Download 3rd NW Content Review Notes

Standards of Learning
Content Review Notes
Grade 7 Mathematics
3rd Nine Weeks, 2016-2017
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Content Review:
Standards of Learning in Detail
Grade 7 Mathematics: Third Nine Weeks
2016-2017
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 3rd 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/fra
mewk_math7.pdf
SOL 7.11
The student, given data in a practical situation, will
a) construct and analyze histograms; and
b) compare and contrast histograms with other types of graphs presenting information
from the same data set.

All graphs tell a story and include a title and labels that describe the data.

A histogram is a form of bar graph in which the categories are consecutive and equal intervals.
The length or height of each bar is determined by the number of data elements falling into a
particular interval.

A frequency distribution shows how often an item, a number, or range of numbers occurs. It can
be used to construct a histogram.

Comparisons, predictions and inferences are made by examining characteristics of a data set
displayed in a variety of graphical representations to draw conclusions.

The information displayed in different graphs may be examined to determine how data are or are
not related, ascertaining differences between characteristics (comparisons), trends that suggest
what new data might be like (predictions), and/or “what could happen if” (inference).
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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 7.11 (Histograms)
1
2
4
3
4
5
5
SOL 7.2
The student will describe and represent arithmetic and geometric sequences using
variable expressions.

In the numeric pattern of an arithmetic sequence, students must determine the difference, called
the common difference, between each succeeding number in order to determine what is added to
each previous number to obtain the next number.
Example 1:
3, 7, 11, 15, 19, …
The common difference is 4 (add 4 to the previous number).
Example 2:
30, 25, 20, 15, 10,…
The common difference is -5 (add -5 to the previous number).

In geometric sequences, students must determine what each number is multiplied by in order to
obtain the next number in the geometric sequence. This multiplier is called the common ratio.
Sample geometric sequences include:
Example 1:
2, 4, 8, 16, 32, …
The common ratio is 2 (multiply times 2).
Example 2:
80, 20, 5, 1.25, …
The common ratio is
1
1
(multiply times or 0.25).
4
4
Example 3:
Below is a geometric sequence. What is the 8th term in the sequence?
3, 9, 27, 81, 243, 729, …
The common ratio is 3 (each number is multiplied by 3 to get the next number).
Multiply 729 • 3 to get the 7th term.
The 7th term is 2,187.
Next, multiply the 7th term by 3.
2,187 • 3 = 6,561
The 8th term in the geometric sequence is 6,561.
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
A variable expression can be written to express the relationship between two consecutive terms of
a sequence.
Examples:
If n represents a number in the sequence 3, 6, 9, 12…, the next term in the sequence
can be determined using the variable expression n + 3.
If n represents a number in the sequence 1, 5, 25, 125…, the next term in the sequence
can be determined by using the variable expression 5n.
_______________________________________________________________________
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 7.2 (Patterns & Sequences)
1
2
What is the common difference of the arithmetic sequence shown below?
-5, -1, 3, 7 …
A 2
B 4
C 6
D 8
3
7
4
5
6
7
8
SOL 7.13
The student will
a) write verbal expressions as algebraic expressions and sentences as equations
and vice versa; and
b) evaluate algebraic expressions for given replacement values of the variables.

An expression is a name for a number.

An expression that contains a variable is a variable expression.

An expression that contains only numbers is a numerical expression.

A verbal expression is a word phrase. (e.g., “the sum of two consecutive integers”)

A verbal sentence is a complete word statement. (e.g., “The sum of two consecutive integers
is five.”)

An algebraic expression is a variable expression that contains at least one variable. (e.g.,
2x – 5)
Examples of Algebraic Expressions and Equivalent Verbal Expressions:

Algebraic Expression
Verbal Expression
x + (x + 1)
The sum of two consecutive integers
2x – 4
Four less than twice a number
3x + 8
Three times a number increased by eight
Key words in translating verbal expressions/sentences to algebraic expressions/equations may
include words and their translations such as: is to =, of to multiplication, more than to +, less
than to –, increased by to +, and decreased by to –.
An algebraic equation is a mathematical statement that says that two expressions are equal.
(e.g., 2x + 1 = 5)
Examples of Algebraic Equations and Equivalent Verbal Sentences:
Algebraic Equation
Verbal Sentence
30 – 40 = x
Forty less than thirty is a number.
x+5=8
The sum of a number and five is eight.
3 + 2x = 15
Three more than twice a number is fifteen.
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
To evaluate an algebraic expression, substitute a given replacement value for a variable and
apply the order of operations. For example, if a = 3 and b = -2 then 5a + b can be evaluated
as:
5(3) + (-2) = 15 + (-2) = 13

The replacement values are the numbers that replace the variables in an algebraic expression.
Example:
If x = (-5), what is the value of this expression?
x + 4 • 10
Step 1:
x + 4 • 10
Step 2:
(-5) + 4 • 10
Step 3:
-5 + 40
Step 4:
The answer is 35.
_______________________________________________________________________
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 7.13 (Verbal Expressions and Algebraic Expressions & Sentences)
1
2
10
3
4
5
6
11
8
9
10
11
12
13
14
15
16
13
18
17
19
19
19
19
19
20
21
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SOL 7.14
The student will
a) solve one- and two-step linear equations in one variable; and
b) solve practical problems requiring the solution of one- and two-step linear
equations.

An equation is a mathematical sentence that states that two expressions are equal.

A one-step equation is defined as an equation that requires the use of one operation to solve.
Example: 1x + 3 = –4
x + 3 – 3 = –4 – 3
x = –7

The inverse operation for addition is subtraction, and the inverse operation for multiplication is
division.

A two-step equation is defined as an equation that requires the use of two operations to solve.
Examples: 2x + 1 = -5;
2x + 1 – 1 = -5 – 1
2x = -6
2x  6

2
2
x = -3
x7
4
3
x7
3  43
3
x  7  12
x  7  7  12  7
x  19
_______________________________________________________________________
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 7.14 (One- And Two-Step Linear Equations)
1
15
2
3
4
6
5
7
16
8
10
9
11
12
13
14
17
16
15
17
18
19
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SOL 7.15
The student will
a) solve one-step inequalities in one variable; and
b) graph solutions to inequalities on the number line.

A one-step inequality is defined as an inequality that requires the use of one operation to solve.
Examples: x – 4 > 9
2n ≤ -14

The inverse operation for addition is subtraction, and the inverse operation for multiplication is
division.

When both expressions of an inequality are multiplied or divided by a negative number, the
inequality symbol reverses.
Example: –3x < 15 is equivalent to x > –5.

Solutions to inequalities can be represented using a number line.
Example 1: x < 2½
Example 2:
s –2≤2
s –2+2 ≤2+2
s ≤4
0
1
2
3
4
5
6
7
Note: When the solution to an inequality is > or <, it is represented on a graph using an open circle
(Example 1 above).
When the solution to an inequality is ≥ or ≤, it is represented on a graph using a closed circle
(Example 2 above).
_______________________________________________________________________
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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 7.15 (One-Step Inequalities in One Variable)
1
2
3
4
20
5
6
6
7
8
21
9
10
11
SOL 7.12
The student will represent relationships with tables, graphs, rules, and words.

Rules that relate elements in two sets can be represented by word sentences, equations, tables of
values, graphs, or illustrated pictorially.

A relation is any set of ordered pairs. For each first member, there may be many second
members.

A function is a relation in which there is one and only one second member for each first member.
Example:
Which number replaces the “?” in the table?
x
x + (-2)
y
-2
-2 + (-2)
-4
-1
?
?
0
0 + (-2)
-2
1
1 + (-2)
-1
2
2 + (-2)
0
The value of “x” is given in the top row. The work for the function is given in the second row.
Replace the “x” in “x + (-2)” so that it reads “-1 + (-2)” to determine the missing value. The
correct answer is “-3”.
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
As a table of values, a function has a unique value assigned to the second variable for each value
of the first variable.

As a graph, a function is any curve (including straight lines) such that any vertical line would
pass through the curve only once.
Examples:
These are examples of graphed functions.
y=x+3
x
-3
-2
-1
0
1
y=x+2
y
0
1
2
3
4
Some relations are functions; all functions are relations.
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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 7.12 (Relations & Functions)
1. Which table contains only values that satisfy the following?
y = 2x
2. Which table contains only values that satisfy the following?
y =x+5
3. The graph displays the relationship between time and profit.
Which equation represents the relationship between time
(t) and profit (P) ?
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4. Which is true for all values in the table ?
5. Which contains only values that make the following true?
y = 2x + 7
6. Which table contains only values that satisfy the following?
y=x–1
7. Which graph appears to contain all the
ordered pairs in the table?
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8.
Graph three points that are on the line represented by y = 2x -1.
The coordinates of the points must be integers.
9. Which table of values represents the same relationship as the rule
?
10. Which rule is best represented by this graph?
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11. Larry charges a customer a one-time fee of $15 plus $40 each week. Which table
has values that represent this situation?
12. Plot three points on the coordinate plane
that
lie on the relation represented by
The coordinates of the points must be
integers.
13. Which number sentence represents the relation shown in this table?
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SOL
Link
7.11
Creating Histograms
http://www.youtube.com/watch?v=g1wUk-JV7JU
7.2
Finding the common difference of an arithmetic
sequence
http://tinyurl.com/ob5e97a
7.2
Compare arithmetic and geometric sequences
http://tinyurl.com/pzlegf3
7.13
Writing and evaluating verbal expressions &
sentences as algebraic expressions & equations
https://www.youtube.com/watch?v=g6jeSuHYhyY
7.13
QR Code
Writing and evaluating verbal expressions &
sentences as algebraic expressions & equations
https://www.youtube.com/watch?v=miyyBR9bto0&list=PL557A7D37C
1462AC3
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7.14
Solving one-step equations
https://www.youtube.com/watch?v=9DxrF6Ttws4
7.14
Solving two-step equations
https://www.youtube.com/watch?v=tcxFE8eh-dU
7.14
Solving two-step equations
https://www.youtube.com/watch?v=mAPB3v-VlwI
7.14
Solving two-step equations using manipulatives
http://www.youtube.com/watch?v=r0Ex1BsU0Jw
7.15
Solving and graphing one-step inequalities
https://www.youtube.com/watch?v=OIM2rVmgwcQ
7.15
Solving and graphing one-step inequalities
https://www.youtube.com/watch?v=jmr9jHlA2-Y
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Vocabulary
SOL 7.11
cumulative
frequency
frequency
distribution
histogram
Includes a running total of the frequencies of
all the previous groups
Shows how often an item, a number, or a range
of numbers occurs
A special kind of bar graph in which the bars
are used to represent the frequency of
numerical data that have been organized in
intervals
SOL 7.2
arithmetic
sequence
common
difference
A sequence in which each term is found by
adding the same number to the previous term
In an arithmetic sequence, the number that is
added to each previous number to obtain the
next number
common ratio
In a geometric sequence, the number that is
multiplied by each previous number to obtain
the next number
geometric
sequence
A sequence in which each term can be found
by multiplying the previous term by the same
number
SOL 7.13
algebraic equation
A mathematical statement that states that two
expressions are equal
algebraic
expression
An expression with at least one
variable
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verbal expression
A word phrase
verbal sentence
A complete word statement
expression
A name for a number
equation
A mathematical sentence that states that
two expressions are equal
SOL 7.14
inverse operation
Operations that "undo" each other; addition
and subtraction are inverse operations.
Multiplication and division are inverse
operations.
one-step equation
An equation that requires only one operation
to solve
two-step equation
An equation that requires two operations to
solve
SOL 7.15
one-step
inequality
An inequality that requires only one operation
to solve
SOL 7.12
function
A rule that pairs exactly one element of a set
with one and only one element of another set
relation
A set of ordered pairs, in which for each first
number there may be many second numbers
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SOL 7.13
Practice Activity Directions: Cut out each card and match the verbal expressions (on the left) with the
algebraic expressions (on the right).
The product of four and a number,
decreased by seven
4x - 7
Triple the number of students in
Erin’s class divided by four is seven.
3x = 7
4
A number subtracted from seven is
four.
7–x=4
Seven less than a number is four.
x–7=4
Four less than seven is a number.
7–4=x
The sum of a number and four is
seven.
x+4=7
Four more than twice a number is
seven.
4 + 2x = 7
The sum of two consecutive integers
x + (x + 1)
Four less than twice a number
2x - 4
Three times a number increased by
seven
3x + 7
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Released Test Answers (3rd Nine Weeks)
SOL 7.11 (Histograms)
1. G
2.
3. C
4.
SOL 7.14 (One- And Two-Step Linear
Equations)
5. B
SOL 7.2 (Patterns & Sequences)
1. A
2. B
3. C
4. D
5. A
6.
a) common difference
b) 4
c) 136
1
7. 5, 5, 3, -3
SOL 7.13 (Verbal Expressions and
Algebraic Expressions & Sentences)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
G
J
F
A
B
A
C
G
F
F
F
G
A
G
SOL 7.13 Continued
15. J
16. J
17. A
18. F
19. A
20. C
21. A
1.
2.
3.
4.
5.
6.
7.
8.
9.
A
B
G
G
J
D
A
A
B
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
C
C
D
C
J
A
B
D
D
13.5 hours
SOL 7.15 (One-Step Inequalities in One
Variable)
1. A
2. J
3. A
4. G
5.
6. C
7. A
8. B
9.
10. B
11. C
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SOL 7.12 (Relations and Functions)
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