini-Lessons
Fraction-Decimal-Percent Equivalences
Teach
Explain how fractions, decimals, and percents are
1 ​ of your spare
used at different times. You might say ​ __
4
time is spent doing homework, that our school has
1.2 times as many students as last year, or that 35%
of students take the bus.
Explain: Each fraction can be equivalent to a decimal
1 ​ 5 0.25 5 25%.
and percent. Example: ​ __
4
Model
Explain why the number 1.2 is equivalent
​1 ​​ and 120%. 1.2 can be written as 1.20,
to both 1​ __
5
which becomes 120% when multiplied by 100.
Remind students that to change a decimal to a
percent, multiply by 100.
Ask Students
Ask students to explain why 6% is the same as 0.06
6
and why 6% is not the same as ​ ___
   ​​. Explain that to
10
change a percent to a decimal, we divide by 100
(move decimal point 2 places to the left).
6
So, 6% 5 0.06. Show that ___
​ 10
  ​ 5 0.6 and is not equal
to 0.06 or 6%.
Practice/Apply
Distribute Reproducible R1. Ask students to do
exercise 1. Then go over this exercise to make
sure everyone understands it.
Answers to Reproducible (R1)
1. B. 0.8
2. No. To convert 67% to a decimal, divide 67 by
100. Move the decimal point in 67 two places to
the left. This gives 0.67. The decimal 6.7 is equal
to 670%.
3. 0.25; 25 4 100 5 0.25
4. 37%; 0.37 3 100 5 37
5. B. 4% 5 0.4
6. B. 0.9 5 90%
Mean
Teach
Practice/Apply
Another word for the mean is the average. Mean is
used to give us an idea of the overall picture for a set
of numbers. We use the mean for scores, grades,
and costs.
Distribute Reproducible R2. Ask students to do
exercise 1. Then go over this exercise to make
sure everyone understands it.
Model
1. B. 40
Answers to Reproducible (R2)
Suppose you wanted to find the mean of 2, 5, 10, and
11. Explain the method: add the numbers and divide
by 4 (the number of numbers). Sum 5 28, mean 5 7.
2. Multiply the mean by 7. Reason: The mean is
the sum divided by 7, so the sum is the mean
multiplied by 7.
Ask Students
3. B. 8
Ask students to find the mean of 100, 500, 200, 700,
and 1,000. Ask students to think of a situation in which
they might need to find the mean. Then ask them to
make up numbers for that situation and find the mean.
4. The sum of 100 numbers is 50(1,000) 1 50(500)
5 50,000 1 25,000 5 75,000.
The mean of 100 numbers is 75,000 4 100 5
750.
5. The sum of the ages is 30 1 33 1 36 1 39 1 42
1 45 1 48 1 51 1 54 5 378.
The mean age is 378 4 9 5 42.
13
T291NAG_Mth_G8_TG_PDF.indd 13
9/3/13 11:10 AM
Name:
Date:
Fraction-Decimal-Percent Equivalences
Every fraction can be written as both a decimal and a percent.
1. What is the decimal equivalent for __
​ 45 ​?
A. 4.5
B. 0.8
C. 0.45
2. Is 67% the same as the decimal 6.7? Explain.
3. Write 25% as a decimal.
4. Write 0.37 as a percent.
5. Which is not true?
A. 60% 5 0.6
B. 4% 5 0.4
C. 125% 5 1.25
6. Which is true?
9   ​5 9%
A.​ ___
B. 0.9 5 90%
C. 90% 5 0.09
© Triumph Learning, LLC
10
R1
T291NAG_Mth_G8_TG_PDF.indd 16
9/3/13 11:10 AM
Answer Keys (continued)
9. A.​a2​ ​; ​a6​ ​4 ​a4​ ​5 ​a6​ 2 4​5 ​a2​ ​
B. quotient of powers property
10. Fraction: ​7​23​, ​822
​ ​
Whole Number: ​1​3​, ​50​ ​, ​31​ ​
11.​54​ ​,​5​3​
12. A: False, B: True, C: True, D: False, E: True, F: False
13. A: 1, B: 16, C: 64, D: 8, E: 2
14. A: No, B: Yes, C: No, D: Yes, E: No, F: No
15. B, D
1   ​, 1,024
16.​ ___
625
Lesson 7
Coached Example
Since the exponent is positive, this is a number greater
than 1.
The exponent of the second factor is 7.
The exponent tells you to move the decimal point in 9.0
seven places to the right.
The number 9.0 3 1
​ 0​7​in standard form is 90,000,000.
About 90,000,000 passengers passed through the
Hartsfield-Jackson Atlanta International Airport in 2008.
Lesson Practice
Lesson 6
Coached Example
The area of the garden above is 121 square yards.
To find the length of one side, take the square root of
that area.
On the lines below, try squaring numbers until you find
one that results in 121.
Possible work:
​10​2​5 10 3 10 5 100 Too low
​11​2​5 11 3 11 5 121 ✓
The length of each side, s, of the garden is 11 yards.
Lesson Practice
1. B
2. B
3. B
4. D
5. C
6. A
7. C
8. C
9. A. (3.4 3 ​10​5​)(3.8 3 ​10​29​) 5 (3.4 3 3.8)(​10​5​3 ​10​29​)
B. 0.001292; Possible work:
3.4 3 3.8 5 12.92
​10​5​3 ​10​29​5 ​10​5 1 (29)​5 ​10​24​
1. B
12.92 3 ​10​24​
2. A
5 1.292 3 1​0​1​3 1​024
​ ​
3. B
5 1.292 3 (1​0​1 1 (24)​)
4. C
5 1.292 3 1
​ 0​23​5 0.001292
5. C
10. A: True, B: True, C: False, D: True
​ 0​26​, 8.6 3 ​10​3​
11. 3.5 3 1
6. D
7. A
8. D
9. A. 8 centimeters; Possible work:
​83​ ​5 8 3 8 3 8 5 64 3 8 5 512 ✓
3
____
So, ​√  512 ​ 5 8.
B. 64 square centimeters; Possible work: Each
edge is 8 centimeters. To find the area of one
face, square the length of one edge:
​82​ ​5 8 3 8 5 64 sq cm.
3
__
3
___
___
___
10.​√  7 ​,  ​√  55 ​,  ​√18 ​,  ​√95 ​ 
11. A: True, B: False, C: True, D: False
12. A: 12, B: 8, C: 19, D: 3
13. A: No, B: Yes, C: Yes, D: No
___ 3 ____ 3 ____
14. Less than 10: ​√50 ​ , ​√  400 ​ 
, ​√  900 ​ 
____   ____ 3 ______
Greater than 10: √
​ 200 ​ 
, ​√  144 ​ 
, ​√  1,200 ​ 
15. 21, 11
12. A: 4,500,000,000; B: 0.000045; C: 4,500;
D: 0.00045; E: 45,000
13. A: No, B: Yes, C: Yes, D: No
14. B
15. 170,000,000: (1.7 3 ​10​4​)(1.0 3 ​10​4​),
1.7 3 ​10​8​
0.000017: (1.7 3 ​10​22​)(1.0 3 ​10​23​),
1.7 3 ​10​25​
Lesson 8
Coached Example
The decimal point was moved 6 places to the right.
The original number is less than 1, so the exponent will
be negative.
0.000007 5 7 3 ​10​26​
Multiply to convert that number of square meters to
square millimeters: (7 3 ​10​26​)(1 3 ​10​6​)
25
T291NAG_Mth_G8_TG_PDF.indd 25
9/3/13 11:11 AM
Cr
os
s
wa
l
kPl
us
,
Ma
t
h,
S
t
ude
ntE
di
t
i
on,
Gr
a
de8
Domain 2 • Lesson 6
Common Core Standard:
Square Roots and Cube Roots
8.EE.2
Getting the Idea
Squaring a number means raising it to the power of 2. For example, ​72​ ​is equivalent to
7 3 7, or 49. So, we say that 49 is a perfect square.
The opposite, or inverse, of squaring a number is taking its square root. We use the radical
symbol (œw ) to represent square roots. To find the square root of a perfect square, think
about what number, when multiplied by itself, will result in that perfect square.
Example 1
Solve for y.
2
​y​ ​5 196
Strategy
Step 1
Determine what number, multiplied by itself, results in 196.
Take the square root of both sides of the equation.
The
opposite of squaring a number is taking its square root.
__
____
2
​ 196 ​ 
​√​y​  ​ ​5 √
____
y5√
​ 196 ​ 
Step 2
Try squaring numbers until you find one that results in 196.
2
1
​ 2​ ​5 12 3 12 5 144 Too low
2
​13​ ​5 13 3 13 5 169 Too low
2
​14​ ​5 14 3 14 5 196 ✓
Step 3
Solve for y.
____
Duplicating any part of this book is prohibited by law.
2
1
​ 4​ ​5 196, so ​√196 ​ 5 14.
____
y5√
​ 196 ​ 5 14
Solution
T291NA_Mth_G8_SE_PDF.indd 59
____
Since ​√196 ​ 5 14, y 5 14.
59
13/09/13 9:53 AM
Cubing a number means raising it to the power of 3. For example, 2
​ 3​ ​is equivalent
to 2 3 2 3 2, or 8. So, we say that 8 is a perfect cube.
The
___ opposite, or inverse, of cubing a number is taking its cube root. We use the symbol
​√   ​  to represent cube roots. To find the cube root of a perfect cube, think about what
number, when cubed, will result in that perfect cube.
3
Example 2
Solve for r.
3
r​ ​ ​ 5 125
Strategy
Step 1
Determine what number, when cubed, results in 125.
Take the cube root of both sides of the equation.
The
opposite of cubing a number is taking its cube root.
__
3
3
____
3
____
3
​√  ​r​  ​ ​5 ​√  125 ​ 
r 5 ​√  125 ​ 
Step 2
Try cubing numbers until you find one that gives a result of 125.
3
You already know that ​2​ ​5 8. Start with 3.
3
3
​ ​ ​5 3 3 3 3 3 5 27 Too low
3
​4​ ​5 4 3 4 3 4 5 64 Too low
3
​5​ ​5 5 3 5 3 5 5 125 ✓
Step 3
Solve for r.
3
____
3
5
​ ​ ​5 125, so ​√  125 ​ 5 5.
3
____
r 5 ​√  125 ​ 
r55
3
____
Since ​√  125 ​ 5 5, r 5 5.
The number under a radical sign is called the radicand. If you do not have a calculator
handy, you may need to estimate the value of a square root or a cube root.
To estimate a square root, find the two perfect squares between which the radicand lies.
Take the square root of each to find the range of your estimate.
To estimate a cube root, find the two perfect cubes between which the radicand lies.
Then take the cube root of each to find the range of your estimate.
Duplicating any part of this book is prohibited by law.
Solution
60 • Domain 2: Expressions and Equations
T291NA_Mth_G8_SE_PDF.indd 60
13/09/13 9:53 AM
Lesson 6: Square Roots and Cube Roots
Example 3
3
____
Between which two consecutive integers is ​√  500 ​?
 
Strategy
Step 1
Find the two perfect cubes between which 500 lies. Then take the cube
root of each to make your estimate.
Try cubing consecutive positive integers.
3
You know from Example 2 that ​5​ ​5 125. Start with 6.
3
6
​ ​ ​5 6 3 6 3 6 5 216
3
​7​ ​5 7 3 7 3 7 5 343
3
​8​ ​5 8 3 8 3 8 5 512
The radicand, 500, is between the perfect cubes 343 and 512.
Step 2
3
____
3
____
Estimate the value of ​√  500 ​. 
3
____
3
____
3
____
​√  343 ​ , ​√  500 ​ , ​√  512 ​ 
7 , ​√  500 ​ , 8
3
____
Solution​√  500 ​ has a value between 7 and 8.
Roots can help you solve measurement problems, such as problems involving the area
of a square or the volume of a cube.
Coached Example
The area of the square garden on the right is 121 square yards.
What is the length, s, of each side of the garden?
Garden
s
2
Duplicating any part of this book is prohibited by law.
The formula for finding the area, A, of a square is A 5 ​s​ ​, where s is
the length of a side.
s
The area of the garden above is _________ square yards.
To find the length of one side, take the _________ root of that area.
On the lines below, try squaring numbers until you find one that
results in _________. That is the value of s.
___________________________________________________________________________
___________________________________________________________________________
The length of each side, s, of the garden is _________ yards.
T291NA_Mth_G8_SE_PDF.indd 61
61
13/09/13 9:53 AM
Lesson Practice
Choose the correct answer.
____
1. What is the value of ​√100 ​? 
A. 4
B. 10
C. 25
D. 50
3
___
4. Between
which two consecutive integers
3 ___
is ​√  11 ​ ?
A.
B.
C.
D.
0 and 1
1 and 2
2 and 3
4 and 5
2. What is the value of ​√  27 ​ ?
A. 3
B. 5
C. 9
D. 13.5
3. Solve for y.
5. Solve for x.
x​ ​2​5 256
A.
B.
C.
D.
x56
x 5 15
x 5 16
x 5 128
3
​y​ ​5 216
y54
y56
y57
y 5 15
6. Between
which two consecutive integers
3 ____
?
is ​√  200 ​ 
A.
B.
C.
D.
66 and 67
20 and 21
6 and 7
5 and 6
Duplicating any part of this book is prohibited by law.
A.
B.
C.
D.
62 • Domain 2: Expressions and Equations
T291NA_Mth_G8_SE_PDF.indd 62
13/09/13 9:53 AM
Lesson 6: Square Roots and Cube Roots
7. Which statement below is true?
__
3
8. Which statement below is true?
__
__
3
__
A.​√4 ​ 5 ​√  4 ​ 
__
___
3
B.​√4 ​ 5 ​√  27 ​ 
___
___
3
C.​√16 ​ 5 ​√  27 ​ 
___
___
3
D.​√16 ​ 5 ​√  64 ​ 
A.​√1 ​ 5 ​√  1 ​ 
__
__
3
B.​√2 ​ 5 ​√  3 ​ 
__
__
3
C.​√4 ​ 5 ​√  9 ​ 
__
___
3
D.​√4 ​ 5 ​√  27 ​ 
9. The wooden block shown below is a cube. It has a volume of 512 cubic centimeters.
s
s
s
A. What is the length of one side, s? (Hint: the formula for the volume, V, of a cube
is V 5 ​s​3​.) Show your work.
B. Indira wants to paint the front face of the block. What is the area of one of the faces?
Show your work.
Duplicating any part of this book is prohibited by law.
T291NA_Mth_G8_SE_PDF.indd 63
63
13/09/13 9:53 AM
10. Use the expressions shown below to label the points on the number line.
3
55
0
3
7
95
2
18
4
6
8
10
11. Select True or False for each equation.
A.
B.
C.
D.
____
​ 121 ​ 5 11
√
3 ___
​√  81 ​ 5 27
___
____
3
​ 25 ​ 5 ​√  125 ​  
√
__
3
​√  9 ​ 5 3
○ True ○ False
○ True ○ False
○ True ○ False
○ True ○ False
A.
144
19
B.
3
512
12
C.
361
8
D.
3
3
27
13. Look at each square root or cube root. Is it equivalent to 4? Select Yes or No.
A.
B.
C.
D.
 
__
​√  8 ​ 
___
3
​√  64 ​ 
___
​ 16 ​ 
√
3 ___
​√  12 ​  
○ Yes ○ No
○ Yes ○ No
○ Yes ○ No
○ Yes ○ No
Duplicating any part of this book is prohibited by law.
12. Draw a line from each square root or cube root to its value.
64 • Domain 2: Expressions and Equations
T291NA_Mth_G8_SE_PDF.indd 64
13/09/13 9:53 AM
Lesson 6: Square Roots and Cube Roots
14. Determine whether each square root or cube root has a value greater than 10 or less than 10.
Write the root in the correct box.
50
3
200
400
3
1,200
144
3
900
Less than 10
Greater than 10
15. Circle the number that makes each equation true.
9
17
19
21
Duplicating any part of this book is prohibited by law.
23
T291NA_Mth_G8_SE_PDF.indd 65
____
 
5√
​ 441 ​ 11
12
3
_____
5 ​√  1,331 ​ 
13
65
13/09/13 9:53 AM