Standards of Learning
Content Review Notes
Grade 7 Mathematics
1st Nine Weeks, 2016-2017
Revised September 2015
2
Mathematics
Content Review Notes
Grade 7 Mathematics: First Nine Weeks
2015-2016
This resource is intended to be a guide for parents and students to improve content
knowledge and understanding. The information below is detailed information about
the Standards of Learning taught during the 1st grading period and comes from the
Mathematics Standards of Learning Curriculum Framework, Grade 7 issued by the
Virginia Department of Education. The Curriculum Framework in its entirety can be
found at the following website:
http://www.doe.virginia.gov/testing/sol/frameworks/mathematics_framewks/2009/f
ramewk_math7.pdf
SOL 7.3
The student will
a) model addition, subtraction, multiplication and division of integers; and
b) add, subtract, multiply, and divide integers (*non – calculator).

The set of integers is the set of whole numbers and their opposites.
(e.g., … –3, –2, –1, 0, 1, 2, 3, …).

Integers are used in practical situations, such as temperature changes (above/below zero),
balance in a checking account (deposits/withdrawals), and changes in altitude (above/below
sea level).
Example:
The temperature in Alaska dropped 15 degrees overnight. If the
previous night’s temperature was -10 degrees, what is the new
temperature?
To find the answer, set up an equation and solve.
(-10) - 15 = ?
ANSWER:
(-10) + (-15) = -25
The answer is -25 degrees.

Concrete experiences in formulating rules for adding and subtracting integers should be
explored by examining patterns using calculators, along a number line and using manipulatives,
such as two-color counters, or by using algeblocks.

Concrete experiences in formulating rules for multiplying and dividing integers should be
explored by examining patterns with calculators, along a number line and using manipulatives,
such as two-color counters, or by using algeblocks.

Simplify numerical expressions involving addition, subtraction, multiplication and division of
integers using order of operations.
3
SOL Practice Items provided by the VDOE,
http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml
Answers are located on the last page of the booklet.
SOL 7.3 (Operations & Practical Problems with Integers)
1. Which expression is equivalent to -5
– (-7)?
4. A dolphin is 30 feet below the
surface of the water. She rises 23
feet, sinks 17 feet, and finally rises
another 27 feet. If there are no
other changes, the dolphin is –
2. The record high temperature for a
certain U.S. State is 104°F. The
record low temperature for the same
state is -14°F. What is the difference
between the record high and low
temperatures for this state?
5. Use the number line to complete
𝒚
the sentence. The value of will
be –
𝒛
3. The change in the number of students
enrolled at a school over six months
is shown in the following table.
6. Evaluate.
The number of students enrolled at
the end of September was 4,327.
What was the number of students
enrolled in the school at the end of
March?
4
7. During a winter’s night, the low
temperature was recorded at
19°F. The wind-chill temperature
that same night was -7°F. What
was the difference between the
wind-chill temperature and the
low temperature?
8. Using the key as a guide, what is
the result of the operation in the
model below?
10. Select each number that can be
placed in the blank to make the
value of this expression a negative
number.
11. a) What is the value of this
expression?
b) Name two numbers that can be
placed in the blank to make the
value of this expression a
negative number.
12. What is the value of the expression?
9. Which number sentence is
represented by this model?
5
SOL 7.16
The student will apply the following properties of operations with real numbers:
a) the commutative and associative properties for addition and multiplication;
b) the distributive property;
c) the additive and multiplicative identity properties;
d) the additive and multiplicative inverse properties; and
e) the multiplicative property of zero.

The commutative property for addition states that changing the order of the addends does not
change the sum. (e.g., 5 + 4 = 4 + 5)

The commutative property for multiplication states that changing the order of the factors does
not change the product. (e.g., 5 · 4 = 4 · 5)

The associative property of addition states that regrouping the addends does not change the
sum. [e.g., 5 + (4 + 3) = (5 + 4) + 3]

The associative property of multiplication states that regrouping the factors does not change
the product. [e.g., 5 · (4 · 3) = (5 · 4) · 3]

Subtraction and division are neither commutative nor associative.

The distributive property states that the product of a number and the sum (or difference) of
two other numbers equals the sum (or difference) of the products of the number and each
other number. [e.g., 5 · (3 + 7) = (5 · 3) + (5 · 7), or 5 · (3 – 7) = (5 · 3) – (5 · 7)]

Identity elements are numbers that combine with other numbers without changing the other
numbers. The additive identity is zero (0). The multiplicative identity is one (1). There are no
identity elements for subtraction and division.

The additive identity property states that the sum of any real number and zero is equal to the
given real number. (e.g., 5 + 0 = 5)

The multiplicative identity property states that the product of any real number and one is equal
to the given real number. (e.g., 8 · 1 = 8)

Inverses are numbers that combine with other numbers and result in identity elements.
1
[e.g., 5 + (–5) = 0; · 5 = 1]
5

The additive inverse property states that the sum of a number and its additive inverse always
equals zero. [e.g., 5 + (–5) = 0]

The multiplicative inverse property states that the product of a number and its multiplicative
1
inverse (or reciprocal) always equals one. (e.g., 4 · = 1)
4

Zero has no multiplicative inverse.

The multiplicative property of zero states that the product of any real number and zero is zero.

Division by zero is not a possible arithmetic operation. Division by zero is undefined.
6
SOL Practice Items provided by the VDOE,
http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml
Answers are located on the last page of the booklet.
SOL 7.16 (Properties of Real Numbers)
1. What real number property of
multiplication is shown in this
equation?
5.
Which property is shown in the
following number sentence?
2. Which of the following expressions is
equivalent to 4.1(8.5 – 6.2)?
6. Which statement is false?
2
5
3. Which property is used in the
following number sentence?
3
4. Which of the following equations
illustrates the multiplicative property
of zero?
7. Anne’s utility bills for three months
were $59, $67, and $33. To add the
utility bills mentally, Anne thought
What property did Anne use?
7
8. Which number sentence
illustrates the commutative
property of multiplication?
12. Which property is illustrated by this
number sentence?
9. If the number sentence is true,
then y is the –
10.
Match the equation to its property.
11
Match the equation to its property.
8
13. Which property is illustrated by this number sentence?
14.
Identify the property illustrated by each equation.
9
SOL 7.1
The student will
a) investigate and describe the concept of negative exponents for powers of ten;
b) determine scientific notation for numbers greater than zero (*non-calculator);
c) compare and order fractions, decimals, percents, and numbers written in
scientific notation (*non-calculator);
d) determine square roots (*non-calculator); and
e) identify and describe absolute value for rational numbers.

Negative exponents for powers of 10 are used to represent numbers between 0 and 1.
(e.g., 10 3 = 13 = 0.001)
10

Negative exponents for powers of 10 can be investigated through patterns such as:
10 2 =100
10 1 = 10
10 0 = 1
10 1 = 11  1 = 0.1
10
10

A number followed by a percent symbol (%) is equivalent to that number with a denominator
of 100.
3
60
(e.g., =
= 0.60 = 60%)
5
100

Scientific notation is used to represent very large or very small numbers.

A number written in scientific notation is the product of two factors — a decimal greater than or
equal to 1 but less than 10, and a power of 10
(e.g., 3.1  105= 310,000 and 2.85 x 10 4 = 0.000285).

Equivalent relationships among fractions, decimals, and percents can be determined by using
manipulatives. (e.g., fraction bars, Base-10 blocks, fraction circles, graph paper, number lines
and calculators)

A square root of a number is a number which, when multiplied by itself, produces the given
number. (e.g., 121 is 11 since 11 x 11 = 121)

The square root of a number can be represented geometrically as the length of a side of the
square.
The absolute value of a number is the distance from 0 on the number line regardless of
direction. The absolute value of a number will always be positive.
(e.g., 1  1 )

2
2
10
SOL Practice Items provided by the VDOE,
http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml
Answers are located on the last page of the booklet.
SOL 7.1 (Negative Exponents; Absolute Value; Square Roots; Scientific Notation;
Fractions, Decimals, and Percents)
1. Which list is ordered from least to greatest?
2. Which number is less than 138%?
1
3. The speed of light is approximately 300,000,000 meters per second. What is the
speed of light expressed in scientific notation?
4. Which set is ordered from least to greatest?
11
5. Which of the following is another way of expressing 2 out of 8?
6. Which list is in orderr from least to greatest?
6
7. The fraction ⅛ is equivalent to –
8. Which number is equivalent to 0.7%?
9. Which is true?
12
10.
Which is correctly written in scientific notation?
11.
A store advertisement reads “Going Out of Business Sale. Everything is ⅝ off.”
What percent is ⅝?
12.
Daphne wrote the fractional part of the quizzes she answered correctly.
Which lists these quiz scores in order from least to greatest?
13.
What is a square root of 100?
14.
Which is a perfect square between 81 and 121?
13
15.
Which of these is a true statement?
16.
Which statement is true?
17.
Which expression is equivalent to 10-5?
18.
Use the given numbers to find an equivalent fraction and decimal.
19.
Select all of these that are equivalent to 10-5.
14
20.
21.
22.
23.
15
Testing Information
1st Benchmark Test
October 19th – 23rd
SOL’s Tested: 7.1ade, 7.3, 7.16
2nd Benchmark Test
December 14th – 18th
SOL’s Tested: 7.1bc, 7.7, 7.6, 7.4, 7.8
- with a cumulative review of all previous SOLs taught
3rd Benchmark Test
March 14th – 18th
SOL’s Tested: 7.8, 7.9, 7.10, 7.11, 7.13, 7.14, 7.15
-
with a cumulative review of all previous SOLs taught
Teacher Made Assessments: 7.2, 7.12, 7.5
16
17
SOL
Link
7.3
Modeling addition of integers using counters and
number lines
https://www.youtube.com/watch?v=l6E0KHKcZOg
7.3
Modeling subtraction of integers using counters and
number lines
https://www.youtube.com/watch?v=RcTaKAkml0I
7.3
Simplifying expressions using integers
https://www.youtube.com/watch?v=oo5DAHo7NHY
7.3
Adding and subtracting integers
https://www.youtube.com/watch?v=oeqkrOTaBp8
7.3
Multiplying and dividing integers
http://tinyurl.com/nsfapp2
QR Code
18
7.16
Applying properties of operations with real numbers:
distributive, associative, commutative, and identity
properties
http://www.youtube.com/watch?v=M3lVR1btlzE
7.16
Applying properties of operations with real numbers:
inverse properties
http://tinyurl.com/o8tvulh
7.1
Order fractions, decimals, and percents
http://www.youtube.com/watch?v=PZDg0_djUtE
7.1
Determine and model absolute value
http://tinyurl.com/q86jjyh
7.1
Square roots
http://www.youtube.com/watch?v=Ymcf14wC9Ck
19
7.1
7.1
Scientific Notation (negative exponents begin at
3:00)
https://www.youtube.com/watch?v=WwmJ5nMmigQ
Powers of 10
http://www.bvps.org/mfischer/Videos.htm
20
SOL 7.3
checking account
balance
An accounting of deposits and
withdrawals of money
deposit
The act of putting money into a bank
withdrawal
The act of taking out money from a bank
integers
Set of whole numbers and their
opposites {…-2, -1, 0, 1, 2…}
sum
The result of addition
difference
The result of subtraction
zero pairs
A pair of numbers whose sum is zero
quotient
The result of division
product
The result of multiplication
base
In a power, the number used as a factor
exponent
In a power, the number that tells how
many times the base is used as a factor
expression
A mathematical phrase that contains
operations, numbers, and/or variables
21
The rules to follow when more than one
operation is used in a numerical
expression
order of operations
(Parentheses, Exponents, Multiplication/Division,
Addition/Subtraction)
powers
Numbers expressed using exponents
SOL 7.16
additive identity
associative property (x,+)
commutative property
(x,+)
The sum of an addend and zero is the addend.
Identity for addition is 0 (zero) since adding
zero to any number will give the number itself.
In other words, 0 + a = a.
The way in which three numbers are
grouped when they are added or
multiplied does not change their sum or
product.
The order in which two quantities are
added or multiplied does not change
their sum or product.
distributive property
To multiply a sum by a number, multiply
each addend of the sum by the number
outside the parentheses.
equation
A mathematical sentence that contains
an equal sign, =
inverse
multiplicative identity
multiplicative property of
zero
Operations that "undo" each other-addition and subtraction are inverse
operations. Multiplication and division
are inverse operations
The product of a factor and one is the
factor. Identity for multiplication is "1,"
because multiplying any number by 1.
ax1=a
The product of any real number and zero is
zero.
22
SOL 7.1
ascending order
Numbers listed in order from smallest to
largest
decimal
The numbers in the base 10 number system,
having one or more places to the right of a
decimal point
denominator
The bottom number of a fraction
descending order
Numbers listed from largest to smallest
equivalent
Having the same value
fraction
A number used to name a part of a
group or a whole; numerator over
denominator.
greater than or equal to
Symbols that describe a relationship in which
the expression on the left is greater than the
expression on the right
less than or
equal to
Symbols that describe a relationship in which
the expression on the left is less than the
expression on the right
numerator
The top number of a fraction
percent
A ratio that compares a number to 100
place value
The value of a digit based on its
position in a number.
product
The result of two numbers being
multiplied together
scientific notation
A number written as a product of a number
that is at least one but less than 10, and a
power of 10
23
Released Test Answers (1st Nine Weeks)
SOL 7.3 (Operations & Practical Problems
with Integers)
1. F
2. D
3. C
4. F
5. B
6. J
7. J
8. G
9. A
10.
11. a) -4
b) any number greater than -21
12.
1) -19
2) -22
3) -18
SOL 7.16 (Properties of Real Numbers)
1. D
2. H
3. A
4. A
5. G
6. A
7. D
8. A
9. H
14.
1.
2.
3.
4.
Distributive
Multiplicative Identity
Commutative Property
Additive Inverse
SOL 7.1 (Negative Exponents; Absolute
Value; Square Roots; Scientific Notation;
Fractions, Decimals, and Percents)
1. G
2. B
3. H
4. J
5. G
6. B
7. H
8. F
9. A
10. G
11. J
12. J
13. H
14. C
15. B
16. B
17. B
18.
19.
10.
11.
12. C
13. C
20. D
21.
22. C
23.
24