A Correlation of
Connected Mathematics Project 3
Grade 8, Algebra 1
©2014
to the
North Carolina
Common Core Math One
Standards for Assessment
Copyright ©2015 Pearson Education, Inc. or its affiliate(s). All rights reserved.
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
The Real Number System N--RN
Extend the properties of exponents to rational exponents.
N-RN.1 Explain how the definition of the
Growing, Growing, Growing:
meaning of rational exponents follows from
5.1: Looking for Patterns Among
extending the properties of integer
Exponents; 5.2: Rules of Exponents; 5.3:
exponents to those values, allowing for a
Extending the Rules of Exponents
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.
N-RN.2 Rewrite expressions involving
radicals and rational exponents using the
properties of exponents.
Growing, Growing, Growing:
5.3: Extending the Rules of Exponents
Note: At this level, focus on fractional exponents with a numerator of 1.
Quantities N--Q
Reason quantitatively and use units to solve problems.
N-Q.1 Use units as a way to understand
Thinking with Mathematical Models:
problems and to guide the solution of multi- 1.1: Bridge Thickness and Strength; 1.2:
step problems; choose and interpret units
Bridge Length and Strength; 3.2: Distance,
consistently in formulas; choose and
Speed, and Time; 4.1: Vitruvian Man:
interpret the scale and the origin in graphs
Relating Body Measurements; 4.2: Older
and data displays.
and Faster
Growing, Growing, Growing:
2.1: Killer Plant Strikes Lake Victoria: yIntercepts Other Than 1; 2.2: Growing
Mold: Interpreting Equations for
Exponential Functions; 3.2: Investing for
the Future: Growth Rates; 4.3: Cooling
Water: Modeling Exponential Decay;
5.4: Operations With Scientific Notation
Frogs, Fleas, and Painted Cubes:
2.1: Trading Land: Representing Areas of
Rectangles; 2.2: Changing Dimensions: The
Distributive Property
1
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
N-Q.2 Define appropriate quantities for the
purpose of descriptive modeling.
Thinking with Mathematical Models:
2.1: Modeling Linear Data Patterns;
3.4: Modeling Data Patterns
Looking for Pythagoras:
2.2: Square Roots; 4.1: Analyzing the
Wheel of Theodorus: Square Roots on a
Number Line; 5.2: Analyzing Triangles
Growing, Growing, Growing:
3.1: Reproducing Rabbits: Fractional
Growth Patterns; 4.1: Making Smaller
Ballots: Introducing Exponential Decay;
4.3: Cooling Water: Modeling Exponential
Decay
It’s in the System:
2.1: Shirts and Caps Again: Solving
Systems With y = mx + b
N-Q.3 Choose a level of accuracy
appropriate to limitations on measurement
when reporting quantities.
Thinking with Mathematical Models:
2.4: Boat Rental Business: Solving Linear
Equations; 4.3: Correlation Coefficients and
Outliers
Looking for Pythagoras:
2.2: Square Roots; 4.2: Representing
Fractions as Decimals; 4.3: Representing
Decimals as Fractions; 4.4: Getting Real:
Irrational Numbers
Growing, Growing, Growing:
1.2: Requesting a Reward: Representing
Exponential Functions; 5.4: Operations
With Scientific Notation
Butterflies, Pinwheels, and Wallpaper:
2.2: Supporting the World: Congruent
Triangles I
It’s in the System:
3.3: Operating at a Profit: Systems of Lines
and Curves
2
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Seeing Structure in Expressions A--SSE
Interpret the structure of expressions.
A-SSE.1 Interpret expressions that
represent a quantity in terms of its context.
Say It with Symbols:
1.1: Tiling Pools: Writing Equivalent
Expressions; 1.4: Diving In: Revisiting the
Distributive Property; 2.2: Predicting Profit:
Substituting Expressions; 3.3: Factoring
Quadratic Equations; 4.3: Generating
Patterns: Linear, Exponential, Quadratic;
5.1: Using Algebra to Solve a Puzzle
Frogs, Fleas, and Painted Cubes:
2.1: Trading Land: Representing Areas of
Rectangles; 2.2: Changing Dimensions: The
Distributive Property; 2.3: Factoring
Quadratic Expressions; 2.4: Quadratic
Functions and Their Graphs
a. Interpret parts of an expression, such as
terms, factors, and coefficients.
Say It with Symbols:
1.1: Tiling Pools: Writing Equivalent
Expressions; 1.2: Thinking in Different
Ways: Determining Equivalence; 1.3: The
Community Pool Problem: Interpreting
Expressions; 1.4: Diving In: Revisiting the
Distributive Property;
2.1: Walking Together: Adding Expressions;
2.2: Predicting Profit: Substituting
Expressions; 3.3: Factoring Quadratic
Equations; 4.3: Generating Patterns:
Linear, Exponential, Quadratic; 5.1: Using
Algebra to Solve a Puzzle
Frogs, Fleas, and Painted Cubes:
2.2: Changing Dimensions: The Distributive
Property; 2.3: Factoring Quadratic
Expressions; 2.4: Quadratic Functions and
Their Graphs
3
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
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.
Say It with Symbols:
1.1: Tiling Pools: Writing Equivalent
Expressions; 1.2: Thinking in Different
Ways: Determining equivalence; 1.3: The
Community Pool Problem: Interpreting
Expressions; 2.1: Walking Together: Adding
Expressions; 2.2: Predicting Profit:
Substituting Expressions; 3.3: Factoring
Quadratic Equations; 4.3: Generating
Patterns: Linear, Exponential, Quadratic;
5.1: Using Algebra to Solve a Puzzle
Growing, Growing, Growing:
3.2: Investing for the Future: Growth
Rates; 3.3: Making a Difference:
Connecting Growth Rate and Growth
Factor; 4.2: Fighting Fleas: Representing
Exponential Decay; 4.3: Cooling Water:
Modeling Exponential Decay
Frogs, Fleas, and Painted Cubes:
2.1: Trading Land: Representing Areas of
Rectangles; 2.2: Changing Dimensions: The
Distributive Property
Note: At this level, limit to linear expressions, exponential expressions with integer exponents and quadratic
expressions.
Say It with Symbols:
1.1: Tiling Pools: Writing Equivalent
Expressions; 1.2: Thinking in Different
Ways: Determining Equivalence; 1.4:
Diving In: Revisiting the Distributive
Property; 2.1: Walking Together: Adding
Expressions; 2.2: Predicting Profit:
Substituting Expressions; 3.3: Factoring
Quadratic Equations
A-SSE.2 Use the structure of an expression
to identify ways to rewrite it. For example,
see x4 – y4 as (x2)2 – (y2)2, thus recognizing
it as a difference of squares that can be
factored as (x2 – y2)(x2 + y2).
Frogs, Fleas, and Painted Cubes:
2.1: Trading Land: Representing Areas of
Rectangles; 2.2: Changing Dimensions: The
Distributive Property; 2.3: Factoring
Quadratic Expressions; 2.4: Quadratic
Functions and Their Graphs
4
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Write expressions in equivalent forms to
A-SSE.3 Choose and produce an equivalent
form of an expression to reveal and explain
properties of the quantity represented by
the expression.
solve problems.
Say It with Symbols:
1.1: Tiling Pools: Writing Equivalent
Expressions; 1.2: Thinking in Different
Ways: Determining Equivalence; 1.4:
Diving In: Revisiting the Distributive
Property;
2.1: Walking Together: Adding Expressions;
2.2: Predicting Profit: Substituting
Expressions; 3.3: Factoring Quadratic
Equations
Frogs, Fleas, and Painted Cubes:
2.1: Trading Land: Representing Areas of
Rectangles; 2.2: Changing Dimensions: The
Distributive Property; 2.3: Factoring
Quadratic Expressions; 2.4: Quadratic
Functions and Their Graphs
a. Factor a quadratic expression to reveal
the zeros of the function it defines.
Say It with Symbols:
3.3: Factoring Quadratic Equations
Frogs, Fleas, and Painted Cubes:
2.3: Factoring Quadratic Expressions;
2.4: Quadratic Functions and Their Graphs
Note: At this level, the limit is quadratic expressions of the form ax2 + bx + c.
Arithmetic with Polynomials & Rational Expressions A--APR
Perform arithmetic operations on polynomials.
A-APR.1 Understand that polynomials form
Say It with Symbols:
a system analogous to the integers,
1.4: Diving In: Revisiting the Distributive
namely, they are closed under the
Property; 2.1: Walking Together: Adding
operations of addition, subtraction, and
Expressions; 2.2: Predicting Profit:
multiplication; add, subtract, and multiply
Substituting Expressions
polynomials.
Frogs, Fleas, and Painted Cubes:
2.2: Changing Dimensions: The Distributive
Property; 2.3: Factoring Quadratic
Expressions
Function Junction:
5.2: Combining Profit Functions: Operating
With Polynomials I; 5.3: Product Time:
Operating With Polynomials II
5
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, limit to addition and subtraction of quadratics and multiplication of linear expressions.
Creating Equations★ A--CED
Create equations that describe numbers
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.
or relationships.
Thinking with Mathematical Models:
2.4: Boat Rental Business; 2.5: Amusement
Park or Movies
Looking for Pythagoras:
2.2: Square Roots; 2.3: Using Squares;
2.4: Cube Roots; 5.1: Stopping Sneaky
Sally
Growing, Growing, Growing:
1.3: Making a New Offer; 2.1: Killer Plant
Strikes Lake Victoria; 2.3: Studying Snake
Populations;
3.3: Making a Difference; 4.2: Fighting
Fleas; 5.5: Revisiting Exponential Functions
Say It with Symbols:
3.1: Selling Greeting Cards; 3.2:
Comparing Costs; 3.4: Solving Quadratic
Equations
Note: At this level, focus on linear and exponential functions.
A-CED.2 Create equations in two or more
variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
Thinking with Mathematical Models:
2.1: Modeling Linear Data Patterns; 2.2: Up
and Down the Staircase; 2.3: Tree Top
Fun; 2.4: Boat Rental Business; 2.5:
Amusement Park or Movies
Growing, Growing, Growing:
1.3: Making a New Offer; 2.1: Killer Plant
Strikes Lake Victoria; 2.3: Studying Snake
Populations; 3.3: Making a Difference;
4.2: Fighting Fleas; 5.5: Revisiting
Exponential Functions
It’s in the System:
1.1: Shirts and Caps; 1.2: Connecting Ax +
By = C and y = mx + b; 1.3: Booster Club
Members
Frogs, Fleas, and Painted Cubes:
2.4: Quadratic Functions and Their Graphs
6
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, focus on linear, exponential and quadratic. Limit to situations that involve evaluating
exponential functions for integer inputs.
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.
Thinking with Mathematical Models:
2.1: Modeling Linear Data Patterns; 2.2: Up
and Down the Staircase; 2.3: Tree Top
Fun; 2.4: Boat Rental Business; 2.5:
Amusement Park or Movies
Growing, Growing, Growing:
1.3: Making a New Offer; 2.1: Killer Plant
Strikes Lake Victoria; 2.3: Studying Snake
Populations; 3.3: Making a Difference;
4.2: Fighting Fleas; 5.5: Revisiting
Exponential Functions
It’s in the System:
1.1: Shirts and Caps; 3.3: Operating at a
Profit: Systems of Lines and Curves
3.5: Finding the Point of Intersection:
Equations and Inequalities
Frogs, Fleas, and Painted Cubes:
4.1: Tracking a Ball: Interpreting a Table
and an Equation
Note: At this level, limit to linear equations and inequalities.
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.
Thinking with Mathematical Models:
3.1: Rectangles With Fixed Area; 3.2:
Distance, Speed, and Time
Say It with Symbols:
3.1: Solving Equations
It’s in the System:
1.2 Connecting Ax + By = C and y = mx +
b
7
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, limit to formulas that are linear in the variable of interest, or to formulas involving squared
or cubed variables.
Reasoning with Equations & Inequalities A--REI
Understand solving equations as a process of reasoning and explain the
reasoning.
A-REI.1 Explain each step in solving a
Students write verbal explanations of their
simple equation as following from the
equation solving practices, rather than
equality of numbers asserted at the
step-by-step property justifications.
previous step, starting from the assumption
that the original equation has a solution.
Thinking with Mathematical Models:
Construct a viable argument to justify a
2.4: Boat Rental Business; 2.5: Amusement
solution method.
Park or Movies
Say It with Symbols:
3.1: Selling Greeting Cards; 3.2:
Comparing Costs; 5.1: Using Algebra to
Solve a Puzzle
Solve equations and inequalities in one variable.
A-REI.3 Solve linear equations and
Thinking with Mathematical Models:
inequalities in one variable, including
2.4: Boat Rental Business; 2.5: Amusement
equations with coefficients represented by
Park or Movies
letters.
Say It with Symbols:
3.1: Selling Greeting Cards; 3.2:
Comparing Costs; 5.1: Using Algebra to
Solve a Puzzle
It’s in the System:
3.1: Comparing Security Services; 3.2:
Solving Linear Inequalities Symbolically;
3.3: Operation at a Profit
Solve systems of equations.
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.
A-REI.6 Solve systems of linear equations
exactly and approximately (e.g., with
graphs), focusing on pairs of linear
equations in two variables.
It’s in the System:
2.2: Taco Truck Lunch: Solving Systems by
Combining Equations I; 2.3: Solving
Systems by Combining Equations II
It’s in the System:
1.1: Shirts and Caps: Solving Equations
With Two Variables; 1.2: Connecting Ax +
By = C and y = mx + b; 1.3: Booster Club
Members: Intersecting Lines; 2.1: Shirts
and Caps Again: Solving Systems With y =
mx + b; 2.2: Taco Truck Lunch: Solving
Systems by Combining Equations I; 2.3:
Solving Systems by Combining Equations II
8
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Represent and solve equations and inequalities graphically.
A-REI.10 Understand that the graph of an
Thinking with Mathematical Models:
equation in two variables is the set of all its 2.1: Modeling Linear Data Patterns; 2.2: Up
solutions plotted in the coordinate plane,
and Down the Staircase; 2.3: Tree Top
often forming a curve (which could be a
Fun; 2.4: Boat Rental Business; 2.5:
line).
Amusement Park or Movies
Growing, Growing, Growing:
1.3: Making a New Offer; 2.1: Killer Plant
Strikes Lake Victoria; 2.3: Studying Snake
Populations; 3.3: Making a Difference; 4.2:
Fighting Fleas; 5.5: Revisiting Exponential
Functions
It’s in the System:
1.1: Shirts and Caps; 1.2: Connecting Ax +
By = C and y = mx + b; 1.3: Booster Club
Members
Frogs, Fleas, and Painted Cubes:
2.4: Quadratic Functions and Their Graphs
Note: At this level, focus on linear and exponential equations.
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 functions.
It’s in the System:
1.1: Shirts and Caps: Solving Equations
With Two Variables; 1.2: Connecting Ax +
By = C and y = mx + b; 1.3: Booster Club
Members: Intersecting Lines
Note: At this level, focus on linear and exponential 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.
It’s in the System:
4.1: Limiting Driving Miles: Inequalities
With Two Variables; 4.2: What Makes a Car
Green?: Solving Inequalities by Graphing I;
4.3: Feasible Points: Solving Inequalities by
Graphing II; 4.4: Miles of Emissions:
Systems of Linear Inequalities
9
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Interpreting Functions F--IF
Understand the concept of a function and use function notation.
F-IF.1 Understand that a function from one
Thinking with Mathematical Models:
set (called the domain) to another set
2.1: Modeling Linear Data Patterns;
(called the range) assigns to each element
3.2: Distance, Speed and Time
of the domain exactly one element of the
range. If f is a function and x is an element Growing, Growing, Growing:
of its domain, then f(x) denotes the output
2.1: Killer Plant Strikes Lake Victoria;
of f corresponding to the input x. The graph 2.2: Growing Mold; 5.5: Revisiting
of f is the graph of the equation y = f(x).
Exponential Functions
Say It with Symbols:
3.1: Selling Greeting Cards; 4.4: What’s
the Function?
Frogs, Fleas, and Painted Cubes:
4.1: Tracking a Ball: Interpreting a Table
and an Equation; 4.4: Painted Cubes:
Looking at Several Functions
Function Junction:
1.1: Filling Functions; 1.2: Domain, Range,
and Function Notation; 5.1: Properties of
Polynomial Expressions and Functions
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.
Frogs, Fleas, and Painted Cubes:
4.2: Measuring Jumps: Comparing
Quadratic Relationships; 4.3: Putting It All
Together: Functions and Patterns of
Change; 4.4: Painted Cubes: Looking at
Several Functions
Function Junction:
1.1: Filling Functions; 1.3: Taxi Fares, Time
Payments, and Step Functions;
1.4: Piecewise-Defined Functions;
5.1: Properties of Polynomial Expressions
and Functions; 5.2: Combining Profit
Functions: Operating With Polynomials II
Note: At this level, the focus is linear and exponential functions.
F-IF.3 Recognize that sequences are
functions, sometimes defined recursively,
whose domain is a 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.
Function Junction:
2.1: Arithmetic Sequences; 2.2: Geometric
Sequences
10
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Interpret functions that arise in applications in terms of the context.
F-IF.4 For a function that models a
Frogs, Fleas, and Painted Cubes:
relationship between two quantities,
4.1: Tracking a Ball: Interpreting a Table
interpret key features of graphs and tables
and an Equation; 4.2: Measuring Jumps:
in terms of the quantities, and sketch
Comparing Quadratic Relationships;
graphs showing key features given a verbal 4.3: Putting It All Together: Functions and
description of the relationship. Key features Patterns of Change; 4.4: Painted Cubes:
include: intercepts; intervals where the
Looking at Several Functions
function is increasing, decreasing, positive,
or negative; relative maximums and
Function Junction:
minimums; symmetries; end behavior; and 1.1: Filling Functions; 1.2: Domain, Range,
periodicity.
and Function Notation; 1.3: Taxi Fares,
Time Payments, and Step Functions;
1.4: Piecewise-Defined Functions;
5.1: Properties of Polynomial Expressions
and Functions; 5.2: Combining Profit
Functions: Operating With Polynomials II
Note: At this level, focus on linear, exponential and quadratic functions; no end behavior or periodicity.
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.
Frogs, Fleas, and Painted Cubes:
4.1: Tracking a Ball: Interpreting a Table
and an Equation; 4.2: Measuring Jumps:
Comparing Quadratic Relationships;
4.3: Putting It All Together: Functions and
Patterns of Change; 4.4: Painted Cubes:
Looking at Several Functions
Function Junction:
1.1: Filling Functions; 1.2: Domain, Range,
and Function Notation; 1.3: Taxi Fares,
Time Payments, and Step Functions;
1.4: Piecewise-Defined Functions;
5.1: Properties of Polynomial Expressions
and Functions; 5.2: Combining Profit
Functions: Operating With Polynomials II
Note: At this level, focus on linear and exponential functions.
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.
Thinking with Mathematical Models:
1.3: Custom Construction Parts; 2.2: Up
and Down the Staircase; 2.3: Tree Top
Fun; 2.4: Boat Rental Business;
2.5: Amusement Park or Movies
Say It with Symbols:
3.1: Selling Greeting Cards;
3.2: Comparing Costs
11
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, focus on linear functions and exponential functions whose domain is a subset of the integers.
Analyze functions using different representations.
F-IF.7 Graph functions expressed
Thinking with Mathematical Models:
symbolically and show key features of the
2.1: Modeling Linear Data Patterns;
graph, by hand in simple cases and using
2.3: Tree Top Fun: Equations for Linear
technology for more complicated cases.
Functions; 2.5: Amusement Park or Movies:
Intersecting Linear Functions
Growing, Growing, Growing:
2.1: Killer Plant Strikes Lake Victoria:
y-Intercepts Other Than 1; 4.3: Cooling
Water: Modeling Exponential Decay
Say It with Symbols:
3.3: Factoring Quadratic Equations
Frogs, Fleas, and Painted Cubes:
1.2: Reading Graphs and Tables;
2.4: Quadratic Functions and Their Graphs;
4.1: Tracking a Ball: Interpreting a Table
and an Equation
Function Junction:
1.3: Taxi Fares, Time Payments, and Step
Functions; 1.4: Piecewise-Defined
Functions; 4.4: Complex Numbers;
5.1: Properties of Polynomial Expressions
and Functions
a. Graph linear and quadratic functions and
show intercepts, maxima, and minima.
Thinking with Mathematical Models:
2.1: Modeling Linear Data Patterns; 2.2: Up
and Down the Staircase: Exploring Slope;
2.4: Boat Rental Service: Solving Linear
Equations;
Say It with Symbols:
3.3: Factoring Quadratic Equations
Function Junction:
4.1: Applying Square Roots; 4.3: The
Quadratic Formula; 4.4: Complex Numbers
Frogs, Fleas, and Painted Cubes:
1.2: Reading Graphs and Tables;
2.4: Quadratic Functions and Their Graphs;
4.1: Tracking a Ball: Interpreting a Table
and an Equation
12
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
e. Graph exponential and logarithmic
functions, showing intercepts and end
behavior, and trigonometric functions,
showing period, midline, and amplitude.
Connected Mathematics Project 3
Grade 8, Algebra 1
Growing, Growing, Growing:
2.1: Killer Plant Strikes Lake Victoria: yIntercepts Other Than 1; 2.2: Growing
Mold: Interpreting Equations for
Exponential Functions; 3.1: Reproducing
Rabbits: Fractional Growth Patterns;
3.2: Investing for the Future: Growth
Rates; 3.3: Making a Difference:
Connecting Growth Rate and Growth
Factor; 4.1: Making Smaller Ballots:
Introducing Exponential Decay;
4.2: Fighting Fleas: Representing
Exponential Decay; 4.3: Cooling Water:
Modeling Exponential Decay
Note: At this level, for part e, focus on exponential functions only.
F-IF.8 Write a function defined by an
expression in different but equivalent forms
to reveal and explain different properties of
the function.
Say It with Symbols:
1.2: Thinking in Different Ways:
Determining Equivalence; 1.3: The
Community Pool Problem: Interpreting
Expressions; 2.2: Predicting Profit:
Substituting Expressions; 3.3: Factoring
Quadratic Equations
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.
Say It with Symbols:
3.3: Factoring Quadratic Equations
Frogs, Fleas, and Painted Cubes:
2.3: Factoring Quadratic Expressions;
2.4: Quadratic Functions and Their Graphs
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A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, only factoring expressions of the form ax2 + bx +c, is expected. Completing the square is not
addressed at this level.
b. Use the properties of 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.
Growing, Growing, Growing:
1.1: Making Ballots: Introducing
Exponential Functions; 1.2: Requesting a
Reward: Representing Exponential
Functions; 1.3: Making a New Offer:
Growth Factors; 2.1: Killer Plant Strikes
Lake Victoria: y-Intercepts Other Than 1;
2.2: Growing Mold: Interpreting Equations
for Exponential Functions; 3.1: Reproducing
Rabbits: Fractional Growth Patterns;
3.3: Making a Difference: Connecting
Growth Rate and Growth Factor; 4.1:
Making Smaller Ballots: Introducing
Exponential Decay; 4.3: Cooling Water:
Modeling Exponential Decay; 5.2: Rules of
Exponents; 5.3: Extending the Rules of
Exponents
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.
Frogs, Fleas, and Painted Cubes:
5.1: Properties of Polynomial Expressions
and Functions
14
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, focus on linear, exponential, and quadratic functions.
Building Functions F--BF
Build a function that models a relationship between two quantities.
F-BF.1 Write a function that describes a
Say It with Symbols:
relationship between two quantities.
3.1: Selling Greeting Cards: Solving Linear
Equations; 3.2: Comparing Costs: Solving
More Linear Equations; 4.2: Area and
Profit—What’s the Connection?: Using
Equations; 4.4: What's the Function?:
Modeling With Functions
Growing, Growing, Growing:
2.2: Growing Mold: Interpreting Equations
for Exponential Functions; 3.1: Reproducing
Rabbits: Fractional Growth Patterns; 4.3:
Cooling Water: Modeling Exponential Decay
Frogs, Fleas, and Painted Cubes:
3.2: Counting Handshakes: Another
Quadratic Function; 4.1: Tracking a Ball:
Interpreting a Table and an Equation; 4.2:
Measuring Jumps: Comparing Quadratic
Functions; 4.3: Painted Cubes: Looking at
Several Functions
Function Junction:
1.3: Taxi Fairs, Time Payments, and Step
Functions; 2.1: Arithmetic Sequences; 4.2:
Completing the Square; 5.2: Combining
Profit Functions
a. Determine an explicit expression, a
recursive process, or steps for calculation
from a context.
Function Junction:
2.1: Arithmetic Sequences; 2.2: Geometric
Sequences
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.
Say It with Symbols:
2.1: Walking Together: Adding Expressions;
2.2: Predicting Profit: Substituting
Expressions
Function Junction:
5.2: Combining Profit Functions: Operating
With Polynomials I; 5.3: Product Time:
Operating With Polynomials II
15
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, limit to addition or subtraction of constant to linear, exponential or quadratic functions or
addition of linear functions to linear or quadratic functions.
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.
Function Junction:
2.1: Arithmetic Sequences; 2.2: Geometric
Sequences
Note: At this level, formal recursive notation is not used. Instead, use of informal recursive notation (such as
NEXT = NOW + 5 starting at 3) is intended.
Build new functions from existing functions.
F-BF.3 Identify the effect on the graph of
Function Junction:
replacing f(x) by f(x) + k, k f(x), f(kx), and 3.1: Sliding Up and Down: Vertical
f(x + k) for specific values of k (both
Translations of Functions; 3.2: Stretching
positive and negative); find the value of k
and Flipping Up and Down: Multiplicative
given the graphs. Experiment with cases
Transformations of Functions; 3.3: Sliding
and illustrate an explanation of the effects
Left and Right: Horizontal Translations of
on the graph using technology. Include
Functions; 3.4: Getting From Here to
recognizing even and odd functions from
There: Transforming y = x2
their graphs and algebraic expressions for
them.
Note: At this level, limit to vertical and horizontal translations of linear and exponential functions.
Even and odd functions are not addressed.
Linear, Quadratic, & Exponential Models★ F-LE
Construct and compare linear and exponential models and solve problems.
F-LE.1 Distinguish between situations that
Say It with Symbols:
can be modeled with linear functions and
3.1: Selling Greeting Cards: Solving Linear
with exponential functions
Equations; 3.2: Comparing Costs: Solving
More Linear Equations; 4.3: Generating
Patterns: Linear, Exponential, Quadratic;
4.4: What's the Function?": Modeling With
Functions
a. Prove that linear functions grow by equal
differences over equal intervals, and that
exponential functions grow by equal factors
over equal intervals.
Say It with Symbols:
4.3: Generating Patterns: Linear,
Exponential, Quadratic
b. Recognize situations in which one
quantity changes at a constant rate per unit
interval relative to another.
Thinking with Mathematical Models:
2.1: Modeling Linear Data Patterns; 2.2: Up
and Down the Staircase: Exploring Slope;
2.3: Tree Top Fun: Equations for Linear
Functions; 2.4: Boat Rental Service:
Solving Linear Equations; 2.5: Amusement
Park or Movies: Intersecting Linear
Functions
Function Junction:
2.1: Arithmetic Sequences
16
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
c. Recognize situations in which a quantity
grows or decays by a constant percent rate
per unit interval relative to another.
Growing, Growing, Growing:
2.1: Killer Plant Strikes Lake Victoria: yIntercepts Other Than 1; 2.2: Growing
Mold: Interpreting Equations for
Exponential Functions; 2.3: Studying Snake
Populations: Interpreting Graphs of
Exponential Functions; 3.1: Reproducing
Rabbits: Fractional Growth Patterns; 3.2:
Investing for the Future: Growth Rates;
3.3: Making a Difference: Connecting
Growth Rate and Growth Factor; 4.1:
Making Smaller Ballots: Introducing
Exponential Decay; 4.2: Fighting Fleas:
Representing Exponential Decay; 4.3:
Cooling Water: Modeling Exponential Decay
Function Junction:
2.2: Geometric Sequences
F-LE.2 Construct linear and exponential
functions, including arithmetic and
geometric sequences, given a graph, a
description of a relationship, or two inputoutput pairs (include reading these from a
table).
Thinking with Mathematical Models:
2.1: Modeling Linear Data Patterns; 2.2: Up
and Down the Staircase: Exploring Slope;
2.3: Tree Top Fun: Equations for Linear
Functions; 2.4: Boat Rental Service:
Solving Linear Equations; 2.5: Amusement
Park or Movies: Intersecting Linear
Functions
Growing, Growing, Growing:
2.1: Killer Plant Strikes Lake Victoria: yIntercepts Other Than 1; 2.2: Growing
Mold: Interpreting Equations for
Exponential Functions; 3.1: Reproducing
Rabbits: Fractional Growth Patterns; 3.2:
Investing for the Future: Growth Rates;
3.3: Making a Difference: Connecting
Growth Rate and Growth Factor; 4.1:
Making Smaller Ballots: Introducing
Exponential Decay; 4.2: Fighting Fleas:
Representing Exponential Decay; 4.3:
Cooling Water: Modeling Exponential Decay
Function Junction:
2.1: Arithmetic Sequences; 2.2: Geometric
Sequences
17
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
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.
Connected Mathematics Project 3
Grade 8, Algebra 1
Thinking with Mathematical Models:
2.1: Modeling Linear Data Patterns; 3.4:
Modeling Data Patterns
Say It with Symbols:
4.1: Pumping Water: Looking at Patterns of
Change; 4.2: Area and Profit—What's the
Connection?: Using Equations; 4.3:
Generating Patterns: Linear, Exponential,
Quadratic; 4.4: What's the Function?:
Modeling With Functions
Note: At this level, limit to linear, exponential, and quadratic functions; general polynomial functions are not
addressed.
Interpret expressions for functions in terms of the situation they model.
F-LE.5 Interpret the parameters in a linear
Thinking with Mathematical Models:
or exponential function in terms of a
2.1: Modeling Linear Data Patterns;
context.
2.2: Up and Down the Staircase: Exploring
Slope; 2.3: Tree Top Fun: Equations for
Linear Functions; 2.4: Boat Rental Service:
Solving Linear Equations; 2.5: Amusement
Park or Movies: Intersecting Linear
Functions
Growing, Growing, Growing:
2.1: Killer Plant Strikes Lake Victoria: yIntercepts Other Than 1; 2.2: Growing
Mold: Interpreting Equations for
Exponential Functions; 3.1: Reproducing
Rabbits: Fractional Growth Patterns; 3.2:
Investing for the Future: Growth Rates;
3.3: Making a Difference: Connecting
Growth Rate and Growth Factor; 4.1:
Making Smaller Ballots: Introducing
Exponential Decay; 4.2: Fighting Fleas:
Representing Exponential Decay; 4.3:
Cooling Water: Modeling Exponential Decay
Congruence G--CO
Experiment with transformations in the plane.
G-CO.1 Know precise definitions of angle,
This standard is outside the scope of
circle, perpendicular line, parallel line, and
Connected Mathematics Project 3
line segment, based on the undefined
Grade 8, Algebra 1.
notions of point, line, distance along a line,
and distance around a circular arc.
18
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, distance around a circular arc is not addressed.
Expressing Geometric Properties with Equations G--GPE
Use coordinates to prove simple geometric theorems algebraically.
G-GPE.4 Use coordinates to prove simple
This geometric standard is outside the
geometric theorems algebraically. For
scope of Connected Mathematics Project 3
example, prove or disprove that a figure
Grade 8, Algebra 1.
defined by four given points in the
coordinate plane is a rectangle; prove or
disprove that the point (1, √3) lies on the
circle centered at the origin and containing
the point (0, 2).
G-GPE.5 Prove the slope criteria for parallel
and perpendicular lines and use them to
solve geometric problems (e.g., find the
equation of a line parallel or perpendicular
to a given line that passes through a given
point).
This geometric standard is outside the
scope of Connected Mathematics Project 3
Grade 8, Algebra 1.
G-GPE.6 Find the point on a directed line
segment between two given points that
partitions the segment in a given ratio.
This geometric standard is outside the
scope of Connected Mathematics Project 3
Grade 8, Algebra 1.
Note: At this level, focus on finding the midpoint of a segment.
G-GPE.7 Use coordinates to compute
perimeters of polygons and areas of
triangles and rectangles, e.g., using the
distance formula.
This geometric standard is outside the
scope of Connected Mathematics Project 3
Grade 8, Algebra 1.
Geometric Measurement & Dimension G-GMD
Explain volume formulas and use them to solve problems.
G-GMD.1 Give an informal argument for the This geometric standard is outside the
formulas for the circumference of a circle,
scope of Connected Mathematics Project 3
area of a circle, volume of a cylinder,
Grade 8, Algebra 1.
pyramid, and cone. Use dissection
arguments, Cavalieri’s principle, and
informal limit arguments.
Note: Informal limit arguments are not the intent at this level.
G-GMD.3 Use volume formulas for
cylinders, pyramids, cones, and spheres to
solve problems.
This geometric standard is outside the
scope of Connected Mathematics Project 3
Grade 8, Algebra 1.
19
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, formulas for pyramids, cones and spheres will be given.
Interpreting Categorical & Quantitative Data S-ID
Summarize, represent, and interpret data on a single count or measurement
variable.
Thinking with Mathematical Models:
S-ID.1 Represent data with plots on the
4.4: Measuring Variability: Standard Deviation;
real number line (dot plots, histograms,
4: Variability and Associations in Data (ACE 10,
and box plots).
15, 23); 5: Variability and Associations in
Categorical Data (ACE 32-33)
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.
Thinking with Mathematical Models:
4.4: Measuring Variability: Standard Deviation;
4: Variability and Associations in Data
(ACE 15-20, 23-24); 5: Variability and
Associations in Categorical Data (ACE 26-29, 33)
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).
Thinking with Mathematical Models:
4.4: Measuring Variability: Standard Deviation;
4: Variability and Associations in Data (ACE 1520, 23-24); 5: Variability and Associations in
Categorical Data (ACE 26-29, 33)
Summarize, represent, and interpret data on two categorical and quantitative
variables.
Thinking with Mathematical Models:
S-ID.5 Summarize categorical data for two
5.1: Wood or Steel? That's the Question:
categories in two-way frequency tables.
Interpret relative frequencies in the context Relationships in Categorical Data; 5.2: Politics of
Girls and Boys: Analyzing Data in Two-Way
of the data (including joint, marginal, and
Tables; 5.3: After-School Jobs and Homework:
conditional relative frequencies). Recognize
Working Backward: Setting Up a Two-Way Table
possible associations and trends in the
data.
S-ID.6 Represent data on two quantitative
variables on a scatter plot, and describe
how the variables are related.
Thinking with Mathematical Models:
4.1: Vitruvian Man: Relating Body
Measurements; 4.2: Older and Faster: Negative
Correlation; 4.3: Correlation Coefficients and
Outliers
a. Fit a function to the data; use functions
fitted to data to solve problems in the
context of the data. Use given functions or
choose a function suggested by the
context. Emphasize linear and exponential
models.
Thinking with Mathematical Models:
4.1: Vitruvian Man: Relating Body
Measurements; 4.2: Older and Faster: Negative
Correlation; 4.3: Correlation Coefficients and
Outliers
b. Informally assess the fit of a function by
plotting and analyzing residuals.
Thinking with Mathematical Models:
4.1: Vitruvian Man: Relating Body
Measurements
20
A Correlation of Connected Mathematics Project 3, Grade 8, Algebra 1, ©2014
to the North Carolina Common Core Math One Standards for Assessment
Common Core Math One Standards
for Assessment
Connected Mathematics Project 3
Grade 8, Algebra 1
Note: At this level, for part b, focus on linear models.
c. Fit a linear function for a scatter plot that
suggests a linear association.
Interpret linear models.
S-ID.7 Interpret the slope (rate of change)
and the intercept (constant term) of a
linear model in the context of the data.
Thinking with Mathematical Models:
4.1: Vitruvian Man: Relating Body
Measurements; 4.2: Older and Faster: Negative
Correlation
Thinking with Mathematical Models:
2.1: Modeling Linear Data Patterns;
2.2: Up and Down the Staircase: Exploring
Slope; 2.3: Tree Top Fun: Equations for Linear
Functions; 2.4: Boat Rental Business: Solving
Linear Functions; 4.1: Vitruvian Man: Relating
Body Measurements; 4.2: Older and Faster:
Negative Correlation
S-ID.8 Compute (using technology) and
interpret the correlation coefficient of a
linear fit.
Thinking with Mathematical Models:
4.3: Correlation Coefficients and Outliers
S-ID 9 Distinguish between correlation and
causation.
Thinking with Mathematical Models:
4.3: Correlation Coefficients and Outliers
21