Grade 8 Mathematics Curriculum Map
Unit Time Line / Skills / Standards / Lesson MaterialsThinking with Mathematical Models
Moving Straight Ahead
6 weeks / Plotting points on a Cartesian plane
Recognizing linear relationships in tables, equations and graphs
Finding the equation of a line from a table and a graph
Matching the different representations of a linear relationship (table, equation, graph)
Graphing linear equations
Finding the slope/rate of change of a line from a table and a graph
Recognizing non-linear graphs
Translating verbal sentences into equations and inequalities
Solving one & two step equations / 7A.7 Draw the graphic representation of a pattern from an equation or from a table of data
7A.8 Create algebraic patterns using charts/tables, graphs, equations, and expressions
7A.10 Write an equation to represent a function from a table of values
8A.3 Describe a situation involving relationships that matches a given graph
8A.4 Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship
8A.15 Understand that numerical information can be represented in multiple ways: arithmetically, algebraically and graphically
8A.16 Find a set of ordered pairs to satisfy a given linear numerical pattern (expressed algebraically); then plot the ordered pairs and draw the line
8G.13 Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change
8G.14 Determine the y-intercept of a line from a graph and be able to explain the y-intercept
8G.15 Graph a line using a table of values
8G.16 Determine the equation of a line given the slope and the y-intercept
8G.17 Graph a line from an equation in slope-intercept form (y=mx+b)
8G.18 Solve systems of equations graphically (only linear, integral solutions, y=mx+b format, no vertical/horizontal lines)
8G.19 Graph the solution set of an inequality on a number line
8G.20 Distinguish between linear and nonlinear equations ax²+bx+c; a=1 (only graphically)
8G.21 Recognize the characteristics of quadratics in tables, graphs, equations, and situations / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
CMP unit Moving Straight Ahead
(Use the Application & Connection problems at the end of the Investigations)
:
Investigation 1
Investigation 2
Investigation 3
Investigation 4
Investigation 5
CMP unit Thinking with Mathematical Models:
Investigation 1
Investigation 4
Impact Book 3:
Section 1.1;1.2;1.3
Teacher Handouts
Use of graphing calculators
Unit Time Line / Skills / Standards / Lesson Materials
Looking for Pythagoras
3 weeks / Identify the legs and hypotenuse of a right triangle and justify this answer using definitions
Substitute into the Pythagorean Theorem and solve the equation to find the missing side of a right triangle.
Know that the Pythagorean Theorem works only on right triangles and that it works on every right triangle.
Substitute into the Pythagorean Theorem to determine if a triangle is a right triangle.
Answer word problems using the Pythagorean Theorem by drawing a diagram.
Identify supplementary and complementary angles
Find a missing angle in a supplementary or complementary pair
Find the missing angle when the measure of all angles adds to 180 degrees.
Find the missing angle when the measure of all angles add to 90 degrees
Write and solve an algebraic equation to find a missing angle in a complementary and supplementary pair
Know that all vertical angles are congruent
Identify vertical angles in the case of two intersecting lines
In the case of two intersecting lines, there are two pairs of vertical angles
Give the measure of all angles when given two intersecting lines and the measure of one angle
Know that when a parallel line is cut by a transversal, 8 angles are formed
Know that all acute angles are congruent and all obtuse angles are congruent when parallel lines are cut by a transversal
Give the measure of all angles formed by parallel lines cut by a transversal when given the measure of one angle
Write and solve an algebraic equation to find a missing angle when two parallel lines are cut by a transversal / 7.G.6 Explore the relationship between the lengths of the three sides of a right triangle to develop the Pythagorean Theorem
7.G.8 Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle
7.G.9 Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator
8.A.12 Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines
8.N.2 Evaluate expressions with integral exponents
8.N.6 Justify the reasonableness of answers using estimation
8.G.1 Identify pairs of vertical angles as congruent
8.G.2 Identify pairs of supplementary and complementary angles
8.G.3 Calculate the missing angle in a supplementary or complementary pair
8.G.4 Determine angle pair relationship when given two parallel lines cut by a transversal
8.G.5 Calculate the missing angle measurements when given two parallel lines cut by a transversal
8.G.6 Calculate the missing angle measurements when given two intersecting lines and an angle / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
CMP unit: Looking for Pythagoras
(Use the Application & Connection problems at the end of the Investigations)
Investigation 1
Investigation 4.2
Teacher handouts
State test Questions
Glencoe: Grade 8 Mathematics, New York Review Series
Unit Time Line / Skills / Standards / Lesson Materials
Say it with Symbols
6 weeks / Evaluate expressions by applying the rules for order of operations
Write symbolic sentences that communicate their reasoning
Link a narrative to a corresponding graph (and link a graph to a corresponding narrative)
Translate a mathematical expression into a verbal expression
Symbolically represent a verbal expression
Recognize equivalent expressions
The Distributive Property
Combining like terms
Adding polynomials
Subtracting polynomials
Using FOIL
Solving equations with variables on both sides
Dividing polynomials
Factoring and ‘undoing’ techniques
Factoring quadratic equations / 7.A.2 Add and subtract monomials with exponents of one
7.A.3 Identify a polynomial as an algebraic expression containing one or more terms
7.A.4 Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation
7.A.7 Draw the graphic representation of a pattern from an equation or from a table of data
7.A.8 Create algebraic patterns using charts/tables, graphs, equations, and expressions
7.A.10 Write an equation to represent a function from a table of values
8.N.6 Justify the reasonableness of answers using estimation
8.A.1 Translate verbal sentences into algebraic inequalities
8.A.2 Write verbal expressions that match given mathematical expressions
8.A.3 Describe a situation involving relationships that matches a given graph
8.A.5 Use physical models to perform operations with polynomials
8.A.6 Multiply and divide monomials
8.A.7 Add and subtract polynomials (integer coefficients)
8.A.8 Multiply a binomial by a monomial or binomial (integer coefficients)
8. A.9 Divide a polynomial by a monomial (integer coefficients) Note: The degree of the denominator is less than or equal to the degree of the numerator for all variables.
8.A.10 Factor algebraic expressions using the GCF
8. A.11 Divide a polynomial by a monomial (integer coefficients) Note: The degree of the denominator is less than or equal to the degree of the numerator for all variables.
8.A.13 Solve multi-step inequalities and graph the solution set on a number line
8.A.14 Solve linear inequalities by combining like terms, using the distributive property, or moving variables to one side of the inequality (include multiplication or division of inequalities by a negative number)
8.A.15 Understand that numerical information can be represented in multiple ways: arithmetically, algebraically and graphically
8.A.19 Interpret multiple representations using equation, table of values and graph / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
CMP Unit: Say it with Symbols
(Use the Application & Connection problems at the end of the Investigations)
Investigation 1: 1.1
Investigation 2: 2.1 2.2,
Investigation 3: 3.2, 3.4
Investigation on Factoring Quadratics in the new Say it with Symbols booklet
Stela’s Boutique booklet
Teacher handouts
Impact Book 3
Chapter 4.1
Pazzazz Worksheets
Unit Time Line / Skills / Standards / Lesson Materials
Frogs, Fleas & Painted Cubes
3 - 4 weeks / Know that a function is a relationship where there is one unique value in the range for every value in the domain.
Use the Vertical Line Test to determine if a relationship is a function.
Use a table of values to determine if data represented is a function.
Generate a table of values given a function using substitution and correct function notation.
Determine the degree of a function. Compare the characteristics of tables and graphs for quadratic and linear relationships
Analyze quadratic relationships by examining tables, graphs & equations
Substitute into a quadratic formula to find a table of values.
Graph a parabola from a table of values.
Understand the significance of x and y intercepts, maximum & minimum points and lines of symmetry
/ 7.A.7 Draw the graphic representation of a pattern from an equation or from a table of data
7.A.8 Create algebraic patterns using charts/tables, graphs, equations, and expressions
7.A.10 Write an equation to represent a function from a table of values
8.N.6 Justify the reasonableness of answers using estimation
8.A.3 Describe a situation involving relationships that matches a given graph
8.A.4 Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship
8.A.5 Use physical models to perform operations with polynomials
8.A.8 Multiply a binomial by a monomial or binomial (integer coefficients)
8.A.9 Divide a polynomial by a monomial (integer coefficients) Note: The degree of the denominator is less than or equal to the degree of the numerator for all variables
8.A.10 Factor algebraic expressions using the GCF
8.A.11 Factor a trinomial in the form ax²+bx+c; a=1 and c having no more than 3 sets of factors
8.A.15 Understand that numerical information can be represented in multiple ways: arithmetically, algebraically and graphically
8.A.17 Define and use correct terminology when referring to function (domain and range)
8.A.18 Determine if a relation is a function
8.A.19 Interpret multiple representations using equation, table of values and graph
8.G.20 Distinguish between linear and nonlinear equations ax²+bx+c; a=1 (only graphically)
8.G.21 Recognize the characteristics of quadratics in tables, graphs, equations, and situations / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
CMP unit: Frogs, Fleas & Painted Cubes
(Use the Application & Connection problems at the end of the Investigations)
Investigation 1: 1.1, 1.2,1.3,
Investigation 2: 2.4
Investigation 3: 3.1, 3.2
Investigation 4: 4.1, 4.3
Impact Book 3
Chapter 7.2, 7.3
Teacher handouts
Pazzazz Worksheets
Unit Time Line / Skills / Standards / Lesson Materials
Kaleidoscopes, Hubcaps & Mirrors
3 weeks / Tell what transformation has been acted upon an image and provide a clear rationale.
Translate an image given its coordinates.
Reflect an image over a given line or axis.
Reflect an image 90 degrees clockwise and counter clockwise and 180 degrees clockwise and counter clockwise.
Explain why the figure appears the same when rotated 180 degrees clockwise or counter clockwise.
Dilate an image by a whole number or a fraction.
Know what characteristics are preserved and changed under each transformation. / 8. G.7 Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations.)
8.G.8 Draw the image of a figure under rotations of 90 and 180 degrees
8.G.9 Draw the image of a figure under a reflection over a given line
8.G.10 Draw the image of a figure under a translation
8.G.11 Draw the image of a figure under a dilation
8.G.12 Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
CMP unit: Kaleidoscopes, Hubcaps & Mirrors
(Use the Application & Connection problems at the end of the Investigations)
(Note that little of this particular book is used)
Impact Book 3
Chapter 5.4, 5.5
Teacher Handouts
Unit Time Line / Skills / Standards / Lesson Materials
Growing, Growing, Growing
3 weeks / Recognize & describe situations in which variables grow and decay exponentially
Using exponents
Represent exponential patterns with tables, graphs and equations
Understanding the symbols used in the equation y = a(b)x
Determine the growth and decay factors in exponential situations
Describing the effects of varying the values of a and b in the equation y = a(b)x
Explore the significance of the shapes of exponential graphs
Use tables, graphs and equations to solve problems involving exponential growth and decay
Compare and contrast exponential and linear relationships / 7.A.7 Draw the graphic representation of a pattern from an equation or from a table of data
7.A.8 Create algebraic patterns using charts/tables, graphs, equations, and expressions
7.A.10 Write an equation to represent a function from a table of values
8.N.1 Develop and apply the laws of exponents for multiplication and division
8.N.2 Evaluate expressions with integral exponents
8.N.6 Justify the reasonableness of answers using estimation
8.A.2 Write verbal expressions that match given mathematical expressions
8.A.3 Describe a situation involving relationships that matches a given graph
8.A.4 Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship
8.A.6 Multiply and divide monomials
8.A.15 Understand that numerical information can be represented in multiple ways: arithmetically, algebraically and graphically
8.A.17 Define and use correct terminology when referring to function (domain and range)
8.A.18 Determine if a relation is a function
8.A.19 Interpret multiple representations using equation, table of values and graph
8.G.13 Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change / Note that the CMP Teachers Guide has suggested questions for each Investigation. Teachers are recommended to read the Teachers Guide before embarking on the unit.
CMP unit: Growing, Growing, Growing
(Use the Application & Connection problems at the end of the Investigations)
Investigation 1: 1.1, 1.2, 1.3
Investigation 2: 2.1, 2.2
Investigation 3: 3.1, 3.2, 3.3
Investigation 4: 4.1, 4.2, 4.3
Unit Project
Impact Book 3
Chapter 3.2
Teacher Handouts
Note: The following performance indicators do not appear in any specific unit and need to be covered during the year and during the Test Review