8th Grade Algebra 1gloucestertownshipschools.entest.org/Math Grade 8ALG.pdf · 2 Math – Algebra 1 Unit 1 – Relationships between Quantities and Reasoning with Equations Standards

Gloucester Township Public Schools

Math Curriculum

8th

Grade Algebra 1

Overview

Mathematics is a universal language enmeshed in both the everyday experiences of human society and the natural world

around us. The Gloucester Township Public School District recognizes that mathematics is a fluid and intricately connected

web of conceptual understandings, as opposed to segmented isolated skills and arbitrary units of study.

A nation that trains and prepares students to become mathematically literate problem solvers is an entity that sends

citizens into the workforce ready to compete in a global economy laden with technology and problem solving opportunities. A

school district that intends to have an accomplished field of mathematicians, engineers, medical professionals, scientists, and

innovative entrepreneurs must plan and prepare standards-based curriculum that adheres to the Common Core Standards,

includes 21st Century technology skills, and explores the variety of careers steeped in mathematics.

In consideration of the rigor and depth of mastery needed by students in our Nation's public school system, we have

constructed the following curriculum guide and supporting documentation for Gloucester Township Public Schools through

adoption of the New Jersey Department of Education Model Curriculum for Mathematics. Every student in our schools shall

have the opportunity to become engaged in an enriching, real world approach to mathematics instruction that is based on solid

educational research and data-driven instruction.

Benchmark and Cross Curricular Key

__Red: ELA

__ Blue: Math

__ Green: Science

__ Orange: Social Studies

__ Purple: Related Arts

__ Yellow: Benchmark Assessment

2

Math – Algebra 1

Unit 1 – Relationships between Quantities and Reasoning with Equations

Standards Topics Activities Resources Assessments N.Q.1 Use units as a way to understand

problems and to guide the solution of multi-

step problems; choose and interpret units

consistently in formulas; choose and

interpret the scale and the origin in graphs

and data displays

Conversions STEM Projects

Unit Projects

Geometer’s Sketchpad

Real-World Math

Throughout text

-STAR Math

Chapter Test: 2A, 2B,

2C, or 2D

All Chapter Quizzes

N.Q.2 Define appropriate quantities for the

purpose of descriptive modeling 8.G.2

Units of Measurement Extend 2.6

-STAR Math


2C, or 2D

All Chapter Quizzes

N.Q.3 Choose a level of accuracy

appropriate to limitations on measurement

when reporting quantities.

Precision

Extend 1.3 -STAR Math


2C, or 2D

All Chapter Quizzes

A.SSE.1 Interpret expressions that represent

a quantity in terms of its context.*

a. Interpret parts of an expression, such as

terms, factors, and coefficients.

*Adding and Subtracting

Polynomials

1.1

1.4

-STAR Math


2C, or 2D

All Chapter Quizzes

A.SSE.1 Interpret expressions that represent

a quantity in terms of its context.*

b. Interpret complicated expressions by

viewing one or more of their parts as single

entity. For example, interpret P(1 + r)n as

the product of P and a factor not depending

on P.

*A.SSE.1: Focus on linear, quadratic, and

an introduction to exponential expressions.

*Dividing Monomials 1.2

1.3

9.7

-STAR Math


2C, or 2D

All Chapter Quizzes

A.CED.1 Create equations and inequalities *Using Equations to Solve 1.5, 2.1, 2.2, 2.3, 2.4, -STAR Math

3

in one variable and use them to solve

problems. Include equations arising from

linear functions.

**A.CED.1: Limit to linear or quadratic

equations.

Problems

*Problem Solving Using

Charts

*Cost, Income, and Value

Problems

*Rate-Time-Distance

Problems

*Area Problem

2.5, 2.9, 3.2, 5.1, 5.2,

5.3, 5.4, 5.5, 7.6, 8.5,

8.6, 8.7, 9.4, 9.5, 10.4,

11.8


2C, or 2D

All Chapter Quizzes

A.CED.2 Create equations in two or more

variables to represent relationships between

quantities; graph equations on coordinate

axes with labels and scales.

*The Graphing Method

*Problem Solving with

Systems of Equations

Extend 1.7 3.1, 3.4, 3.5, 3.6, 4.1,

4.2, 4.3, 4.4, 4.5, 4.6,

4.7, 6.1, 6.2, 6.3, 6.4,

6.5, 7.5, 7.5, 8.6, 8.7,

8.8, 9.1, 9.2, 9.4, 9.5,

10.1, 10.4, 11.2, 11.8

-STAR Math


2C, or 2D

All Chapter Quizzes

A.CED.3 Represent constraints by

equations or inequalities, and by systems of

equations and/or inequalities, and interpret

solutions as viable or non-viable options in a

modeling context. For example, represent

inequalities describing nutritional and cost

constraints on combinations of different

foods.

*Problems Without

Solutions

*Solving Problems

Involving Inequalities

*Inequalities in Two

Variables

*Systems of Linear

equations

*Linear Program

4.2

5.6

6.1

6.2

-STAR Math


2C, or 2D

All Chapter Quizzes

A.CED.4 Rearrange formulas to highlight a

quantity of interest, using the same

reasoning as in solving equations. For

example, rearrange Ohm’s laws V= IR to

highlight resistance R.

***A.CED.4: Exclude cases that require

extraction of roots or inverse functions.

*Transforming Formulas 2.8

4.1

-STAR Math


2C, or 2D

All Chapter Quizzes

A.REI.1 Explain each step in solving a

simple equation as following from the

equality of numbers asserted at the previous

step, starting from the assumption that the

*Transforming Equations:

Addition and Subtraction

*Multiplication and Division

*Using Several

1.5, 2.2, 2.3, 2.4, 2.5,

2.6, 2.9, 8.6, 8.7, 8.9

-STAR Math


2C, or 2D

4

original equation has a solution. Construct a

viable argument to justify a solution

method.

Transformations

*Proof in Algebra

All Chapter Quizzes

A.REI.3 Solve linear equations and

inequalities in one variable, including

equations with coefficients represented by

letters.

*Transforming Equations:

Addition and Subtraction

*Multiplication and Division

*Using Several

Transformations

*Solving Inequalities

*Solving Problems

Involving Inequalities

Explore 2.2

Explore 2.3

Explore 5.2

1.5, 2.2, 2.3, 2.4, 2.5,

2.6, 2.7, 2.8, 2.9, 5.1,

5.2, 5.3, 5.4, 5.5

-STAR Math


2C, or 2D

All Chapter Quizzes

5

Math – Algebra 1

Unit 2- Linear Relationships

Standards Topics Activities Resources Assessments N-RN.1. Explain how the definition of the

meaning of rational exponents follows from

extending the properties of integer

exponents to those values, allowing for a

notation for radicals in terms of rational

exponents. For example, we define 𝟓𝟏

𝟑 to be

the cube root of 5 because we want (𝟓𝟏

𝟑)𝟑

=

𝟓(

𝟏

𝟑)(𝟑)

to hold, so (𝟓𝟏

𝟑)𝟑

must equal 5.

*Fractional Exponents STEM Projects

Unit Projects


Real-World Math

7.3 -STAR Math


2C, or 2D

All Chapter Quizzes

N-RN.2. Rewrite expressions involving

radicals and rational exponents using the

properties of exponents.


Radicals

Extend 10.3 7.3

10.3

-STAR Math


2C, or 2D

All Chapter Quizzes

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.

*The graphing Method -STAR Math


2C, or 2D

All Chapter Quizzes


simultaneous linear equations.

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.

*The graphing Method

* The Substitution Method

*The Addition-or

Subtraction Method

*Multiplication with the

Addition-or-Subtraction

Method

-STAR Math


2C, or 2D

All Chapter Quizzes

6


simultaneous linear equations

c. Solve real-world and mathematical

problems leading to two linear equations in

two variables. For example, given

coordinates for two pairs of points,

determine whether the line through the first

pair of points intersects the line through the

second pair.

*Solving Problems with

Two Variables


Addition-or Subtraction

Method

-STAR Math


2C, or 2D

All Chapter Quizzes

A.REI.5 Prove that, given a system of two

equations in two variables, replacing one

equation by the sum of that equation and a

multiple of the other produces a system with

the same solutions.



Method

6.4 -STAR Math


2C, or 2D

All Chapter Quizzes

A.REI.6 Solve systems of linear equations

exactly and approximately (e.g., with

graphs), focusing on pairs of linear

equations in two variables.


*The Substitution Method

* Addition-or Subtraction

Method



Method

Extend 6.1

Extend 6.5

6.1

6.2

6.3

6.4

6.5

-STAR Math


2C, or 2D

All Chapter Quizzes

A.REI.10 Understand that the graph of an

equation in two variables is the set of all its

solutions plotted in the coordinate plane,

often forming a curve (which could be a

line).

*Equations in Two Variable

*Points, Lines, and Their

Graphs

1.6, 1.7, 3.1, 3.2, 3.4,

7.5, 9.1, 10.1

-STAR Math


2C, or 2D

All Chapter Quizzes

A.REI.11 Explain why the x-coordinates of

the points where the graphs of the equations

y = f(x) and y = g(x) intersect are the

solutions of the equation f(x) = g(x); find

the solutions approximately, e.g., using

technology to graph the functions, make

tables of values, or find successive

approximations. Include cases where f(x)

and/or g(x) are linear, polynomial, rational,

absolute value, exponential, and logarithmic


*The Graph of

𝑦 = |𝑎𝑥 + 𝑏| + 𝑐

Extend 6.1

Extend 7.5

Extend 9.3

Extend 11.8

-STAR Math


2C, or 2D

All Chapter Quizzes

7

functions.

A.REI.12 Graph the solutions to a linear

inequality in two variables as a half-plane

(excluding the boundary in the case of a

strict inequality), and graph the solution set

to a system of linear inequalities in two

variables as the intersection of the

corresponding half-planes.

*Inequalities in two

Variables

*Systems of Linear

Inequalities

Extend 5.6

Extend 6.6

5.6

6.6

-STAR Math


2C, or 2D

All Chapter Quizzes

8.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.

*Functions Defined by

Tables and Graphs


Equations

-STAR Math


2C, or 2D

All Chapter Quizzes

8.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 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.

*Comparing Functions -STAR Math


2C, or 2D

All Chapter Quizzes

8.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. 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.

-STAR Math


2C, or 2D

All Chapter Quizzes

F.IF.1 Understand that a function from one

set (called the domain) to another set (called

the range) assigns to each element of the


Tables and Graphs

1.7 -STAR Math


8

domain exactly one element of the range. If

f is a function and x is an element of its

domain, then f(x) demotes the output of f

corresponding to the input x. The graph of

f is graph of the y = f(x).


Equations

2C, or 2D

All Chapter Quizzes

F.IF.2 Use function notation, evaluate

functions for inputs in their domains, and

interpret statements that use function

notation in terms of a context.

1.7 -STAR Math


2C, or 2D

All Chapter Quizzes

F.IF.3 Recognize that sequences are

functions, sometimes defined recursively,

whose domain is subset of the integers. For

example, the Fibonacci sequence is defined

recursively by f(0) = f(1) = 1 f(n+1) = f(n)

+ f(n-1) for n ≥ 1.

3.5

7.7

7.8

-STAR Math


2C, or 2D

All Chapter Quizzes

8.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.

*Slope of a Line

*Interpret Rate of Change

-STAR Math


2C, or 2D

All Chapter Quizzes

8.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.

-STAR Math


2C, or 2D

All Chapter Quizzes

9

F-IF.4. For a function that models a

relationship between two quantities,

interpret key features of graphs and tables in

terms of the quantities, and sketch graphs

showing key features given a verbal

description of the relationship. Key features

include: intercepts; intervals where the

function is increasing, decreasing, positive,

or negative; relative maximums and

minimums; symmetries; end behavior; and

periodicity.

Explore 3.1

Extend 4.1

1.8

3.1

7.5

9.1

9.7

10.1

-STAR Math


2C, or 2D

All Chapter Quizzes

F.IF.5 Relate the domain of a function to

its graph and, where applicable, to the

quantitative relationship it describes. For

example, if the function h(n) gives the

number of person-hours it takes to assemble

n engines in a factory, then the positive

integers would be an appropriate domain for

the function.*

1.7

7.5

7.6

9.1

10.1

-STAR Math


2C, or 2D

All Chapter Quizzes

F-IF.6. Calculate and interpret the average

rate of change of a function (presented

symbolically or as a table) over a specified

interval. Estimate the rate of change from a

graph.

Explore 3.3

Extend 7.7

Explore 9.1

3.3 -STAR Math


2C, or 2D

All Chapter Quizzes

F-IF.7. Graph functions expressed

symbolically and show key features of the

graph, by hand in simple cases and using

technology for more complicated cases.

a. Graph linear and quadratic functions and

show intercepts, maxima, and minima.

*Linear and Quadratic

Functions

Extend 3.2

Extend 4.1

Explore 9.3

Extend 9.3

3.1

3.2

3.4

4.1

9.1

9.3

-STAR Math


2C, or 2D

All Chapter Quizzes

F-IF.7. Graph functions expressed

symbolically and show key features of the

graph, by hand in simple cases and using

technology for more complicated cases.

b. Use the properties of exponents to

Extend 3.2

Extend 4.1

Explore 9.3

Extend 9.3

3.1

3.2

3.4

4.1

9.1

-STAR Math


2C, or 2D

10

interpret expressions for exponential

functions. For example, identify percent rate

of change in functions such as y = (1.02)t, y

= (0.97)t, y = (1.01)12t, y = (1.2)t/10, and

classify them as representing exponential

growth or decay.

9.2

9.3

All Chapter Quizzes

F.IF.9 Compare properties of two functions

each represented in a different way

(algebraically, graphically, numerically in

tables, or by verbal descriptions). For

example, given a graph of one quadratic

function and an algebraic expression for

another, say which has the larger maximum.

1.7

3.6

4.3

7.8

9.1

9.3

-STAR Math


2C, or 2D

All Chapter Quizzes

F.BF.1 Write a function that describes a

relationship between two quantities.

-a-Determine an explicit expression, a

recursive process, or steps for calculation

from a context.

1.7, 3.1, 3.4, 3.6, 4.1,

4.2, 4.3, 4.4, 4.5, 4.6,

4.7, 7.6, 7.8

-STAR Math


2C, or 2D

All Chapter Quizzes

F.BF.1 Write a function that describes a

relationship between two quantitites.*

-b-Combine standard function types using

arithmetic operations. For example, build a

function that models the temperature of a

cooling body by adding a constant function

to a decaying exponential, and relate these

functions to the model.

4,2

7,6

9.3

-STAR Math


2C, or 2D

All Chapter Quizzes

F-BF.2. Write arithmetic and geometric

sequences both recursively and with an

explicit formula, use them to model

situations, and translate between the two

forms.

7.8 -STAR Math


2C, or 2D

All Chapter Quizzes

F.BF.3 Identify the effect on the graph of Extend 4.1 -STAR Math

11

replacing f(x) by f(x)+k, k f(x), f(kx), and

f(x+k) for specific values of k (both positive

and negative); find the value of k given the

graphs. Experiment with cases and illustrate

an explanation of the effects on the graph

using technology. Include recognizing even

and odd functions from their graphs and

algebraic expressions for them.

Explore 7.5

Explore 9.3


2C, or 2D

All Chapter Quizzes

F-LE.1. Distinguish between situations that

can be modeled with linear functions and

with exponential functions.

3. Prove that linear functions grow

by equal differences over equal

intervals, and that exponential

functions grow by equal factors

over equal intervals.

3.3

3.5

7.7

9.6

-STAR Math


2C, or 2D

All Chapter Quizzes




b. Recognize situations in which one

quantity changes at a constant rate per unit

interval relative to another.

3.5

3.6

9.6

-STAR Math


2C, or 2D

All Chapter Quizzes




c. Recognize situations in which a quantity

grows or decays by a constant percent rate

per unit interval relative to another.

9.6 -STAR Math


2C, or 2D

All Chapter Quizzes

F-LE.2. Construct linear and exponential

functions, including arithmetic and

geometric sequences, given a graph, a

description of a relationship, or two input-

output pairs (include reading these from a

table).

3.5

3.6

7.5

7.6

7.7

-STAR Math


2C, or 2D

All Chapter Quizzes

12

F.LE.3 Observe using graphs and tables that

a quantity increasing exponentially

eventually exceeds a quantity increasing

linearly, quadratically, or (more generally)

as a polynomial function.

9.6 -STAR Math


2C, or 2D

All Chapter Quizzes

F.LE.5 Interpret the parameters in a linear

or exponential function in terms of a

context.

Extend 4-1 3.4

4.1

7.5

7.6

-STAR Math


2C, or 2D

All Chapter Quizzes

13

Math – Algebra 1

Unit 3- Descriptive Statistics

Standards Topics Activities Resources Assessments S-ID.1. Represent data with plots on the real

number line (dot plots, histograms, and box

plots).

*Statistics STEM Projects

Unit Projects


Real-World Math

12.3

12.4

-STAR Math


2C, or 2D

All Chapter Quizzes

S-ID.2 Use statistics appropriate to the

shape of the data distribution to compare

center (median, mean) and spread

(interquartile range, standard deviation) of

two or more different data sets.

*Statistics Extend 12.8 12.3

12.4

-STAR Math


2C, or 2D

All Chapter Quizzes

S-ID.3. Interpret differences in shape,

center, and spread in the context of the data

sets, accounting for possible effects of

extreme data points (outliers).

12.3

12.4

-STAR Math


2C, or 2D

All Chapter Quizzes

8.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.

-STAR Math


2C, or 2D

All Chapter Quizzes

8.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.

-STAR Math


2C, or 2D

All Chapter Quizzes

14

8.SP.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

additional hour of sunlight each day is

associated with an additional 1.5 cm in

mature plant height.

-STAR Math


2C, or 2D

All Chapter Quizzes

8.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. 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?

-STAR Math


2C, or 2D

All Chapter Quizzes

S-ID.5. Summarize categorical data for two

categories in two-way frequency tables.

Interpret relative frequencies in the context

of the data (including joint, marginal, and

conditional relative frequencies). Recognize

possible associations and trends in the data.



2C, or 2D

All Chapter Quizzes

S-ID.6. Represent data on two quantitative

variables on a scatter plot, and describe how

the variables are related.

a. Fit a function to the data; use functions

fitted to data to solve problems in the

Extend 9.6 4.5

4.6

-STAR Math


2C, or 2D

15

context of the data. Use given functions or

chooses a function suggested by the context.

Emphasize linear, quadratic, and

exponential models.

All Chapter Quizzes




b. Informally assess the fit of a function by

plotting and analyzing residuals.

4.6 -STAR Math


2C, or 2D

All Chapter Quizzes




c. Fit a linear function for a scatter plot that

suggests a linear association.

4.5

4.6

-STAR Math


2C, or 2D

All Chapter Quizzes

S-ID.7. Interpret the slope (rate of change)

and the intercept (constant term) of a linear

model in the context of the data.

Extend 4.1 4.1 -STAR Math


2C, or 2D

All Chapter Quizzes

S-ID.8. Compute (using technology) and

interpret the correlation coefficient of a

linear fit.

4.6 -STAR Math


2C, or 2D

All Chapter Quizzes

S-ID.9. Distinguish between correlation and

causation.



2C, or 2D

All Chapter Quizzes

16

Math – Algebra 1

Unit 4 – Expressions and Equations

Standards Topics Activities Resources Assessments A.SSE.1 Interpret

expressions that represent a

quantity in terms of its

context*

a. Interpret parts of an

expression, such as terms,

factors, and coefficients.


Polynomials

*Factoring Integers

STEM Projects

Unit Projects


Real-World Math

1.1

1.4

-STAR Math

Chapter Test: 2A, 2B, 2C, or

2D

All Chapter Quizzes

A.SSE.1 Interpret

expressions that represent a

quantity in terms of its

context*

b. Interpret complicated

expressions by viewing one

or more of their parts as a

single entity. For example,

interpret P(1 + r)n as the

product of P and a factor not

depending on P.

*Multiplying Monomials

*Dividing Monomials

1.2

1.3

9.7

-STAR Math


2D

All Chapter Quizzes

A.SSE.2 Use the structure of

an expression to identify

ways to rewrite it. For

example, see x4 – y

4 as (x

2)

2

– (y2)

2, thus recognizing it as

a difference of squares that

can be factored as (x2 – y

2)(x

2

+ y2).

*Monomial Factors of

Polynomials

*Difference of Two Squares

*Squares of Binomials

Explore 8.5

Explore 8.6

1.1, 1.2, 1.3, 1.4, 7.1, 7.2,

7.3, 7.4, 8.5, 8.6, 8.7, 8.8, 8.9

-STAR Math


2D

All Chapter Quizzes

A.SSE.3 Choose and

produce an equivalent form

*Solving Equations by

Factoring

8.5

8.6

-STAR Math

17

of an expression to reveal

and explain properties of the

quantity represented by the

expression.

a. Factor a quadratic

expression to reveal the zeros

of the function it defines.

8.7

8.8

8.9


2D

All Chapter Quizzes

A.SSE.3 Choose and





expression.

b. Complete the square in a

quadratic expression to

reveal the maximum or

minimum value of the

function it defines.


Functions

*Completing the Square

Extend 9.4 9.3

9.4

-STAR Math


2D

All Chapter Quizzes

A.SSE.3 Choose and





expression.

c. Use the properties of

exponents to transform

expressions for exponential

functions. For example the

expression 1.15t can be

rewritten as (1.151/12)12t ≈



2D

All Chapter Quizzes

18

1.01212t to reveal the

approximate equivalent

monthly interest rate if the

annual rate is 15%

A.APR.1 Understand that

polynomials form a system

analogous to the integers,

namely, they are closed

under the operations of

addition, subtraction, and

multiplication; add, subtract,

and multiply polynomials.

*Basic Assumptions Explore 8.1

Explore 8.3

8.1

8.2

8.3

8.4

-STAR Math


2D

All Chapter Quizzes

A.CED.1 Create equations

and inequalities in one

variable and use them to

solve problems. Include

equations arising from linear

and quadratic functions, and

simple rational and

exponential functions

*A Problem Solving Plan

*Solving Linear Equations

and Problem Solving with

Linear Equations

*Solve Problems Involving

Inequalities

*Solving Problems Involving

Quadratic Equations

1.5, 2.1, 2.2, 2.3, 2.4, 2.5,

2.9, 3.2, 5.1, 5.2, 5.3, 5.4,

5.5, 7.6, 8.5, 8.6, 8.7, 9.4,

9.5, 10.4, 11.8

-STAR Math


2D

All Chapter Quizzes

A.CED.2 Create equations in

two or more variables to

represent relationships

between quantities; graph

equations on coordinate axes

with labels and scales.

*Problem Solving with

Systems of Equations

Extension 1.7

3.1, 3.4, 3.5, 3.6, 4.1, 4.2,

4.3, 4.4, 4.5, 4.6, 4.7, 6.1,

6.2, 6.3, 6.4, 6.5, 7.5, 7.6,

8.6, 8.7, 8.8, 9.1, 9.2, 9.4,

9.5, 10.1, 10.4, 11.2, 11.8

-STAR Math


2D

All Chapter Quizzes

A.CED.4 Rearrange

formulas to highlight a

quantity of interest, using the

same reasoning as in solving

equations. For example,

rearrange OHM’s law V= IR

to highlight resistance R.

*Transforming Formulas

2.8

4.1

-STAR Math


2D

All Chapter Quizzes

19

A.REI.4 Solve quadratic

equations in one variable.

a. Use the method of

completing the square to

transform any quadratic

equation in x into an

equation of the form (x – p)2

= q that has the same

solutions. Derive the

quadratic formula for this

form.


*Methods of Solution

9.4

10.2

-STAR Math


2D

All Chapter Quizzes

A.REI.4 Solve quadratic

equations in one variable.

b. Solve quadratic equations

by inspection (e.g., for x2 =

49), taking square roots,

completing the square, the

quadratic formula and

factoring, as appropriate to

the initial form of the

equation. Recognize when

the quadratic formula gives

complex solutions and

write them as a ± bi for real

numbers a and b.

*Square Roots of Variable

Expressions

*Quadratic Equations with

Perfect Squares


*The Quadratic Formula

*Complex Numbers

Solving Equations by

Factoring

*Methods of Solution

8.6

8.7

8.8

9.2

9.4

9.5

-STAR Math


2D

All Chapter Quizzes

A.REI.7 Solve a simple

system consisting of linear

equation and quadratic

equation in two variables

algebraically and graphically.

For example, find the points

of intersection between the

line y = -3x and the circle x2

+ y2 = 3.



2D

All Chapter Quizzes

20

Math – Algebra 1

Unit 5 – Quadratic Functions and Modeling Standards Topics Activities Resources Assessments

N.RN.3 Explain why the

sum or product of two

rational numbers is rational;

that the sum of a rational

number and an irrational

number is irrational; and that

the product of a non-zero

rational number and an

irrational number is

irrational.

STEM Projects

Unit Projects


Real-World Math

Extension 10.2

-STAR Math


2D

All Chapter Quizzes

8.G.6 Explain a proof of the

Pythagorean Theorem and its

converse.

*The Pythagorean Theorem -STAR Math


2D

All Chapter Quizzes

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.



2D

All Chapter Quizzes

8.G.8

Apply the Pythagorean

Theorem to find the distance

between two points in a

coordinate system.



2D

All Chapter Quizzes

21

F.IF.4 For a function that

models a relationship

between two quantities,

interpret key features of

graphs and tables in terms of

the quantities, and sketch

graphs showing key features

given a verbal description of

the relationship. Key

features include: intercepts;

intervals where the function

is increasing, decreasing,

positive or negative; relative

maximums and minimums;

symmetries; end behavior;

and periodicity.

Explore 3.1

Extend 4.1

1.8

3.1

7.5

9.1

9.7

10.1

-STAR Math


2D

All Chapter Quizzes

F.IF.5 Relate the domain of

a function to its graph and,

where applicable, to the

quantitative relationship it

describes. For example, if

the function h(n) gives the

number of person-hours it

takes to assemble n engines

in a factory, then the positive

integers would be an

appropriate domain for the

function.*

1.7

7.5

7.6

9.1

10.1

-STAR Math


2D

All Chapter Quizzes

F.IF.6 Calculate and

interpret the average rate of

change of a function

(presented symbolically or as

a table) over a specified

interval. Estimate the rate of

change from a graph.

Explore 3.3

Extend 7.7

Extend 9.1

3.3 -STAR Math


2D

All Chapter Quizzes

F.IF.7 Graph functions

expressed symbolically and

show key features of the

graph, by hand in simple

*Points, Lines, and Their

Graphs

*Slope of a Line

Extend 3.2

Extend 4.1

Explore 9.3

Extend 9.3

3.1

3.2

3.4

4.1

-STAR Math


2D

22

cases and using technology

for more complicated cases.

-a-Graph linear and

quadratic functions and show

intercepts, maxima and

minima

*Slope-Intercept Form of a

Linear Equation

Linear and Quadratic

Functions

9.1

9.2

9.3

All Chapter Quizzes

F.IF.7 Graph functions

expressed symbolically and

show key features of the

graph, by hand in simple

cases and using technology

for more complicated cases.

-b-Graph square root, cube

root, and piecewise-defined

functions, including step

functions and absolute value

functions. Exponential,

growth or decay.

Extend 9.7

Extend 10.1

9.7

10.1

-STAR Math


2D

All Chapter Quizzes

F-IF.8. Write a function

defined by an expression in

different but equivalent

forms to reveal and explain

different properties of the

function.

a. Use the process of

factoring and completing the

square in a quadratic

function to show zeros,

extreme values, and

symmetry of the graph, and

interpret these in terms of a

context.

*Solving Equations by

Factoring


Functions


Extend 9.4 9.2

9.4

-STAR Math


2D

All Chapter Quizzes

F-IF.8. Write a function

defined by an expression in

different but equivalent

forms to reveal and explain

different properties of the

function.

b. Use the properties of



2D

All Chapter Quizzes

23

exponents to interpret

expressions for exponential

functions. For example,

identify percent rate of

change in functions such as y

= (1.02)t, y = (0.97)t, y =

(1.01)12t, y = (1.2)t/10, and

classify them as representing

exponential growth or decay.

F.IF.9 Compare properties

of two functions each

represented in a different

way (algebraically,

graphically, numerically in

tables, or by verbal

descriptions). For example,

given a graph of one

quadrant function and an

algebraic expression for

another say which has the

larger maximum.

1.7

3.6

4.3

7.8

9.1

9.3

-STAR Math


2D

All Chapter Quizzes

F.BF.1 Write a function that

describes a relationship

between two quantities.

-a-Determine an explicit

expression, a recursive

process, or steps for

calculation from a context.

1.7, 3.1, 3.4, 3.6, 4.1, 4.2,

4.3, 4.4, 4.5, 4.5, 4.7, 7.6, 7.8

-STAR Math


2D

All Chapter Quizzes

F.BF.1 Write a function that

describes a relationship

between two quantities.

-b-Combine standard

function types using

arithmetic operations. For

example, build a function

that models the temperature

of a cooling body by adding

a constant function to a

decaying exponential, and

4.2

7.6

9.3

-STAR Math


2D

All Chapter Quizzes

24

relate these functions to the

model.

F.BF.3 Identify the effect on

the graph of replacing f(x)

by f(x)+k, k f(x), f(kx), and

f(x+k) for specific values of

k (both positive and

negative); find the value of k

given the graphs.

Experiment with cases and

illustrate an explanation of

the effects on the graph

using technology. Include

recognizing even and odd

functions from their graphs

and algebraic expressions for

them.

Extend 4.1

Explore 7.5

Explore 9.3

-STAR Math


2D

All Chapter Quizzes

F.BF.4 Find inverse

functions.

-a-solve an equation of the

form f(x) = c for a simple

function f that has an inverse

and write an expression for

the inverse. For example,

f(x)=2x3 or f(x)=(x+1)/(x-1)

for x≠1

Explore 10.1

4.7

-STAR Math


2D

All Chapter Quizzes

F.LE.3 Observe using

graphs and tables that a

quantity increasing

exponentially eventually

exceeds a quantity increasing

linearly, quadratically, or

(more generally) as a

polynomial function.

9.6

-STAR Math


2D

All Chapter Quizzes

25

Appendix A

Adaptations for Special Education Students, English Language Learners, and Gifted and Talented Students

Making Instructional Adaptations

Instructional Adaptations include both accommodations and modifications.

An accommodation is a change that helps a student overcome or work around a disability or removes a barrier to learning for

any student.

Usually a modification means a change in what is being taught to or expected from a student.

-Adapted from the National Dissemination Center for Children with Disabilities

ACCOMMODATIONS MODIFICATIONS

Required when on an IEP or 504 plan, but can be implemented for any student to support their learning.

Only when written in an IEP.

Special Education Instructional Accommodations

Teachers will use Approaching Level Tier 2: Strategic Intervention in RtI Differentiated Instruction section of Glencoe

lessons.

Teachers will use the Targeted Strategic Intervention from the Glencoe Online Support.

Teachers shall implement any instructional adaptations written in student IEPs.

Teachers will implement strategies for all Learning Styles (Appendix B)

Teacher will implement appropriate UDL instructional adaptations (Appendix C )

26

Gifted and Talented Instructional Accommodations

Teachers will use Beyond Level in RtI Differentiated Instruction section of Glencoe lessons

Teachers will use the Enrichment Masters from the Glencoe Online Support

Teacher will implement Adaptations for Learning Styles (Appendix B)

Teacher will implement appropriate UDL instructional adaptations (Appendix C)

English Language Learner Instructional Accommodations

Teachers will use the ELL Differentiated English Language Learner Support section of Glencoe lessons.

Teachers will use the Differentiated ELL Support from the Glencoe Online Support.

Teachers will implement the appropriate

Teachers will implement the appropriate instructional adaptions for English Language Leaners (Appendix E)

27

APPENDIX B

Learning Styles Aadapted from The Learning Combination Inventories (Johnson, 1997)and VAK (Fleming, 1987)

Accommodating Different Learning Styles in the Classroom: All learners have a unique blend of sequential, precise, technical, and confluent learning styles. Additionally, all learners have a preferred mode of processing information- visual, audio, or kinesthetic. It is important to consider these differences when lesson planning, providing instruction, and when differentiating learning activities. The following recommendations are accommodations for learning styles that can be utilized for all students in your class. Since all learning styles may be represented in your class, it is effective to use multiple means of presenting information, allow students to interact with information in multiple ways, and allow multiple ways for students to show what they have learned when applicable.

Visual Utilize Charts, graphs, concept maps/webs, pictures, and cartoons Watch videos to learn information and concepts Encourage students to visualize events as they read math word problems Use flash cards to practice basic math facts Model by demonstrating tasks or showing a finished product Have written directions available for student Use power point presentations

28

Color code and highlight operation symbols (+, -, x, ÷) Color code and highlight key words in math word problems

Audio Allow students to give oral presentations or explain concepts verbally Present information and directions verbally or encourage students to read directions aloud to themselves. Allow students to work in pairs Utilize songs and rhymes Ask for choral responses in instruction, example have the entire class chant in unison multiples, evens/odds, or skip counting by 2s, 5,s or 10s Repeat, clarify, or reword directions Verbally guide students through task steps

Kinesthetic Act out concepts and dramatize events Use flash cards Use manipulatives Allow students to deepen knowledge through hands on projects

Sequential: following a plan. The learner seeks to follow step-by-step directions, organize and plan

work carefully, and complete the assignment from beginning to end without interruptions. Accommodations: Repeat/rephrase directions Provide a checklist or step by step written directions Break assignments in to chunks

29

Provide samples of desired products

Help the sequential students overcome these challenges: over planning and not finishing a task, difficulty reassessing and improving a plan, spending too much time on directions and neatness and overlooking concepts

Precise: seeking and processing detailed information carefully and accurately. The learner takes detailed

notes, asks questions to find out more information, seeks and responds with exact answers, and reads and writes in a highly specific manner. Accommodations: Provide detailed directions for assignments Provide checklists Provide frequent feedback and encouragement

Help precise students overcome these challenges: overanalyzing information, asking too many questions, focusing on details only and not concepts

Technical: working autonomously, "hands-on," unencumbered by paper-and-pencil requirements. The

learner uses technical reasoning to figure out how to do things, works alone without interference, displays knowledge by physically demonstrating skills, and learns from real-world experiences Accommodations: Allow to work independently or as a leader of a group Give opportunities to solve problems and not memorize information Plan hands-on tasks Explain relevance and real world application of the learning Will be likely to respond to intrinsic motivators, and may not be motivated by grades

Help technical students overcome these challenges: may not like reading or writing, difficulty remaining focused while seated, does not see the relevance of many assignments, difficulty paying attention to lengthy directions or lectures

Confluent: avoiding conventional approaches; seeking unique ways to complete any learning task. The

learner often starts before all directions are given; takes a risk, fails, and starts again; uses imaginative ideas and unusual approaches; and improvises. Accommodations: Allow choice in assignments Encourage creative solutions to problems Allow students to experiment or use trial and error approach

30

Will likely be motivated by autonomy within a task and creative assignments

Help confluent students overcome these challenges: may not finish tasks, trouble proofreading or paying attention to detail

31

APPENDIX C

Universal Design for Learning Adaptations

Adapted from Universal Design For Learning

Teachers will utilize the examples below as a menu of adaptation ideas.

Provide Multiple Means of Representation

Strategy #1: Options for perception

Goal/Purpose Examples To present information through different modalities such as vision, hearing, or touch.

Use visual demonstrations, illustrations, and models

Present a power point presentation.

Use appropriate manipulatives, such as base 10 block,

counters, or pattern blocks

Differentiate operation symbols by color coding

Draw pictures when possible

Use interactive websites and apps

Use modeling to help students solve problems

Provide examples of a correctly solved problem at the

32

beginning of each lesson

Have students work each step in a different color

Use songs and rhymes to help remember information

Use mnemonics like “Please Excuse My Dear Aunt Sally”

(order of operations) to remember sequenced steps

Simplify and rephrase vocabulary in word problems

Strategy #2: Options for language, mathematical expressions and symbols

Goal/Purpose Examples To make words, symbols, pictures, and mathematical notation clear for all students.

Use larger font size and/or magnifiers Highlight important parts of problems, example: key words or operation signs Use place value charts, number grids, and operation tables (addition/subtraction and multiplication/division tables) Allow students to trace important visual patterns Use graph paper to keep numbers aligned

33

Put boxes around each problem to visually separate them Simplify and rephrase vocabulary in word problem Turn lined paper vertically so the student has ready made columns Color code and highlight keywords in math word problems

Strategy #3: Options for Comprehension

Purpose Examples To provide scaffolding so students can access and understand information needed to construct useable knowledge.

Use diagrams.

Use semantic maps and diagrams Chunk pieces of information together, example: learn facts in sets of 3 Review previous lessons

34

Use a buddy system to clarify Use mnemonic aids to signal steps, example “Does McDonalds Sell Cheese Burgers” (long division: divide, multiply, subtract, check, bring down) Provide students with a strategy to use for solving word problems Use graph paper to keep numbers aligned Use modeling to help students solve problems Introduce concepts using real life examples whenever possible Teach fact families and build fluency with games and understanding When teaching number lines use tape or draw a number line on the floor for students to walk on

Provide Multiple Means of Action and Expression

Strategy #4: Options for physical action

35

Purpose Examples To provide materials that all learners can physically utilize

Use of computers when available Preferential or alternate seating Provide assistance with organization Provide graph paper to organize place value Provide appropriate manipulatives Use flash cards Provide highlighters for students when solving problems Allow students to use desk top copies of fact sheets, multiplication/division tables etc. Use individual dry-erase boards

Strategy #5: Options for expression and communication

Purpose Examples

36

To allow the learner to express their knowledge in different ways

Allow oral responses or presentations Students show their knowledge with charts and graphs Give students extra time to respond to oral questions Have students verbally or visually explain how to solve a math problem

Strategy #6: Options for executive function

Purpose Examples To scaffold student ability to set goals, plan, and monitor progress

Provide clear learning goals, scales, and rubrics Model skills Utilize checklists Give examples of desired finished product Chunk longer assignments into manageable parts Teach and practice organizational skills Use a problem solving strategy checklist so that students can monitor their progress Teach students to use self-questioning techniques Reduce the number of practice or test problems on a

37

page

Provide Multiple Means of Engagement

Strategy #7: Options for recruiting interest

Purpose Examples To make learning relevant, authentic, interesting, and engaging to the student.

Provide choice and autonomy on assignments Use colorful and interesting designs, layouts, and graphics Use games, challenges, or other motivating activities Provide positive reinforcement for effort Use manipulatives Provide learning aids such as calculators and/or operation tables (addition/subtraction and multiplication/division tables)

38

Introduce concepts using real life examples whenever possible Use individual dry-erase boards Use magnetic manipulatives examples: numbers, operation signs, ten frames, base ten blocks, etc.

Strategy #8: Options for sustaining effort and persistence

Purpose Examples To create extrinsic motivation for learners to stay focused and work hard on tasks.

Show real world applications of the lesson Utilize collaborative learning Assign a peer tutor Incorporate student interests into lesson Praise growth and effort Recognition systems Behavior plans Repeat directions as needed Provide immediate feedback

39

Strategy #9: Options for self-regulation

Purpose Examples To develop intrinsic motivation to control behaviors and to develop self-control.

Give prompts or reminders about self-control Self-monitored behavior plans using logs, records, journals, or checklists Ask students to reflect on behavior and effort Post class rules using pictures and words Post daily schedule using pictures and words Circulate around the room Develop a signal for when a break is needed Provide consistent praise to elevate self-esteem Model and role play problem solving Desensitize students to anxiety causing events

40

Appendix D

Gifted and Talented Instructional Accommodations

How do the State of NJ regulations define gifted and talented students?

Those students who possess or demonstrate high levels of ability, in one or more content areas, when compared to their chronological peers in the local district and who require modification of their educational program if they are to achieve in accordance with their capabilities.

What types of instructional accommodations must be made for students identified as gifted and talented?

The State of NJ Department of Education regulations require that district boards of education provide appropriate K-12 services for gifted and talented students. This includes appropriate curricular and instructional modifications for gifted and talented students indicating content, process, products, and learning environment. District boards of education must also take into consideration the PreK-Grade 12 National Gifted Program Standards of the National Association for Gifted Children in developing programs..

What is differentiation?

Curriculum Differentiation is a process teachers use to increase achievement by improving the match between the learner’s unique characteristics:

Prior knowledge Cognitive Level

Learning Rate Learning Style

Motivation Strength or Interest

And various curriculum components:

Nature of the Objective Teaching Activities

Learning Activities Resources

Products

41

Differentiation involves changes in the depth or breadth of student learning. Differentiation is enhanced with the use of appropriate classroom

management, retesting, flexible small groups, access to support personal, and the availability of appropriate resources, and necessary for gifted

learners and students who exhibit gifted behaviors (NRC/GT, University of Connecticut).

42

43

Gifted & Talented Accommodations Chart

Adapted from Association for Supervision and Curriculum Development

Teachers will utilize the examples below as a menu of adaptation ideas.

Strategy Description Suggestions for Accommodation

High Level Questions

Discussions and tests, ensure the highly able learner is presented with questions that draw on advanced level of information, deeper understanding, and challenging thinking.

Require students to defend answers

Use open ended questions

Use divergent thinking questions

Ask student to extrapolate answers when given incomplete information

Tiered assignments

In a heterogeneous class, teacher uses varied levels of activities to build on prior knowledge and prompt continued growth. Students use varied approaches to exploration of essential ideas.

Use advanced materials

Complex activities

Transform ideas, not merely reproduce them

Open ended activity

Flexible Skills Grouping

Students are matched to skills work by virtue of readiness, not with assumption that all need same spelling task, computation drill, writing assignment, etc. Movement among groups is common, based on readiness on a given skill and growth in that skill.

Exempt gifted learners from basic skills work in areas in which they demonstrate a high level of performance

Gifted learners develop advanced knowledge and skills in areas of talent

Independent Projects

Student and teacher identify problems or topics of interest to student. Both plan method of investigating topic/problem and identifying type of product student will develop. This product should address the problem and demonstrate the student’s ability to apply skills and knowledge to the problem or topic

Primary Interest Inventory

Allow student maximum freedom to plan, based on student readiness for freedom

Use preset timelines to zap procrastination Use process logs to document the process

involved throughout the study

Learning Centers

Centers are “Stations” or collections of materials students can use to explore, extend, or practice skills and content.

Develop above level centers as part of classroom instruction

44

For gifted students, centers should move beyond basic exploration of topics and practice of basic skills. Instead it should provide greater breadth and depth on interesting and important topics.

Interest Centers or Interest Groups

Interest Centers provide enrichment for students who can demonstrate mastery/competence with required work/content. Interest Centers can be used to provide students with meaningful learning when basic assignments are completed.

Plan interest based centers for use after students have mastered content

Contracts and Management Plans

Contracts are an agreement between the student and teacher where the teacher grants specific freedoms and choices about how a student will complete tasks. The student agrees to use the freedoms appropriately in designing and completing work according to specifications.

Allow gifted students to work independently using a contract for goal setting and accountability

Compacting A 3-step process that (1) assesses what a student knows about material “to be” studied and what the student still needs to master, (2) plans for learning what is not known and excuses student from what is known, and (3) plans for freed-up time to be spent in enriched or accelerated study.

Use pretesting and formative assessments

Allow students who complete work or have mastered skills to complete enrichment activities

45

46

Appendix E

English Language Learner Instructional Accommodations

Adapted from World-class Instructional Design and Assessment guidelines (2014), Teachers to English Speakers of Other Languages guidelines, State

of NJ Department of Education Bilingual

Math

Instruction:

Provide bilingual dictionaries.

Simplify language, clarify or explain directions.

Build background (discuss, allow for questions, and use visuals if applicable) prior to giving assessment make the text meaningful.

Pre-teach difficult vocabulary.

Highlight key word or phrases.

Allow ELL students to hear word problems twice and have a second opportunity to check their answers.

Allow ELL students extended time for word problems.

Provide specific seating arrangement (close proximity for direct instruction, teacher assistance, and buddy).

Response:

Allow for oral explanations

Allow the use of word walls and vocabulary banks.

Documents

8th Grade Algebra 1gloucestertownshipschools.entest.org/Math Grade 8ALG.pdf · 2 Math – Algebra 1 Unit 1 – Relationships between Quantities and Reasoning with Equations Standards