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Mississippi
Table
of Contents
Correlation Chart
Mississippi
Competencies,
Objectives,
and Depth of
Knowledge
Levels
Letter to the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Letter to the Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Mississippi Correlation Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 1
Number and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Lesson 1
Powers and Square Roots . . . . . . . . . . . . . . . .12
1d
(DOK 2)
Lesson 2
Scientific Notation . . . . . . . . . . . . . . . . . . . . . . .17
1e, 1f
(DOK 1)
Lesson 3
Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
1b
(DOK 2)
Lesson 4
Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . .28
1b
(DOK 2)
Lesson 5
Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . .33
1b
(DOK 2)
Lesson 6
Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
1b
(DOK 2)
Lesson 7
Relate Decimals, Fractions, and Percents . . . .46
1c, 1i
(DOK 1, 3)
Lesson 8
Rates and Proportions . . . . . . . . . . . . . . . . . . .52
1g, 4d
(DOK 1, 2)
Lesson 9
Applications of Percents . . . . . . . . . . . . . . . . . .57
1g
(DOK 1)
Lesson 10 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
1b, 1h
(DOK 2)
Lesson 11 Order of Operations . . . . . . . . . . . . . . . . . . . . .70
1a
(DOK 1)
Lesson 12 Number Properties . . . . . . . . . . . . . . . . . . . . . .80
2e
(DOK 1)
Lesson 13 Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
2a
(DOK 2)
Lesson 14 Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
2a, 2d, 2f (DOK 1, 2)
Lesson 15 Expressions, Equations, and Inequalities . . . . .95
2b, 2c
(DOK 1, 2)
Lesson 16 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106
3f
(DOK 2)
Lesson 17 Congruence and Similarity . . . . . . . . . . . . . . .111
3c
(DOK 2)
Lesson 18 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . .115
3c
(DOK 2)
Chapter 1 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . . 74
Chapter 2
Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Chapter 2 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . 100
Chapter 3
Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
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Mississippi MCT2 Coach, Gold Edition, Mathematics, Grade 7
Lesson 19 Translations, Reflections, and Rotations . . . . .120
3d
(DOK 2)
Lesson 20 Dilations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128
3d
(DOK 2)
Lesson 21 Pythagorean Theorem . . . . . . . . . . . . . . . . . . .133
3e
(DOK 2)
Lesson 22 Three-Dimensional Figures . . . . . . . . . . . . . . .137
3a, 3b
(DOK 1, 2)
Lesson 23 Units of Measure . . . . . . . . . . . . . . . . . . . . . . .148
4a
(DOK 2)
Lesson 24 Perimeter and Circumference . . . . . . . . . . . . .154
4b
(DOK 2)
Lesson 25 Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158
4b
(DOK 2)
Lesson 26 Surface Area and Volume . . . . . . . . . . . . . . . .164
4c
(DOK 3)
Lesson 27 Measures of Central Tendency . . . . . . . . . . . .176
5b
(DOK 2)
Lesson 28 Frequency Tables and Scatter Plots . . . . . . . .181
5c
(DOK 2)
Lesson 29 Box-and-Whisker Plots and Histograms . . . .186
5a, 5c
(DOK 2)
Lesson 30 Line Graphs and Circle Graphs . . . . . . . . . . . .191
5a, 5c
(DOK 2)
Lesson 31 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . .197
5d
(DOK 2)
Chapter 3 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . 142
Chapter 4
Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Chapter 4 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . 170
Chapter 5
Data Analysis and Probability . . . . . . . . . . . . . . . . . . . . . 175
Chapter 5 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . 203
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
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1
Powers and Square Roots
1d (DOK 2)
Getting the Idea
When you multiply a number by itself, the product is called the square of the number.
2
For example, the square of 3 is 9, because 3 3 9. It can also be written as 3 . The
3 is called the base, which is the factor being multiplied. The 2 is called the exponent,
2
which is the number of times you are multiplying the base. 3 can be referred to as three
squared or 3 to the 2nd power, where “2nd power” refers to the exponent 2.
The square of a whole number is called a perfect square. The perfect squares are
0, 1, 4, 9, 16, 25, and so on. Do you see the pattern? These numbers are simply
2
2
2
2
2
2
0 , 1 , 2 , 3 , 4 , 5 , and so on.
EXAMPLE 1
2
What is 15 ?
STRATEGY
Multiply the base by itself.
15 15 225
SOLUTION
15 225
2
EXAMPLE 2
What is 73?
STRATEGY
STEP 1
Show the complete multiplication and do the math.
Show the multiplication.
Use 7 as a factor 3 times.
73 7 7 7
STEP 2
Do the math.
7 7 7 49 7 343
SOLUTION
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3
7 343
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Lesson 1: Powers and Square Roots
What number would you have to square (multiply by itself) to get 9? Another way to ask this
question is: What is the__square root of 9? The answer is 3, because 3 3 9. The square
root of 9 is written as √ 9 . So, the square of 3 is 9 and the square root of 9 is 3. Because a
perfect square is the square of a whole number, the square root of a perfect square must be a
whole number.
EXAMPLE 3
___
What is √ 36 ?
STRATEGY
Which number, when squared, equals 36?
6 6 6 36
2
SOLUTION
___
√ 36 6
Sometimes, you need to estimate the square root of a number that is not a perfect square. To
do this, find the two consecutive whole numbers that the square root falls between.
EXAMPLE 4
____
Between which two whole numbers is √ 139 ?
STRATEGY
Use guess-and-test.
____
STEP 1
Compare √ 139 to the squares of 10 and 20.
10 10 100
20 20 400
____
Since 139 is between 100 and 400, √ 139 is between 10 and 20.
STEP 2
Find the squares of numbers between
____ 10 and 20 until you find the two
consecutive whole numbers that √ 139 falls between.
Since 139 is closer to 100 than 400, start with 11.
11 11 121
12 12 144
____
Since 139 is between 121 and 144, √ 139 is between 11 and 12.
SOLUTION
____
√ 139 lies between 11 and 12.
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Mississippi MCT2 Coach, Gold Edition, Mathematics, Grade 7
COACHED EXAMPLE
What is 24?
THINKING IT THROUGH
The base is __________ and the exponent is __________.
Use the number __________ as a factor __________ times.
24 __________ __________ __________ __________
Simplify.
24 __________
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Lesson 1: Powers and Square Roots
Lesson Practice
Choose the correct answer.
1.
5.
A. 9–10
What is 172?
B. 8–9
A. 219
C. 7–8
B. 239
D. 6–7
C. 269
D. 289
2.
6.
Which number is a perfect square?
A. 49
B. 56
D. 88
7.
___
What is √ 64 ?
A. 6
B. 7
D. 9
What is 53?
A.
15
B.
25
C.
53
A.
5
B.
9
C.
49
4
What is 4 ?
A.
16
B.
44
C.
256
D. 4,444
C. 8
4.
2
Which is the best estimate of (3.07) ?
D. 327
C. 72
3.
___
√ 77 is between which two numbers?
____
8.
What is √ 441 ?
A. 19
B. 21
C. 23
D. 27
D. 125
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Mississippi MCT2 Coach, Gold Edition, Mathematics, Grade 7
OPEN-ENDED QUESTION
9.
The_____
distance from the northeast corner to the southwest corner of a rectangular swimming pool
is √ 1,764 feet.
Part A:
What is the distance in feet from the northeast corner to the southwest corner,
written as a whole number?
Part B:
Explain how you found your answer.
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