Eighth Grade CMP2 Correlations to the Alabama Course of Study
Compiled by Cathey Ritter
Secondary Math Specialist AMSTI—UM
CMP2 Unit
Alabama Course of Study Objective
Thinking With Mathematical Models
Investigation 1 “Exploring Data Patterns”
8AL 5c Classifying variables in a function as independent or
Problem 1 Testing Bridge Thickness—Finding Patterns and Making dependent.
Predictions
8AL 1a Applying GCF, LCM, and prime and composite numbers,
Problem 2 Testing Bridge Lengths—Finding Patterns and Making including justification for the reasonableness of results, when working
Predictions
with rational numbers.
Problem 3 Custom Construction Parts—Extending Patterns
8AL 1c Utilizing alternative representations to solve problems
involving rational numbers.
8AL 1d Applying proportional reasoning to application-based
situations.
Investigation 2 “Linear Models and Equations”
8AL 5c Classifying variables in a function as independent or dependent.
Problem 1 Linear Models
8AL 5b Classifying relations as linear or nonlinear by examining table,
Problem 2 Equations for Linear Relationships
graphs, or simple equations.
Problem 3 Solving Linear Equations
Problem 4 Intersecting Linear Models
Investigation 3 “Inverse Variation”
8AL 10 Determine the perimeter and area of regular and irregular
Problem 1 Rectangles With Fixed Area—Relating Length and Width
plane shapes.
Problem 2 Bridging the Distance—Inverse Variation Patterns
8AL 13 Use given and collected data from samples or populations to
Problem 3 Average Cost—Inverse Variation Patterns
construct graphs and interpret data.
Growing, Growing, Growing
Investigation 1 “Exponential Growth”
Problem 1 Making Ballots—Introducing Exponential Relationships
Problem 2 Requesting a Reward—Representing Exponential
Relationships
Problem 3 Making a New Offer—Growth Factors
Problem 4 Getting Costs in Line—Comparing Growth Patterns
Investigation 2 “Examining Growth Patterns”
Problem 1 Killer Plant Strikes Lake Victoria—y-Intercepts Other Than 1
Problem 2 Growing Mold—Interpreting Exponential Equations
Problem 3 Studying Snake Populations—Interpreting Exponential
Graphs
8AL 2 Apply one or more of the laws of exponents to simplify
expressions containing natural number exponents.
8AL 5c Classifying variables in a function as independent or dependent.
8AL 5b Classifying relations as linear or nonlinear by examining table,
graphs, or simple equations.
8AL 2 Apply one or more of the laws of exponents to simplify
expressions containing natural number exponents.
8AL 5c Classifying variables in a function as independent or dependent.
8AL 5b Classifying relations as linear or nonlinear by examining table,
graphs, or simple equations.
Investigation 3 “Growth Factors and Growth Rates”
Problem 1 Reproducing Rabbits—Fractional Growth Factors
Problem 2 Investing for the Future—Growth Rates
Problem 3 Making a Difference—Connecting Growth Rate and Growth
Factor
8AL 2 Apply one or more of the laws of exponents to simplify
expressions containing natural number exponents.
8AL 5c Classifying variables in a function as independent or dependent.
8AL 5b Classifying relations as linear or nonlinear by examining table,
graphs, or simple equations.
Investigation 4 “Exponential Decay”
Problem 1 Making Smaller Ballots—Introducing Exponential Decay
Problem 2 Fighting Fleas—Representing Exponential Decay
Problem 3 Cooling Water—Modeling Exponential Decay
8AL 2a Writing numbers using scientific notation.
8AL 5c Classifying variables in a function as independent or dependent.
8AL 5b Classifying relations as linear or nonlinear by examining table,
graphs, or simple equations.
Investigation 5 “Patterns With Exponents”
Problem 1 Predicting the Ones Digit
Problem 2 Operating With Exponents
Problem 3 Exploring Exponential Equations
8AL 2 Apply one or more of the laws of exponents to simplify
expressions containing natural number exponents.
8AL 2a Writing numbers using scientific notation.
8AL 5c Classifying variables in a function as independent or dependent.
8AL 5b Classifying relations as linear or nonlinear by examining table,
graphs, or simple equations.
Say It With Symbols
Investigation 1 “Equivalent Expressions”
Problem 1 Tiling Pools—Writing Equivalent Expressions
Problem 2 Thinking in Different Ways—Determining Equivalence
Problem 3 The Community Pool Problem—Interpreting Expressions
Problem 4 Diving In—Revisiting the Distributive Property
Investigation 2 “Combining Expressions”
Problem 1 Walking Together—Adding Expressions
Problem 2 Predicting Profit—Substituting Equivalent Expressions
Problem 3 Area and Profit
Investigation 3 “Solving Equations
Problem 1 Solving Linear Equations
Problem 2 Comparing costs—Solving More Linear Equations
Problem 3 Factoring Quadratic Expressions
Problem 4 Solving Quadratic Equations
Investigation 4 “Looking Back at Functions”
Problem 1 Pumping Water—Looking at Patterns of Change
Problem 2 Generating Patterns—Linear, Exponential, and Quadratic
Problem 3 Sorting Functions
Investigation 5 “Reasoning With Symbols”
Problem 1 Using Algebra to Solve a Puzzle
Problem 2 Odd and Even Revisited
Problem 3 Squaring Odd Numbers
8AL 6 Solve multistep linear equations, including equations requiring
the use of the distributive property.
8Al 10 Determine the perimeter and area of regular and irregular
plane shapes.
8AL 13 Use given and collected data from samples of populations to
construct graphs and interpret data.
8AL 4b Calculating the slope of a linear relation given as a table or
graph.
8AL 5 Solve problems involving linear functions.
8AL 5b Classifying relations as linear or nonlinear by examining table,
graphs, or simple equations.
8AL 11 Determine surface area and volume of rectangular prisms,
cylinders, and pyramids.
8Al 11a Determine surface area and volume of solid figures, including
cones and spheres.
8AL 11b Estimating surface area and volume of solid figures, including
cones and spheres.
8AL 11c Determining appropriate units of measures to describe
surface area and volume.
8Al 11d Developing formulas for determining surface area and volume
of rectangular prisms.
Samples and Populations
Investigation 1 “Comparing Data Sets”
Problem 1 From Line Plots to Histograms
Problem 2 Using Histograms
Problem 3 Box-and-Whisker Plots
Problem 4 Making a Quality Choice—Analyzing Data
Investigation 2 “Choosing a Sample From a Population”
Problem 1 Asking About Honesty—Using a Sample to Make
Predictions
Problem 2 Selecting a Sample
Problem 3 Choosing Random Samples
Problem 4 Choosing a Sample Size
Investigation 3 “Solving Real-World Problems”
Problem 1 Solving an Archeological Mystery—Comparing and
Analyzing Data
Problem 2 Simulating Cookies—Using a Simulation to Make a Decision
Investigation 4 “Relating Two Variables”
Problem 1 Are Quality Ratings and Prices Related?—Interpreting
Scatter Plots
Problem 2 Writing an Equation to Describe a Relationship
Problem 3 Human Development Index and Life Expectancies—
Analyzing a Relationship
8AL 13 Use given and collected data from samples of populations to
construct graphs and interpret data.
8AL 13 Use given and collected data from samples of populations to
construct graphs and interpret data.
8AL 14 Determine the theoretical probability of an event.
8AL 14a Calculating the probability of complementary events and
mutually exclusive events.
8Al 14c Determining the probability of an event through simulation.
8AL 13a Estimating a line of best fit from a scatterplot to make
predictions.
8AL 13b Determining the measure of central tendency that is the most
appropriate for a given situation.
Looking for Pythagoras
Investigation 1 “Coordinate Grids”
Problem 1 Driving Around Euclid—Locating Points and finding
Distances
Problem 2 Planning Parks—Shapes on a Coordinate Grid
Problem 3 Finding Areas
Investigation 2 “Squaring Off:
Problem 1 Looking for Squares
Problem 2 Square Roots
Problem 3 Using Squares to Find Lengths
Investigation 3 “The Pythagorean Theorem”
Problem 1 The Pythagorean Theorem
Problem 2 A Proof of the Pythagorean Theorem
Problem 3 Finding Distances
Problem 4 Measuring the Egyptian Way—Lengths That Form a Right
Triangle
Investigation 4 “Using the Pythagorean Theorem”
Problem 1 Analyzing the Wheel of Theodorus
Problem 2 Stopping Sneaky Sally—Finding Unknown Side Lengths
Problem 3 Analyzing Triangles
Problem 4 Finding the Perimeter
8AL 7 Solve problems using the Pythagorean Theorem.
8AL 7e Calculating distances on the coordinate plane using the
Pythagorean Theorem.
8AL 10 Determine the perimeter and area of regular and irregular
plane shapes.
8AL 7a Verifying the Pythagorean Theorem.
8AL 7b Applying the Pythagorean Theorem to determine if a triangle is
a right triangle.
8AL 7c Applying the Pythagorean Theorem to solve multistep
application-based problem.
8AL 7d Applying the Triangle Inequality Theorem.
8AL 11
8AL 7a Verifying the Pythagorean Theorem.
8AL 7b Applying the Pythagorean Theorem to determine if a triangle is
a right triangle.
8AL 7c Applying the Pythagorean Theorem to solve multistep
application-based problem.
8AL 7e Calculating distances on the coordinate plane using the
Pythagorean Theorem.
Frogs, Fleas, and Painted Cubes
Investigation 1 “Introduction to Quadratic Relationships”
Problem 1 Staking a Claim—Maximizing Area
Problem 2 Reading Graphs and Tables
Problem 3 Writing an Equation
Investigation 2 “Quadratic Expressions”
Problem 1 Trading Land—Representing Areas of Rectangles
Problem 2 Changing One Dimension—Quadratic Expressions
Problem 3 Changing Both Dimensions—The Distributive Property
Problem 4 Factoring Quadratic Expressions
Problem 5 A Closer Look at Parabolas
Investigation 3 “Quadratic Patterns of Change”
Problem 1 Exploring Triangular Numbers
Problem 2 Counting Handshakes—Another Quadratic Relationship
Problem 3 Examining Patterns of Change
Investigation 4 “What is a Quadratic Function?”
Problem 1 Tracking a Ball—Interpreting a Table and an Equation
Problem 2 Measuring Jumps—Comparing Quadratic Relationships
Problem 3 Putting It All Together—Functions and Patterns of Change
Problem 4 Painted Cubes—Looking at Several Functions
8AL 1 Use various strategies and operations to solve problems
involving real numbers.
8AL 4c Graphing linear relations by plotting x-and y- intercepts.
8AL 5c Classifying variables in a function as independent or
dependent.
8AL 5b Classifying relations as linear or nonlinear by examining table,
graphs, or simple equations.
8AL 1 Use various strategies and operations to solve problems
involving real numbers.
8AL 4c Graphing linear relations by plotting x-and y- intercepts.
8AL 5c Classifying variables in a function as independent or
dependent.
8AL 6 Solve multistep linear equations, including equations requiring
the use of the distributive property.
8AL 1 Use various strategies and operations to solve problems
involving real numbers.
8AL 4c Graphing linear relations by plotting x-and y- intercepts.
8AL 5c Classifying variables in a function as independent or
dependent.
8AL 1 Use various strategies and operations to solve problems
involving real numbers.
8AL 4c Graphing linear relations by plotting x-and y- intercepts.
8AL 5c Classifying variables in a function as independent or
dependent.
The Shapes of Algebra
Investigation 1 “Equations for Circles and Polygons”
Problem 1 Equations for Circles
Problem 2 Parallels and Perpendiculars
Problem 3 Finding Midpoints
Investigation 2 “Linear Equations and Inequalities”
Problem 1 Graphs of Linear Systems
Problem 2 Linear Inequalities
Problem 3 Solving Linear Inequalities
Investigation 3 “Equations With Two or More Variables”
Problem 1 Many Ways to Reach a Goal—Solving Equations With Two
Variables
Problem 2 Connecting y=mx+b with ax+by=c
Problem 3 Intersections of Lines
Investigation 4 “Solving Systems of Linear Equations Symbolically”
Problem 1 The y=mx+b Case
Problem 2 The ax+by=c Case—Solving Systems of Linear Equations by
Writing Equivalent Forms
Problem 3 Solving Systems by Substitution
Problem 4 solving Systems by Combination
Investigation 5 “Linear Inequalities”
Problem 1 Limiting Driving Miles—Graphing “No More Than”
Situations
Problem 2 Limiting Carbon Dioxide Emissions—Solving Linear
Inequalities by Graphing
Problem 3 Graphs of Linear Inequalities
Problem 4 Systems of Linear Inequalities
8AL 3 Use order of operations to evaluate and simplify algebraic
expressions.
8AL 3a Applying the substitution principle to evaluate algebraic
expressions.
8Al 4 Graph linear relations by plotting points or by using the slope
and y-intercept.
8AL 4a Determining slopes and y-intercepts of lines.
8AL 4b Calculating the slope of a linear relation given as a table or
graph.
8AL 4c Graphing linear relations by plotting x- and y-intercepts.
8AL 5 Solve problems involving linear functions.
8AL 5b Classifying relations as linear or nonlinear by examining tables,
graphs, or simple equations.
8AL 5c Determining if a relation is a function from information in
tables, sets of ordered pairs, equations, graphs, or mappings.
Kaleidoscopes, Hubcaps, and Mirrors
Investigation 1 “Three Types of Symmetry”
Problem 1 Reflection Symmetry
Problem 2 Rotation Symmetry
Problem 3 Symmetry in Kaleidoscope Designs—Analyzing Symmetries
Problem 4 Translation Symmetry
Investigation 2 “Symmetry Transformations”
Problem 1 Describing Line Reflections
Problem 2 Describing Rotations
Problem 3 Describing Translations
Problem 4 Using Symmetry to Think About Tessellations
Investigation 3 “ Exploring Congruence”
Problem 1 Relating Symmetry and Congruence
Problem 2 Congruent Triangles
Problem 3 The Matching Game—Congruent Triangles
Problem 4 Polystrip Triangles and Quadrilaterals—Side Lengths and
Congruence
Investigation 4 “Applying Congruence and Symmetry”
Problem 1 finding Distances Without Measuring
Problem 2 Using Symmetry to Find Properties of Shapes
Investigation 5 “Transforming Coordinates”
Problem 1 Coordinate Rules for Reflections
Problem 2 Coordinate Rules for Translations
Problem 3 Coordinate Rules for Rotations
Problem 4 Coordinate Rules for Transformation Combinations
8AL 8 Compare quadrilaterals, triangles, and solids using their
properties and characteristics.
8Al 8a Formulating mathematical arguments about the relationships
among types of quadrilaterals and triangles.
8Al 8b Identifying angle bisectors, perpendicular bisectors, congruent
angles, and congruent shapes.
8Al 8c Constructing congruent and similar polygons, congruent angles,
congruent segments, and parallel and perpendicular lines.
8AL 9 Determine measures of special angel pairs, including adjacent,
vertical, supplementary, complementary angles, and angles formed by
parallel lines by a transversal.
8AL 12 Determine lengths of missing sides and measures of angles in
similar and congruent shapes.
8AL 12a Applying proportional reasoning to identify similar and
congruent shapes.
8AL 12b Using dilations on the coordinate plane to determine
measures of similar shapes.
8AL 12c Determining ratios of perimeters and areas of similar
triangles, trapezoids, and parallelograms.
*****I could not find evidence that the following objectives are covered in the 8th grade CMP2 materials:
8AL 1b Using vocabulary associated with sets, including union, subsets, empty sets, and intersection.
8AL 14b Determining the probability of two independent events or two dependent events.