Eighth Grade Mathematics
Instr Seq / COS # / Course of Study Objective / Suggested Lesson Resources/Activities / Lesson Plan(description, number, etc.) / Date Implemented /
The Number System
Know that there are numbers that are not rational, and approximate them by rational numbers.
3 / 8.1 / Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. [8-NS1] / Real # Properties:
76237 (WS) MA7ZZ23(Q)
Rational/Irrational #’s:
M8003 M8004(Q)
Repeating Decimals to Fractions:
M8011 M8012 M8013(Q) Rational # Equivalents:
AL109(WS) AL-2K02(Q) / Holt Grade 8: 1.1 and 3.7
Larson Pre-Algebra: 5.1 and 9.4
3 / 8.2 / Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 2).[8-NS2]
Example: By truncating the decimal expansion of , show that is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. / Compare/Order #’s:
M8023 M8024 M8025(Q)
M8026(R) M8027(R) M8028(Q) / Holt Grade 8: 3.7 Extension
Larson Pre-Algebra: 5.1 and 9.4
Expressions and Equations
Work with radicals and integer exponents.
2 / 8.3 / Know and apply the properties of integer exponents to generate equivalent numerical expressions. [8-EE1]
Example: / Exponents:
M7001 M7002 M7003(Q)
M7004(R) M7005(R) M7006(Q)
Integers as Exponents:
8062(WS) MA8ZZ24(Q) / Holt Grade 8: 3.1, 3.2, and lab after 3.6
Larson Pre-Algebra: 4.5 and 4.6
3 / 8.4 / Use square root and cube root symbols to represent solutions to equations of the form and , where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is irrational. [8-EE2] / Roots:
M8017 M8018 M8019(Q)
M8020(R) M8021(GA) M8022(Q)
Squares and Square Roots:
8066(GA/WS) MA8ZZ12(Q)
Powers and Roots:
AL021(GA/WS) AL-2B09(Q)
Irrational #’s as Decimals:
AL110(GA/WS) AL-2K03(Q) / Holt Grade 8: 3.5 and lab after 3.6
Larson Pre-Algebra: 1.2 and 4.6
2 / 8.5 / Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. [8-EE3]
Example: Estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. / Scientific Notation:
M7007 M7008 M7009(Q)
M7010(R) M7011 M7012(Q)
Exponents and Scientific Notation:
AL048(WS) AL-2E03(Q) / Holt Grade 8:
3.3
Larson Pre-Algebra:
4.7
2 / 8.6 / Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. [8-EE4] / Scientific Notation Representation:
M7013 M7014(Q)
Scientific Notation:
M8001 M8002(Q) AL048(R)
Computing in Scientific Notation:
AL049 AL-2E04(Q) / Holt Grade 8: 3.4 and lab following
Larson Pre-Algebra:
4.7
Understand the connections among proportional relationships, lines, and linear equations.
3 / 8.7 / Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]
Example: Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. / Remedial Intro to Proportions:
M7057
Slope of a Line:
M8207 M8208 M8209(Q)
M8210(R) M8211(R) M8212(Q)
AL089(WS) AL-2104(Q) / Holt Grade 8:
4.1, 4.2, and 8.2
Larson Pre-Algebra:
6.1, 6.2, 6.3, 8.4
3 / 8.8 / Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8-EE6] / Writing Equations in Slope-Intercept Form:
M8213 M8214(Q)
Finding Function Rules:
M8215 M8216 M8217(Q)
M8218(R) M8219(R) M8220(Q) / Holt Grade 8:
Functions: 2.4, 2.5
Similar Figures: 4.3
Lab “Explore Slope” following 8.1
Larson Pre-Algebra:
6.4 Similarity
8.1, 8.4, and 8.6
Analyze and solve linear equations and pairs of simultaneous linear equations.
1 / 8.9 / Solve linear equations in one variable. [8-EE7] / *See 8.9a and 8.9b / *See 8.9a and 8.9b
1 / 8.9a / Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation of the form x = a, a = a, or a = b results (where a and b
are different numbers). [8-EE7a] / Remedial Solving One-Step Equations:
M7302(R) M7304(Q)
Add/Subtract to Solve Equations:
8064(WS) MA8ZZ26(Q)
Multiply/Divide to Solve Equations:
8120(WS) MA8ZZ06(Q) / Holt Grade 8: 1.5, 1.6, 7.1-7.3 with labs and extensions
Larson Pre-Algebra:
3.3
1 / 8.9b / Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions, using the distributive property and collecting like terms. [8-EE7b] / Solving Equations with Fractions:
AL029(WS) AL-2C05(Q)
Remedial Solving Two-Step Equations:
M7296 M7297 M7298(Q)
Solving Two-Step Equations:
8079(WS) 8121 MA8ZZ01(Q)
Solving Multi-Step Equations:
AL030(WS) AL-2C06(Q) / Holt Grade 8: 1.5, 1.6, 7.1-7.3 with labs and extensions
Larson Pre-Algebra:
2.3-2.7, 3.1-3.3, 5.7
3 / 8.10 / Analyze and solve pairs of simultaneous linear equations. [8-EE8] / *Note: All listed activities for 8.10a-c flow together.
3 / 8.10a / Understand that solutions to a system of two linear equations in two variables correspond to points of intersections of their graphs because points of intersection satisfy both equations simultaneously. [8-EE8a] / Common Solutions/Intersecting Lines:
AL099(WS) AL-2J03(Q) / Holt Grade 8: 7.4, 8.6
Larson Pre-Algebra:
8.8
3 / 8.10b / Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. [8-EE8b]
Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. / Solving Linear Equation Systems by Substitution:
AL100(WS) AL-2J04
Solving Linear Equation Systems by Elimination:
AL101(WS) AL-2J05(Q) / Holt Grade 8: 7.4, 8.6
Larson Pre-Algebra:
8.8
3 / 8.10c / Solve real-world and mathematical problems leading to two linear equations in two variables. [8-EE8c]
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. / Graphing Systems of Linear Equations:
AL102(WS) AL-2J06(Q) / Holt Grade 8: 7.4, 8.6
Larson Pre-Algebra:
8.8
Functions
Define, evaluate, and compare functions.
3 / 8.11 / 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. (Function notation is not required in Grade 8.) [8-F1] / Remedial Function Tables and Graphs:
M7237(R) M7238(Q)
Lines as Functions:
AL091(WS) AL-2l06(Q)
Graphing Linear Equations Review:
8081(WS) 8123(R) MA8ZZ48(Q) / Holt Grade 8: 2.4, 9.3
Larson Pre-Algebra:
8.1
3 / 8.12 / Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8-F2]
Example: Given a linear function represented by a table of values and linear function represented by an algebraic expression, determine which function has the greater rate of change. / Tables and Ordered Pairs:
M8187(R) M8188(Q)
Equations and Lines:
M8189(R) M8190(Q)
Finding a Function Rules:
M8215 M8216 M8217(Q)
M8218(R) M8219 M8220(Q) / Holt Grade 8: 2.5 and “Use Multiple Representations” lab, 9.4
Larson Pre-Algebra:
8.2-8.5
3 / 8.13 / 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. [8-F3]
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. / Slope-Intercept Form:
M8213 M8214(Q)
Determine if a Function is Linear:
M8221 M8222 M8223(Q)
M8224(R) M8225 M8226(Q)
Graphing Equations:
AL087(WS) AL-2l02(Q) / Holt Grade 8: Lab on p.355
Larson Pre-Algebra:
8.2, Focus on Functions p.412A, 8.5
Use functions to model relationships between quantities.
3 / 8.14 / 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 linear function in terms of the situation it models and in terms of its graph or a table of values. [8-F4] / Slope of a Line:
M8207 M8208 M8209(Q)
M8210(R) M8211 M8212(Q)
Slopes of Lines:
AL089(WS) AL-2l04(Q) / Holt Grade 8: 8.3 and 8.4
Larson Pre-Algebra:
8.4-8.6
3 / 8.15 / Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8-F5] / X- and Y- Intercepts:
M8205 M8206(Q)
Intercepts of Lines:
AL088(WS) AL-2l03(Q)
Graphs Without Numbers:
AL095(WS) AL-2l10(Q) / Holt Grade 8: 2.3, 8.1, 8.5
Larson Pre-Algebra: 8.2, 8.3, 8.6.
Geometry
Understand congruence and similarity using physical models, transparencies, or geometry software.
4 / 8.16 / Verify experimentally the properties of rotations, reflections, and translations: [8-G1]
4 / 8.16a / a. Lines are taken to lines, and line segments are taken to line segments of the same length. [8-G1a] / Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations M8137Quiz 2 Transformations M8138 / Holt Grade 8: Lab p.220, 5.6
Larson Pre-Algebra:
12.4-12.6
4 / 8.16b / b. Angles are taken to angles of the same measure. [8-G1b] / Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations M8137Quiz 2 Transformations M8138 / Holt Grade 8: Lab p.220, 5.6
Larson Pre-Algebra:
12.4-12.6
4 / 8.16c / c. Parallel lines are taken to parallel lines. [8-G1c] / Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations M8137Quiz 2 Transformations M8138 / Holt Grade 8: Lab p.220, 5.6
Larson Pre-Algebra:
12.6
42 / 8.17 / Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. [8-G2] / Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations M8137Quiz 2 Transformations M8138 / Holt Grade 8: 5.5, Lab p.237
Larson Pre-Algebra:
6.3, 6.4, 12.4-12.6
4 / 8.18 / Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. [8-G3] / Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations M8137Quiz 2 Transformations M8138 / Holt Grade 8: Lab p.174, 4.4, 5.7, 5.8
Larson Pre-Algebra:
12.4-12.7
4 / 8.19 / Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. [8-G4] / Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations M8137Quiz 2 Transformations M8138 / Holt Grade 8: Lab p.168, 4.3
Larson Pre-Algebra:
6.4, 12.4-12.7
4 / 8.20 / Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. [8-G5]
Example: Arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give argument in terms of transversals why this is so. / Interior and Exterior Angles:
M7125 M7126(Q)
Angle Measurement:
M7127 M7128 M7129(Q)
M7130(R) M7131(R) M7132(Q)
M7151 M7152 M7153(Q)
M7154 M7155 M7156(Q)
Angles and Lines:
76267(WS) MA7ZZ41(Q)
Lines and Angles I:
8083(WS)
Lines and Angles II:
8125 MA8ZZ02(Q)
Angle Measures in a Triangle:
AL120(WS) AL-2L03(Q)
/ Holt Grade 8: 5.2, 5.3, Lab p.212
Larson Pre-Algebra:
Focus p.494, Concept Activity p.691, 12.2, 12.3
Understand and apply the Pythagorean Theorem.
4 / 8.21 / Explain a proof of the Pythagorean Theorem and its converse. [8-G6] / Pythagorean Theorem:
8092(WS) 8130 MA8ZZ02(Q) / Holt Grade 8: Lab p.131, Lab p.136
Larson Pre-Algebra: Activity p.493A
4 / 8.22 / Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. [8-G7] / Remediation on Pythagorean Theorem:
M7133(R) M7134(R/Q) M7136(R)
M7137(Q) M7138(R) M7139(R)
M7140(R/Q) 76270(R/WS) 76271(R)
MA7ZZ15(R/Q)
Grade-level Pythagorean Theorem:
M8121 M8122 M8123(Q)
M8124 M8125 M8126(Q)
AL033(WS) AL-2C09(Q) / Holt Grade 8: 3.8
Larson Pre-Algebra: 9.3, 9.4, 9.6, 10.6
4 / 8.23 / Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8-G8] / *No activities found in Compass* / Holt Grade 8: 3.9
Larson Pre-Algebra: 9.4, 9.5
Statistics and Probability
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
4 / 8.24 / Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. [8-G9] / Volume:
M8145 M8146 M8147(Q)
M8148 M8149 M8150(Q)
Volumes of Prisms and Cylinders:
8090(WS) MA8ZZ07(Q)
Volumes of Pyramids and Cones:
8091(WS) MA8ZZ09(Q) / Holt Grade 8: Lab p.266, 6.2, Lab p.274, 6.3, 6.4
Larson Pre-Algebra: 10.7, pgs. 578-583, pgs. 586-591
Investigate patterns of association in bivariate data.
1 / 8.25 / 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. [8-SP1] / Scatter Plots I: 8096(WS)
Scatter Plots II:
8134 MA8ZZ39(Q) / Holt Grade 8: 9.1
Larson Pre-Algebra: 1.8, 2.6, 3.1, 3.6, 7.7, 8.6, Focus p.447A-447B, 11.3
1 / 8.26 / 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. [8-SP2] / Scatter Plots I: 8096(WS)
Scatter Plots II:
8134 MA8ZZ39(Q) / Holt Grade 8: Lab p.394
Larson Pre-Algebra: 8.6, Technology Activity p.445
3 / 8.27 / Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8-SP3]
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. / *No activities found in Compass* / Holt Grade 8: 9.2
Larson Pre-Algebra: 8.4, 8.5, p.436-437B, 8.6
4 / 8.28 / 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. [8-SP4]
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? / Histograms:
8095(WS) 8133 MA8ZZ10(Q)
Organizing Data:
AL067(WS) AL-2G01(Q) / Holt Grade 8: Extension p.396
Larson Pre-Algebra: Two-Way Tables Focus p.647A-647B
The Number System [NS]
• Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations [EE]
• Work with radicals and integer exponents.
• Understand the connections among proportional relationships, lines, and linear equations.
• Analyze and solve linear equations and pairs of simultaneous linear equations.
Functions [F]
• Define, evaluate, and compare functions.
• Use functions to model relationships between quantities.
Geometry [G]
• Understand congruence and similarity using physical models, transparencies, or geometry software.
• Understand and apply the Pythagorean Theorem.
• Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Statistics and Probability [SP]
• Investigate patterns of association in bivariate data.
*Key: (R) –remediation; (Q)-quiz; (WS)-worksheet