CCGPS Review Packet Math 8 - Thomas County Schools Review Packet Math 8 ... Alternate Exterior Angles: a pair of angles on opposite sides of the ... Alternate Interior Angles:

CCGPS Review Packet Math 8

Common Core Georgia Performance Standards

~ per unit ~


UNIT 1

Geometry

Standard: MCC8.G.1 Verify experimentally the properties of rotations, reflections, and translations;

a. Lines are taken to lines, and line segments to line segments of the

same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

Graph the triangle ABC at A(-2,3), B(-2,8), and C(-6,3). Translate using (x+10,y-2); then, rotate 90 degrees clockwise about the origin; last, reflect over the y-axis. Label all points appropriately.

How does the original figure relate to the transformed figure? Include details about side lengths and angles.

Meaningful Vocabulary

Transformation: A change in position or size

Congruent: Same size and shape

Reflection: A transformation that "flips" a figure

over a line of reflection.

Rotation: A transformation that turns a figure about

a fixed point through a given angle and a given

direction.

Translation: A transformation that “slides” a figure”

Rigid: Unchanging; Congruent

Geometry

Standard: MCC8.G.2 Understand that a two-dimensional figure is congruent to another if the

second can be obtained from the first by a sequence of rotations,

reflections, and translations; given two congruent figures, describe a

sequence that exhibits the congruence between them.

Graph triangle XYZ at X(1,5), Y(5,8), and Z(4,3). Reflect it over the x-axis and translate 2 units down. Label all points appropriately.

Starting Coordinates:

Ending Coordinates:

Are the two figures congruent? Explain.




Reflection: A transformation that "flips" a figure over a line of

reflection.

Rotation: A transformation that turns a figure about a fixed

point through a given angle and a given direction.



Geometry

Standard MCC8.G.2 Understand that a two-dimensional figure is congruent to another if the

second can be obtained from the first by a sequence of rotations,

reflections, and translations; given two congruent figures, describe a

sequence that exhibits the congruence between them.

Graph the original figure: A(-2,-8), B(-10,-6) C(-5,3). Graph the transformed figure: A’(2,-5), B’(10,-3), C’(5,6).

What transformation(s) are necessary to go from the original figure to the transformed figure?





Reflection: A transformation that "flips" a figure over

a line of reflection.

Rotation: A transformation that turns a figure about

a fixed point through a given angle and a given

direction.



Geometry

Standard MCC8.G.3 Describe the effect of dilations, translations, rotations, and

reflections on two-dimensional figures using coordinates.


X(2,-3), Y(7,-8), Z(5,-4)

Ending Coordinates:


A(1,4) B(1,1), C(5,3)

Ending Coordinates:

Rotation of 180 degrees about the origin

Translation rule: (x+2, y-8)





reflection.

Rotation: A transformation that turns a figure about a fixed

point through a given angle and a given direction.



Graph A(-6,-2), B(2,8), C(4,-2) and dilate with a scale factor of 1/2. Label all points appropriately.


Ending Coordinates:


Geometry

Standard MCC8.G.4 Understand that a two-dimensional figure is similar to another if

the second can be obtained from the first by a sequence of

rotations, reflections, translations, and dilations; given two

similar two-dimensional figures, describe a sequence that

exhibits the similarity between them.



Dilation: enlarging or shrinking an image; produces a similar

figure

Geometry

Standard MCC8.G.4 Understand that a two-dimensional figure is similar to another

if the second can be obtained from the first by a sequence of

rotations, reflections, translations, and dilations; given two

similar two-dimensional figures, describe a sequence that

exhibits the similarity between them.

Graph the original figure: X(-2,-8), Y(-6,-6), Z(-4,4). Graph the transformed figure: X’(-1,-4), Y’(-3,-3), Z’(-2,2).

What transformation(s) are necessary to go from the pre-image to the image?

Are the two figures similar? Explain.



Dilation: enlarging or shrinking an image; produces a similar figure


reflection.


Rotation: A transformation that turns a figure about a fixed point

through a given angle and a given direction.



Geometry

Standard MCC8.G.5 Use informal arguments to establish facts about

the angle sum and exterior angle of triangles,

about the angles created when parallel lines are

cut by a transversal, and the angle-angle criterion

for similarity of triangles.


Alternate Exterior Angles: a pair of angles on opposite sides of the

transversal but outside the parallel lines

Alternate Interior Angles: a pair of angles on opposite sides of the

transversal but inside the parallel lines

Corresponding Angles: angles that are in the same position when

parallel lines are cut by a transversal

Parallel Lines: lines that are the same distance apart

Similar: having the same shape, but not necessarily the same size

Supplementary Angles: angles whose sum is 180 degrees

Transversal: a lines that cuts across two or more lines

Lines m and n are parallel cut by transversal, t.

Name all pairs of corresponding angles. Are they congruent or supplementary?

Name all pairs of vertical angles. Are they congruent or supplementary?

m n

t

1 2 3 4

5 6 7 8

5 6 7 8

1 2 3 4

t

m n

Lines m and n are parallel cut by transversal, t.

Geometry

Standard MCC8.G.5 Use informal arguments to establish facts about the angle

sum and exterior angle of triangles, about the angles

created when parallel lines are cut by a transversal, and

the angle-angle criterion for similarity of triangles.

Given triangle: Given triangle:

What does this diagram tell us about the sum of the interior angles of a triangle?

What is the value of angle 4 in the diagram?

Angle 1 = 50⁰ Angle 2 = 90⁰ Angle 3 = 40⁰


Angle Sum: the sum of the interior angles in a shape

Exterior Angle: an angle formed outside a polygon when one

side is extended.

Similar: having the same shape, but not necessarily the same

size

Supplementary Angles: angles whose sum is 180 degrees

Transversal: a lines that cuts across two or more lines


UNIT 2

Expressions and Equations

Standard MCC8.EE.1 Know and apply the properties of integer exponents to

generate equivalent numerical expressions.

For example, 32 x 3-5 = 3-3 = 1/33 = 1/27.

Simplified expression:

Simplify using the law of exponents . (Show work here.)

Simplified expression:


Equivalent: having same value

Exponent: the small number used to show the number of times

the base is multiplied by itself

Integer: positive or negative number or zero (no fractions or

decimals)

Laws of Exponents: rules used to simplify expressions

containing exponents

Simplify: to reduce the complexity

Simplify using the law of exponents . (Show work here.)


Standard MCC8.EE.2 Use square root and cube root symbols to represent

solutions to equations of the form x2 = p and x3 = p,

where p is a positive rational number; evaluate square

roots of small perfect squares and cube roots of small

perfect cubes; know that the square root of 2 is

irrational.

Evaluate the square roots. Evaluate the cube roots.

Evaluate the perfect squares. Evaluate the perfect cubes.


Cube Root: one of three identical factors of a number

Irrational Number: number that cannot be written as a

fraction

Perfect Cube: a result of multiplying a number by itself 3

times

Perfect Square: a result of multiplying a number by itself 2

times

Rational Number: a number that can be written as a fraction

Square Root: one of two identical factors of a number


Standard MCC8.EE.3 Use numbers expressed in the form of a single digit times an

integer power of 10 to estimate very large or very small quantities,

and to express how many times as much one is more than the

other. For example, estimate the population of the United States as

3 x 108 and the population of the world as 7 x 109, and determine that the

world population is more than 20 times larger.

Express the above number in scientific notation.

Is this number very large or very small? Justify.

Express the above number in standard form.

Is this number very large or very small? Justify.


Scientific Notation: a way of writing a very large

or very small number using a number between 1

and 10 multiplied by a power of 10

Standard Form: writing a number as a single term


Standard MCC8.EE.4 Perform operations with numbers expressed in scientific notation,

including problems where both decimal and scientific notation are

used; use scientific notation and choose units of appropriate size

for measurements of very large or very small quantities (e.g., use

millimeters per year for seafloor spreading); interpret scientific

notation that has been generated by technology.

Given problem/word problem: (information given is fiction)

A gnat has about 43,000,000 cells. A fly has about 1.7 x 103 times as many cells as a gnat. About how many cells does a fly have?

Solve.

What does the solution mean within the context of the problem?

Given problem/word problem:

The population of Laos is 6.64 x 106. The population of Vietnam is 8.8 x 107. The population of Thailand is 6.68 x 107. What is the total population of the three countries?

Solve.

What does the solution mean within the context of the problem?


Scientific Notation: a way of writing a very large

or very small number using a number between 1

and 10 multiplied by a power of 10

Standard Form: writing a number as a single term


Standard MCC8.EE.7.a Give examples of linear equations in one variable with one solution,

infinitely many solutions, or no solutions; show which of these

possibilities is the case by successively transforming the given

equation into simpler forms, until an equivalent equation of the form

x=a, a=a, or a=b results (where a and b are different numbers).

Solve the equation.

How many solutions does this equation have? Justify.

Solve the equation.

How many solutions does this equation have? Justify.

Show all steps.


Coefficient- a number that is multiplied by a

variable

Distributive Property- simplifying an expression

by multiplying a number by each term inside the

parenthesis

Like Terms- terms where the variable is raised to

the same power


Standard 8.EE.7.b Solve linear equations with rational number coefficients,

including equations whose solutions require expanding

expressions using the distributive property and collecting the

terms.

Solve the linear equation. Show all steps. Solve the linear equation. Show all steps.


Coefficient- a number that is multiplied by a

variable

Distributive Property- simplifying an expression

by multiplying a number by each term inside the

parenthesis

Like Terms- terms where the variable is raised to

the same power

The Number System

Standard 8.NS.1 Know that numbers are rational are irrational; understand

informally that every number has a decimal expansion; for

rational numbers show that a decimal expansion repeats

eventually, and convert a decimal expansion which repeats

eventually into a rational number.

Meaningful Vocabulary:

Irrational Number- a number that cannot be written

as a fraction

Rational Number- a number that can be written as a

ratio

Characteristics of rational numbers: Characteristics of irrational numbers:

Rational numbers: Irrational numbers:

The Number System

Standard MCC8.NS.2 Use rational approximations of irrational numbers to

compare the size of irrational numbers, locate them

approximately on a number line diagram, and estimate the

value of expressions (e.g., pi squared). For example, by

truncating the decimal expansion of the square root of 2, show

that the square root of 2 is between 1 and 2, then between 1.4

and 1.5, and explain how to continue on to get better

approximations.

Meaning Vocabulary:

Approximate- to estimate a number, often rounding it of

Estimate- to make a rough or approximate calculation

Irrational Number- a number that cannot be written as a fraction

Number Line- a line marked with numbers that are evenly spaced

Rational Number- a number that can be written as a fraction

Square Root- one of two identical factors of a number

Place the given irrational numbers on the number line.


UNIT 3

Geometry

Standard MCC8.G.6 Explain a proof of the Pythagorean Theorem and its converse.


Converse- opposite statement

Proof- the process of showing that something is true

Pythagorean Theorem- a formula relating the three side

lengths of a right triangle

Right Triangle- a triangle with one 90 degree angle

Use the 3, 4, 5 right triangle given. Use the grid to illustrate the squares of the sides to prove the Pythagorean Theorem.

Explain how the diagram to the left illustrates the Pythagorean Theorem and its converse.

Geometry

Standard MCC8.G.6; MCC8.G.7 Apply the Pythagorean Theorem and its converse to

determine unknown side lengths in right triangles in

real-world and mathematical problems in two and three

dimensions.

Given problem:

Solve for the missing side length in the given right triangle.

Figure: 25 15 b

Solve.

Given problem:

Triangle ABC has side lengths of 5 centimeters, 8 centimeters, and 10 centimeters. Is it a right triangle?

Sketch:

Solve.


Pythagorean Theorem- a formula relating the three side lengths of a

right triangle


Three-dimensional- having three dimensions: length, width and height

Two-dimensional- having two dimensions: length and width

Geometry

Standard MCC8.G.8 Apply the Pythagorean Theorem to find the distance

between two points in a coordinate system.

Find the distance between the two points: Use the space below to find the distance between given locations/points.


Pythagorean Theorem- a formula relating the three side lengths

of a right triangle


Geometry

Standard MCC8.G.9 Know the formulas for the volumes of cones, cylinders, and

spheres and use them to solve real-world and mathematical

problems.


Volume- the amount of space occupied by a 3D object,

measured in cubic units

Formula:

Solve.

Formula:

Formula:

Solve. Solve.

10cm 6cm

12 in 8 in

12 in


Standard MCC8.EE.2 Use square root and cube root symbols to represent

solutions to equations of the form x2 = p and x3 = p,

where p is a positive rational number; evaluate square

roots of small perfect squares and cube roots of small

perfect cubes; know that the square root of 2 is

irrational.


Cube Root- one of three identical factors of a number that is the

product of those factors

Perfect Cube- a number that results from multiplying an integer by

itself twice

Perfect Square- a number that results from multiplying an integer

by itself

Rational Numbers- any number that can be written as a ratio

Square Root- one of two identical factors of a number that is the

product of those factors

Evaluate the square roots. Evaluate the cube roots.


UNIT 4

Functions

Standard MCC8.F.1 Understand that a function is a rule that assigns to each

input exactly one output; the graph of a function is the set

of ordered pairs consisting of an input and the

corresponding output.


Function- a rule that determines a relationship between 2

variables

Function Table- a set of inputs with corresponding outputs

in a chart

Input values- x-values; domain

Ordered Pair- a pair of numbers to show a position on a

coordinate plane

Output values- y-value; range

Given function:

Function Table: Graph:

x y

f(x) = -2x + 3 [Remember… “f(x)” means the same as “y”.]

Functions

Standard MCC8.F.2 Compare properties of two functions each represented

in a different way (algebraically, graphically, numerically

in tables, or by verbal descriptions). For example, given a

table of values and an algebraic expression, determine which

function has the greater rate of change.

Compare the verbal description to the graph:

What is Blake’s speed?______ What is Jenny’s speed?______

Compare the table to the graph:

Function 1 has a rate of change of _____ and Function 2 has a rate of change of _____, so which function has a greater rate of change or are they the same?_____________________________________


Compare- to note similarities (and/or differences)

Function- a rule that determines a relationship between 2

variables

Ordered Pair- a pair of numbers to show a position on a

coordinate plane

Rate of Change- slope; the change in the y value divided by

the change in the x value

A brother and sister are racing 30

meters to the end of the street.

Since Blake is younger, his sister

Jenny lets him have a 6–meter

head start. The graph show the

distance that Blake runs during

the race.

Compare the rates

of change for the

two linear

functions.

Which function

has a greater rate

of change, or are

they the same?

Dis

tan

ce (i

n m

eter

s)

The equation y = 3x can be used to represent y, the total

distance in meters that Jenny has run after x seconds have

passed. Who is running at a faster speed? How much faster?

x y

-4 -12

-2 -9

0 -6

2 -3

4 0

Verbal description and graph:

Table and graph:

Number of Seconds

36

30

24

18

12

6

0

0 2 4 6 8 10 12

Blake’s Race

Jenny’s Race:

Function 1 Function 2


UNIT 5


Standard MCC8.EE.5 Graph proportional relationships, interpreting the unit rate

as the slope of the graph; compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-

time equation to determine which of two moving objects has

greater speed.


Interpret- to explain

Linear Equation- a function that produces a line on a

coordinate grid

Proportional Relationship- when two quantities vary directly

with one another

Slope- rate of change; the change in the y value divided by the

change in the x value

Unit Rate- a comparison of two measurements in which one

term has a value of one

PART 1 – Interpret unit rate as slope:

Interpret unit rate as slope:

Slope =

Which train is traveling faster?

How do you know?

What is the speed of North Train? What is the speed of South Train?

Two trains, North Train and South Train, are traveling at a constant rate of speed. The equation y = 130x shows the total distance in miles, y, traveled by North Train over x hours. The graph shows the relationship between time and distance for South Train.

Tota

l Dis

tan

ce (

mile

s)

Time (hours)

PART 2 – Compare two different proportional relationships:

480

360

240

120

0

South Train

1 2 3 4 x

y


Standard MCC8.EE.6 Use similar triangles to explain why the slope m is the same

between any two distinct points on a non-vertical line in the

coordinate plane; derive the equation y=mx for a line through

the origin and the equation y = mx+b for a line intercepting

the vertical axis at b.


Origin- the coordinates of the origin are (0, 0).

Proportional Relationships- a relationship between

two equal ratios

Slope- the “steepness” of a line; represented by the

letter m; the ratio of the “rise” over “run” between two

points on the graph.

Evaluate the slope through similar triangles.

Does the slope of a line change when using different points to

to determine it? _____________

Find the ratio of the vertical and horizontal side lengths for each triangle. Use the coordinates of the points to find the rate of change. (You may use a table or the slope formula.)

(Use the two similar triangles and the line graphed to help you answer the question.)

12 11 10

9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 10 11 12

(2, 2)

(4, 5)

(8, 11)

3

2

6

4

Functions

Standard MCC8.F.3 Interpret the equation y = mx+b as defining a linear

function, whose graph is a straight line; give

examples of functions that are not linear.


Equation- a mathematical statement containing an equal sign to

show that two expressions are equal

Function- a mathematical relationship between two values


Linear- relating points to form a line

Nonlinear- points that do not produce a line

Linear Equations: Non-linear Equations:

Write an equation for the function and identify the rate of change and initial value.

Is the graph a function?___________ Is the graph a linear function?___________

Which equation does not represent a linear function?_________ How do you know?________________________________

Input (x) Output (y)

0 -1

1 2

2 5

3 8

A. y = ½ x + 2

B. y = x2

C. y = 2x

D. y = x - 2


UNIT 6

Functions

Standard MCC8.F.4 Construct a function to model a linear relationship between

two quantities. Determine the rate of change and initial

value of the function from a description of a relationship or

from two (x,y) values, including reading these from a table

or from a graph. Interpret the rate of change and initial

value of a linear function in terms of the situation it models,

and in terms of its graph or a table of values.

Given problem: To bowl at the local bowling alley, it costs $3 per game plus a $4 shoe rental. The total cost, y, in dollars depends on x, the number of games played. Write an equation to represent this situation and identify the slope and initial value (y-intercept). Then, make a table values to represent the situation. Graph the situation using the m and b values of your equation.

Function Table:

Graph:

x y


Construct- to make or create

Equation- a mathematical statement containing an equal sign

Function- a mathematical relationship between two values

Function Table- outlining a set of inputs with corresponding

outputs in a chart

Initial Value- the starting quantity; beginning; y-intercept

Model- to describe mathematically

Rate of Change- slope; change in y value divided by the

change in the x value

Rate of change:

What does the rate of change represent within the context of the problem:

Initial value:

What does the initial value represent within the content of the problem?

Equation:

Functions

Standard MCC8.F.5 Describe qualitatively the functional relationship between two

quantities by analyzing a graph (e.g., where the function is

increasing or decreasing, linear or nonlinear); sketch a graph

that exhibits the qualitative features of a function that has been

described verbally.

On Thursday, Luther went for a long walk, stopping to feed the ducks at one point. The graph below represents his walk.

What is the slope of segment from (0, 0) to (2, 6)? What does the slope of that segment represent?


Analyze- to separate material into its parts or elements

Exhibits- shows

Function- a mathematical relationship between two quantities

Qualitatively- relating to categories, variables, or real-world

Quantity- amount; number of something

Relationship- a connection

What is the slope of the segment from (2, 6) to (3, 6)? What does the slope of that segment represent?

What is the slope of the segment from (3, 6) to (5, 11)? What does the slope of that segment represent?

Tota

l Dis

tan

ce (

mile

s)

Number of Hours

12

10

8

6

4

2

0 1 2 3 4 5

Luther’s Walk

Functions

Standard MCC8.F.5 Describe qualitatively the functional relationship between

two quantities by analyzing a graph (e.g., where the

function is increasing or decreasing, linear or nonlinear);

sketch a graph that exhibits the qualitative features of a

function that has been described verbally.

Use the description to create a graph.

Ben went rollerblading. He skated away from his home for 20 minutes for a total distance of 6 miles. He took a 10 minute break and skated back home for 30 minutes. Make a graph showing the distance he traveled away and back to his home. Describe the relationship between the two variables (relate it to the

context of the problem).

10 20 30 40 50 60 70 80 90 0

9

8

7

6

5

4

3

2

1

Time (in minutes)

Dis

tan

ce f

rom

Ho

me

(in

mile

s)


Analyze- to separate material into its parts or elements

Exhibits- shows

Function- a mathematical relationship between two quantities

Qualitatively- relating to categories, variables, or real-world

Quantity- amount; number of something

Relationship- a connection

Statistics and Probability

Standard MCC8.SP.1 Construct and interpret scatter plots for bivariate

measurement data to investigate patterns of

association between two quantities; describe

patterns such as clustering, outliers, positive or

negative association, linear association, and

nonlinear association.

Bivariate- involving or relating to two variables

Clustering- data points that tend to crowd together

Construct- to make or create


Negative Correlation- x increases while y decreases (opposite)

Outlier- a data point far away from the majority of the other data

points

Positive Correlation- x increases and y increases also

Scatter Plot- a graph with points to show a relationship between two

variables

Use the given data to create a scatter plot. Be sure to include all appropriate labels.

Describe any patterns and/or relationships seen in the scatter plot.

Day Sun. Mon. Tues. Wed. Thurs. Fri. Sat.

Daily High Temp

(in °F) 84 90 92 87 87 95 93

Bottles of Water

Sold at a Baseball

game 10 30 36 18 20 48 5


Standard MCC8.SP.2 Know that straight lines are widely used to model

relationships between two quantitative variables; for scatter

plots that suggest a linear association, informally fit a straight

line, and informally assess the model fit by judging the

closeness of the data points to the line.

Use the given data on the scatter plot that has been created. Be sure to observe all labels (title, y -axis, x-axis). If a linear model is appropriate, sketch in a line of best fit.

What type of correlation exists?

Does a linear model seem appropriate for this data? Why or why not?

Write a statement to justify the type of correlation.

Meaningful Vocabulary: Bivariate- involving or relating to two variables Clustering- data points that tend to crowd around a particular point in a set of values Linear Model- representing a situation with a line on a graph Negative Correlation- x increases while y decreases (opposite) Outlier- a data point far away from the majority of the other data points Positive Correlation- x increases and y increases also Quantitative- data that can be counted or measured Scatter Plot- a graph with points to show a relationship between two variables Variable- a letter representing a quantity

Selling Price of Aging Cars

36,000 32,000 28,000 24,000 20,000 16,000 12,000

8,000 4,000

0 1 2 3 4 5 6 7 8 9 0

Age (years)

Selli

ng

Pri

ce (

do

llars

)


Standard MCC8.SP.3 Use the equation of a linear model to solve problems

in the context of bivariate measurement data,

interpreting the slope and y-intercept.



Linear Equation- a function that produces a line on a coordinate

grid

Linear Model- representing a situation with a line on a graph

Slope- rate of change; rise over run; initial value; beginning point

y-Intercept- the location where a line crosses the y axis

Equation:

Define the variables.

Identify the slope.

Interpret the slope within the context of the problem.

Identify the y-intercept.

Interpret the y-intercept within the context of the problem.

Equation:

Define the variables.

Identify the slope.

Interpret the slope within the context of the problem.

Identify the y-intercept.

Interpret the y-intercept within the context of the problem.

Adding fertilizer to plants:

Times

fertilizer

was added

Number of

Additional

Blooms

0 0

1 2

2 4

3 6

4 8

On-Demand Movies Viewed

Weeks Since Release

Nu

mb

er o

f V

iew

s (t

ho

usa

nd

s)

20

18

16

14

12

10

8

6

4

2

0 1 2 3 4 5 6


Standard MCC8.SP.4 Understand that patterns of association can also be seen in

bivariate categorical data by displaying frequencies and relative

frequencies in a two-way table; construct and interpret a two-

way table summarizing data on two categorical variables

collected from the same subjects; use relative frequencies

calculated for rows or columns to describe possible association

between the two variables.


Association- a connection or relationship


Categorical Variable- a variable that has a fixed number of

values

Frequency- the number of times a particular items appears in

a set of data

Two-Way Table- used to display data that pertains to two

different categories

Two-way table: Figure Relative Frequency of each:

Student Survey

Student John George Hannah Javon Ciera Leila Nicole Kristin Lily Bryan

Chores Yes Yes No No No Yes Yes Yes No Yes

Allowance Yes Yes No No No Yes Yes No Yes No

Allowance No Allowance Total

Chores

No Chores

Total

Allowance No Allowance Total

Chores

No Chores

Total


UNIT 7


Standard MCC8.EE.8.a Understand that solutions to a system of two linear

equations in two variables correspond to points of

intersection of their graphs, because points of intersection

satisfy both equations simultaneously.


Intersection- the location where two lines cross



grid

Satisfy- to make true

Simultaneous- at the same time

System of Equations- relating two linear equations to each other

Variable- a letter representing a quantity

Given system of equations:

Solve.

Solve the system by graphing each equation.


Standard MCC8.EE.8.b Solve systems of two linear equations in two

variables algebraically, and estimate solutions by

graphing the equations; solve simple cases by

inspection.

Given system of equations: How many solutions does this system have? Justify.

Solve.





grid






Standard MCC8.EE.8.c Solve real-world and mathematical problems leading

to two linear equations in two variables.

Given ordered pairs:

(-1, -3) (2, 3)

Do these lines intersect? If so, at what point?

Equation of the line through the above ordered pairs:

Given ordered pairs:

(-2, 4) (5, -3)

Equation of the line through the above ordered pairs:




Linear Equation- a function that produces a line on a coordinate grid






Standard MCC8.EE.8.c Solve real-world and mathematical problems leading to

two linear equations in two variables.

Description of word problem.

Timothy sold school festival tickets as a fundraiser. Adult and children bought 14 tickets from him. He collected a total of $38 from these ticket sales. Adult tickets cost $4 each, and child tickets cost $1 each.

Create two equations that represent both situations. Solve the system. (You can use any method to solve that you choose.)

What does the answer mean within the context of the problem?


Intersection- the location where two or more lines cross


Linear Equations- a function that produces a line on a

coordinate grid



Documents

CCGPS Review Packet Math 8 - Thomas County Schools Review Packet Math 8 ... Alternate Exterior Angles: a pair of angles on opposite sides of the ... Alternate Interior Angles: