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Transcript
```Eighth Grade Mathematics Curriculum
Month
Standard
Code
September
7.NS.1.a
7.NS.1.b
7.NS.1.c
7.NS.1.d
7.EE.1
Standard
Unit Title: Review of Algebraic
fundamentals
7.NS.1 Apply and extend previous
and subtraction on a horizontal or
vertical number line diagram.
a. Describe situations in which
opposite quantities combine to
make 0.
b. Understand p + q as the number
located a distance |q| from p, in the
positive or negative direction
depending on whether q is positive
or negative. Show that a number
and its opposite have a sum of 0
sums of rational numbers by
describing real-world contexts.
c. Understand subtraction of
p – q = p + (–q). Show that the
distance between two rational
numbers on the number line is the
absolute value of their difference,
and apply this principle in realworld contexts.
Learning Activities
Assessment
 Write variable
expressions for
word phrases
 Use order of
operations with
variables
divide, multiply of
integers
 Evaluate
expressions
 Understand the
basic functions of
calculator and
graphing calculator
 Checkpoint quizzes
 Test
 Teacher
Observation
 Class discussions
 Homework
 Problem of the day
 Journal entry
Interdisciplinary
Connections
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
 Physical
Education and
Health
2.1.8.E.4
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Language Arts
L.8.2.a
L.8.2.c
SL.8.1.d
W.8.1.c
W.8.2.d
 World
Language
7.1.NM.B.2
d. Apply properties of operations as
rational numbers.
7.EE.1 Use properties of
operations to generate equivalent
expressions.
1. Apply properties of operations as
and expand linear expressions with
rational coefficients.
September –
October
8.EE.7.a
8.EE.7.b
A-REI.3
Unit Title: Solving One-Step and
Two-step and Multi-step
Equations and Inequalities
8.EE.7 Analyze and solve linear
equations and pairs of simultaneous
linear equations.
:Solve linear equations in one
variable:
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
 Review key
properties of
identify,
commutative,
associative and
distributive
 Simplify variable
expressions
 Solve one step
equations by
subtraction
 Solve one step
equations by
multiplying or
dividing
 Solve inequalities
subtracting
 Solve inequalities
by multiplying or
 Daily Lesson
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Class discussions
 Homework
 Problem of the day
 Journal entry
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
5.2.8.E.1
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
numbers).
b. Solve linear equations with
rational number coefficients,
including equations whose
solutions require expanding
expressions using the distributive
property and collecting like terms.
 Language Arts
L.8.2.a
L.8.2.c
SL.8.1.d
W.8.1.c
W.8.2.d
dividing
 Solve two and
multi step
equations and
inequalities
A-REI.3 Solve equations and
inequalities in one variable
3. Solve linear equations and
inequalities in one variable,
including equations with
coefficients represented by letters.
October
8.NS.1
8.NS.2
8.EE.7.a
8.EE.7.b
A-REI.3
Unit Title: Using Decimals in
Equations
8.NS Know that there are numbers
that are not rational, and
approximate them by rational
numbers.
1. Know that numbers that are not
rational are called irrational.
Understand informally that every
number has a decimal expansion;
for rational numbers show that the
decimal expansion repeats
eventually, and convert a decimal
8.EE.7 Analyze and solve linear
equations and pairs of simultaneous
linear equations.
 Round and
estimate decimals
 Write formulas
 Solve equations
with decimals
 Recognize that
repeating decimals
correspond to
fractions and
determine their
fractional
equivalents
 Construct
meanings for
common irrational
numbers, such pi
and the square root
of 2
 Daily Lesson
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Class discussions
 Homework
 Problem of the day
 Journal entry
 Graphing calculator
activity – Mean and
Median
activity
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
 Technology
8.1.4.A.1
8.1.8.A.4
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Language Arts
L.8.2.a
L.8.2.c
SL.8.1.d
W.8.1.c
W.8.2.d
Solve linear equations in one
variable:
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).
b. Solve linear equations with
rational number coefficients,
including equations whose
solutions require expanding
expressions using the distributive
property and collecting like terms.
A-REI.3 Solve equations and
inequalities in one variable
3. Solve linear equations and
inequalities in one variable,
including equations with
coefficients represented by letters.
November
8.EE.1
8.EE.3
8.EE.4
8.NS.1
8.NS.2
7.NS.3
Unit Title: Factors, Fractions,
and Exponents
8.EE.1 1. Know and apply the
properties of integer exponents to
generate equivalent numerical
 Use exponentiation
to find whole
number powers of
numbers.
 Use and explain
procedures for
 Daily Lesson
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
expressions. For example, 32 × 3–5
= 3–3 = 1/33 = 1/27.
8.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 than the other. For
example, estimate the population of
the United States as 3 × 108 and
the population of the world as 7 ×
109, and determine that the world
population is more than 20 times
larger.
8.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
notation that has been generated by
technology.
8.NS.1 Know that numbers that are
not rational are called irrational.
Understand informally that every
number has a decimal expansion;
for rational numbers show that the
decimal expansion repeats
eventually, and convert a decimal





performing
calculations
subtraction,
multiplication,
division and
exponentiation
with integers and
all number types
Use negative
exponents
Multiply and
divide in scientific
notation
Understand and
use rational and
irrational numbers
Solve least
common multiple
word problems
Find common
factors and prime
factorization of
two or more
numbers





Class discussions
Homework
Problem of the day
Journal entry
Graphing calculator
activity –
Evaluating
expressions
 Calculator –
Scientific Notation
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Social Studies
6.3.8.C.1
 Language Arts
SL.8.1.d
W.8.1.c
W.8.2.d
8.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., π2). For example,
by truncating the decimal expansion of
√2, show that √2 is between 1 and
2, then between 1.4 and 1.5, and
explain how to continue on to get
better approximations.
7.NS Apply and extend previous
understandings of operations with
and divide rational numbers.
3. Solve real-world and
mathematical problems involving
the four
operations with rational numbers
December
January
8.NS.2
8.EE.1
8.EE.7.a
8.EE.7.b
Unit Title: Operations with
Fractions
8.NS Know that there are numbers
that are not rational, and
approximate them by rational
numbers.
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., π2). For example,
by truncating the decimal expansion of √2,
 Compare and order
numbers of all
named types:
rational numbers,
percents,
exponents, and
numbers in
scientific notation
 Find the least
common multiple
 To write fractions
as decimals
 To write
 Daily Lesson
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Class discussions
 Homework
 Problem of the day
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
show that √2 is between 1 and 2, then between
1.4 and 1.5, and explain how to continue on to
get better approximations.
integer exponents.
1. Know and apply the properties of integer
exponents to generate
equivalent numerical expressions. For example,
32 × 3–5 = 3–3 = 1/33 = 1/27.
8.EE.7.a
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).







8.EE.7.b Solve linear equations
with rational number coefficients,
including equations whose
solutions require expanding
expressions using the distributive
property and collecting like terms.
January –
February
8.EE.5
8.EE.8.a
8.EE.8.b
8.EE.8.c
8.F.1
8.F.2
Unit Title: Linear Functions
8.EE.5 Understand the connections
between proportional relationships,
lines, and linear equations.
Graph proportional relationships,

terminating and
repeating decimals
as fractions
subtract fractions
and mixed
numbers
To multiply and
divide fractions
Use dimensional
analysis to convert
units of measure
Solving equations
subtracting
fractions
Solving equations
by multiplying
fractions
Solve multi-step
equations with
fractions and
decimals
To find powers of
products
To find powers of
quotients
 To review the
coordinate plane
 To determine
whether a relation
is a function
 To graph relations
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Language Arts
SL.8.1.d
W.8.1.c
W.8.2.d
 Daily Lesson
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
8.F.3
8.F.4
8.F.5
8.SP.1
8.SP.2
8.SP.3
8.SP.4
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.
8.EE.8 Analyze and solve pairs of
simultaneous linear equations.
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.
b. Solve systems of two linear
equations in two variables
algebraically, and estimate
solutions by graphing the equations.
Solve simple cases by inspection.
For example, 3x + 2y = 5 and 3x +
2y = 6 have no solution because 3x
+ 2y cannot simultaneously be 5
and 6.
c. Solve real-world and
two linear equations in two
variables.
8.F Define, evaluate, and compare
and functions
 To use tables,
graphs, or listed
numerically to
determine the slope
of the function.
 To find solutions
of equations with
two variables
 To graph linear
equations with two
variables
 To find the slope
of a line
 To use slopeintercept form in
graphing a linear
equation
 To write a function
rule for a word
relationship
 To write a function
rule by analyzing a
table or graph
 To interpret and
draw scatter plots
 To use scatter plots
to find trends
 To solve systems
of equations of
linear equations by
graphing
 To solve systems
of linear equations
to solve problems
 To solve systems
of linear
inequalities by





Class discussions
Homework
Problem of the day
Journal
Graphing calculator
activities
 Rap song
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Visual and
Performing
Arts
1.3.8.B.2
1.3.8.B.4
 Language Arts
L.8.2.a
L.8.2.c
SL.8.1.d
W.8.1.c
W.8.2.d
functions.
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.1
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 linear function
represented by a table
of values and a linear function
represented by an algebraic
expression,
determine which function has the
greater rate of change.
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.
For example, the function A = s2
giving the area of a square as a
function
of its side length is not linear
because its graph contains the
points (1,1),
(2,4) and (3,9), which are not on a
straight line.
graphing
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)
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.
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.
8.SP. Investigate patterns of
association in bivariate data.
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.
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.
3. Use the equation of a linear
model to solve problems in the
context of bivariate measurement
data, interpreting the slope and
intercept.
For example, in a linear model for
a biology experiment, interpret a
slope
of 1.5 cm/hr as meaning that an
day is
cm in mature plant height.
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. For example, collect
data from students in your class on
whether or not they have a curfew
on school nights and whether or not
they have assigned chores at home.
Is there evidence that those who
have a curfew also tend to have
chores?
February –
March
8.G.1.a
8.G.1.b
8.G.1.c
8.G.2
8.G.3
8.G.4
8.G.5
Unit Title: Geometry – Spatial
thinking
8.G.1 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.
8.G.2. Understand that a twodimensional 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.
 Identify vertical
angles
 Identify
complementary
angles
 Identify
supplementary
angles
 Identify
corresponding
angles
 Identify missing
measures on a
least two parallel
lines and one
transversal
 To identify
corresponding
parts of congruent
triangles
 To determine
whether triangles
are congruent
 To graph
translations
 To describe
 Daily Lesson
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Class discussions
 Homework
 Problem of the day
 Journal
 Graphing calculator
activities
 “Angle” challenge
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Language Arts
L.8.2.a
L.8.2.c
SL.8.1.d
W.8.1.c
W.8.2.d
8.G.3. Describe the effect of
dilations, translations, rotations,
and reflections on two-dimensional
figures using coordinates.
8.G.4. Understand that a twodimensional 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.
March
8.G.9
7.G.4
7.G.6
8.G.5. Use informal arguments to
establish facts about the angle sum
and exterior angle of triangles,
parallel lines are cut by a
transversal, and the angle-angle
criterion for similarity of
triangles. For example, arrange
three copies of the same triangle so
that the sum of the three angles
appears to form a line, and give an
argument in terms of transversals
why this is so.
Unit Title: Area and Volume
8.G.9 Know the formulas for the
volumes of cones, cylinders, and
spheres and use them to solve real-
translations
 To identify a line
of symmetry
 To graph a
reflection of a
geometric figure
 To graph rotations
 To identify
rotational
symmetry
 To describe the
effect of dilations
on twodimensional
figures using
coordinates
 Find the area and
perimeter of
geometric figures
combining
triangles,
 Daily Lesson
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
world and mathematical problems.
7.G. Solve real-life and
mathematical problems involving
angle measure,
area, surface area, and volume.
4. Know the formulas for the area
and circumference of a circle and
use them to solve problems; give an
informal derivation of the
relationship between the
circumference and area of a circle.
6. Solve real-world and
mathematical problems involving
area, volume and surface area of
two- and three-dimensional objects
composed of triangles,
right prisms.
April - May
8.EE.2
8.G.6
8.G.7
8.G.8
8.NS.1
8.NS.2
Unit Title: Pythagorean
Theorem and Square Roots
integer exponents.
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
parallelograms,
trapezoids, and
circles or parts of
circles
 Review surface
area of prisms,
cylinders, cones,
spheres
 Find the volume of
cones, cylinders,
and spheres
 Use the volume of
cones, cylinders
and spheres to
solve real-world
problems





 To find square
roots of numbers
 To classify real
numbers
 Find square roots
 Find cube roots
 Use the
Pythagorean
Theorem
 Identify special
 Daily Lesson
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Class discussions
 Homework
 Problem of the day
 Journal
Class discussions
Homework
Problem of the day
Journal
Volume Challenge
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Language Arts
L.8.2.a
L.8.2.c
SL.8.1.d
W.8.1.c
W.8.2.d
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
 Science
5.1.8.A.2
number. Evaluate square roots of
small perfect squares and cube
roots of small perfect cubes. Know
that √2 is irrational.
8.NS.1 Know that numbers that are
not rational are called irrational.
Understand informally that every
number has a decimal expansion;
for rational numbers show that the
decimal expansion repeats
eventually, and convert a decimal
expansion which repeats eventually
into a rational number.
8.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.
8.G.6 Explain a proof of the
Pythagorean Theorem and its
converse.
8.G.7 Apply the Pythagorean
Theorem to determine unknown
side lengths
in right triangles in real-world and
mathematical problems in two and
three dimensions.
8.G.8. Apply the Pythagorean
properties of 4545-90 and 30-6090 triangles.
 Use the distance
and midpoint
formulas
 “Tree Angles”
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Language Arts
L.8.2.a
L.8.2.c
SL.8.1.d
W.8.1.c
W.8.2.d
MAY - JUNE
S-CP.1
S-CP.2
S-CP.3
Theorem to find the distance
between two points in a coordinate
system.
Unit Title: Probability
S-CP Understand independence
and conditional probability and
use them to interpret data
S-CP.1. Describe events as subsets
of a sample space (the set of
outcomes) using characteristics (or
categories) of the outcomes, or as
unions, intersections, or
complements of other events (“or,”
“and,” “not”).
S-CP.2. Understand that two events
A and B are independent if the
probability of A and B occurring
together is the product of their
probabilities, and use this
characterization to determine if
they are independent.
S-CP.3. Understand the conditional
probability of A given B as P(A and
B)/P(B), and interpret independence
of A and B as saying that the
conditional probability of A given B
is the same as the probability
of A, and the conditional
probability of B given A is the same
as the probability of B.
JUNE
A-APR.1
Unit Title: Introduction to
 To use a tree
diagram and the
Counting Principle
 To find theoretical
probability by
counting outcomes
 To calculate
probabilities of
independent events
 To calculate
probabilities of
dependent events
 To use
permutations
 To use
combinations
 To find
experimental
probability
 To use simulations
 To choose a
sample for a
survey of
population
 To make estimates
 Daily Lesson
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Class discussions
 Homework
 Problem of the day
 Journal
 Probability activity
 Scientific
Calculator activity
 Graphing
Calculator activity
 Daily Lesson
 Science
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
 Physical
Education
2.5.8.C.1
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Language Arts
L.8.2.a
L.8.2.c
SL.8.1.d
W.8.1.c
W.8.2.d
 Science
Polynomials
A-APR Arithmetic with
Polynomials and Rational
Expressions
Perform arithmetic operations on
polynomials
1. Understand that polynomials
form a system analogous to the
integers, namely, they are closed
subtract, and multiply polynomials
subtracting
polynomials
 Multiplying a
polynomial by a
polynomial
 Multiplying
binomials
Quizzes
 Checkpoint quizzes
 Chapter Test
 Teacher
Observation
 Class discussions
 Homework
 Problem of the day
5.1.8.A.2
5.1.8.B.2
5.1.8.C.2
5.1.8.D.1
5.1.12.D.2
 Physical
Education
2.5.8.C.1
 Technology
8.1.4.A.1
8.1.P.C.1
 21st Century
Life and
Career Skills
9.1.8.A.1
9.1.12.A.1
9.1.4.B.1
9.1.8.B.1
 Language Arts
SL.8.1.d
W.8.1.c
W.8.2.d
```