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Math 8

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Math 8 Standards of Learning Resources Click on the SOL Number to view the resources

Number and Number Sense

8.1 The student will

(a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers;

(b) recognize, represent, compare, and order rational numbers expressed in scientific notation; and

(c) compare and order decimals, fractions, percents, and numbers written in scientific notation.

8.2 The student will describe orally and in writing the relationship between the subsets of the real number system.

Computation and Estimation

8.3 The student will solve practical problems involving rational numbers, percents, ratios, and proportions. Problems will be of varying complexities and will involve real-life data, such as finding a discount and discount prices and balancing a checkbook.

8.4 The student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables. Problems will be limited to positive exponents.

8.5 The student, given a whole number from 0 to 100, will identify it as a perfect square or find the two consecutive whole numbers between which the square root lies.

Measurement

8.6 The student will verify by measuring and describe the relationships among vertical angles, supplementary angles, and complementary angles and will measure and draw angles of less than 360°.

8.7 The student will investigate and solve practical problems involving volume and surface area of rectangular solids (prisms), cylinders, cones, and pyramids.

eometry

8.8 The student will apply transformations (rotate or turn, reflect or flip, translate or slide, and dilate or scale) to geometric figures represented on graph paper. The student will identify applications of transformations, such as tiling, fabric design, art, and scaling.

8.9 The student will construct a three-dimensional model, given the top, side, and/or bottom views.

8.10 The student will

(a) verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement; and

(b) apply the Pythagorean Theorem to find the missing length of a side of a right triangle when given the lengths of the other two sides 

Probability and Statistics

8.11 The student will analyze problem situations, including games of chance, board games, or grading scales, and make predictions, using the knowledge of probability.

8.12 The student will make comparisons, predictions, and inferences, using information displayed in frequency distributions; box-and-whisker plots; scattergrams; line, bar, circle, and picture graphs; and histograms.

8.13 The student will use a matrix to organize and describe data.

Patterns, Functions, and Algebra

8.14 The student will

(a) describe and represent relations and functions, using tables, graphs, and rules; and

(b) relate and compare tables, graphs, and rules as different forms of representation for relationships.

8.15 The student will solve two-step equations and inequalities in one variable, using concrete materials, pictorial representations, and paper and pencil.

8.16 The student will graph a linear equation in two variables, in the coordinate plane, using a table of ordered pairs.

8.17 The student will create and solve problems, using proportions, formulas, and functions.

8.18 The student will use the following algebraic terms appropriately: domain, range, independent variable, and dependent variable.

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Objective:

8.1 The student will

(a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers;

(b) recognize, represent, compare, and order rational numbers expressed in scientific notation; and

(c) compare and order decimals, fractions, percents, and numbers written in scientific notation.

Text Resources:

1.2, 1.3

AIMS Resources:

Historical Connections in Mathematics, Vol. III: "Lagrange's Four Square Theorem"

Historical Connections in Mathematics, Vol. II: "The Curious Cab," "Calculator Fun"

Machine Shop: "Nuts and Bolts"

What's Next? Vol. 3: "The Binomial Theorem"

Suggested Manipulatives:

Technology and Web Resources:

Order of Operations

Other Resources:

Pre-Algebra Step-by-Step, Frank Schaeffer Publications

Pre-Algebra with Pizzazz,Steve & Janis Marcy

Assessment Suggestions:

Stanford 9 Test Objective

Suggestions for Integration:

.
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Objective:

8.2 The student will describe orally and in writing the relationship between the subsets of the real number system.

Text Resources:

9.3

AIMS Resources:

Historical Connections in Mathematics, Vol III: "Fibonacci Discoveries"

Historical Connections in Mathematics, Vol. II: "Perfect Numbers," "Counting Partitions"

Historical Connections in Mathematics, Vol. I: ""Number Shapes," ""Square, Oblong, & Triangular Numbers," "Pythagorean Discoveries"

What's Next? Vol 3: "Connections That Count"

What's Next? Vol 1: "Figuratively Speaking"

Suggested Manipulatives:

Technology and Web Resources:

Other Resources:

Pre-Algebra Step-by-Step, Frank Schaeffer Pub.

Assessment Suggestions:

Suggestions for Integration:

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Objective:

8.3 The student will solve practical problems involving rational numbers, percents, ratios, and proportions. Problems will be of varying complexities and will involve real-life data, such as finding a discount and discount prices and balancing a checkbook.

Text Resources:

1.1, 2.1-2.8, 3.1, 3.2, 3.4, 3.5, 6.4, 8.6, 8.9 8.3

AIMS Resources:

 

Fun with Foods: "Salad Daze," "Paper Caper," "Fractions Fondue," "Waste Not, Want Not"

Find your Bearings: "Surf 'n Sand"

Find Your Bearings: "Bird's Eye View," "Shop 'til You Drop," "Mystery Mountain"

Through the Eyes of the Explorers: "Plane Table Mapping," "It's a Court Case," "Pacing the Yard," "Honey, I Shrunk the..."

Floaters and Sinkers: "Where Do You Draw the Line?", "A Displaced Object," "A Salty Solution," "Orange's Life Jacket," "Orange's Secret," "It Floats, It Sinks"

Macine Shop:"Sandbagging the Seesaw"

What's Next? Vol 3: "How Fast Can You Throw"

Suggested Manipulatives:

Technology and Web Resources:

Calculator

The Challenge of the Unkown film: "Dinosaurs"

Decimals, Whole Numbers, and Exponents

Other Resources:

Pre-Algebra Step-by-Step: Frank Schaeffer Pub., pp. 19-34

Estimation by Design, etc.: Russell Jacobs, p. 3

National Teacher Training Institute folder: p.175

Essential Mathematics For Life: Whole Numbers:

Scott Foresman, pp. 23, 123, 144-148, 154-158

National Teacher Training Institute folder, p. 191

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

.
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Objective:

8.4 The student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables. Problems will be limited to positive exponents.

Text Resources:

1.3

AIMS Resources:

Mostly Magnets: "What's the Attraction?", "Magnets Apart"

Machine Shop: "Nuts and Bolts"

Historical Connections in Mathematics Vol. 1: "Pascal's Triangle Activities," "Square, Oblong, and Triangular Numbers"

Suggested Manipulatives:

Technology and Web Resources:

Multiple Binomials

Other Resources:

Algebra by Design, Russell Jacobs, pp. 3-4

Pre-Algebra with Pizzazz,Steve & Janis Marcy

Algebra with Pizzazz, Steve & Janis Marcy

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

.
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Objective:

8.5 The student, given a whole number from 0 to 100, will identify it as a perfect square or find the two consecutive whole numbers between which the square root lies.

Text Resources:

9.1, 9.2

AIMS Resources:

Historical Connections in Mathematics Vol. II: "Heron's Square Root Method," "Heron's Formula"

Historical Connections in Mathematics Vol. III: "Fibonacci Discoveries," "Lagrange's Four Square Theorem"

Suggested Manipulatives:

Technology and Web Resources:

FACTORING LARGE NUMBERS

Other Resources:

Middle School Math with Pizzazz, Steve & Janis Marcy, pp. 71-72

Pre-Algebra with Pizzazz, Steve & Janis Marcy, Book CC

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

.
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Objective:

8.6. The student will verify by measuring and describe the relationships among vertical angles, supplementary angles, and complementary angles and will measure and draw angles of less than 360°.

Text Resources:

5.1

AIMS Resources:

The Sky's the Limit: "How High Is It?", "Water Rockets," "Unbelievable Flying Objects," "More Unbelievable Flying Objects," "..But Will It Fly?"

What's Next? Vol. 2: "A Matter of Degrees"

Suggested Manipulatives:

Protractor, straight edge

Technology and Web Resources:

Conjectures in Geometry

Other Resources:

Introduction to Geometry, Frank Schaeffer Pub.

Middle School Math with Pizzazz, Steve & Janis Marcy, Book D, P. 28, 30, 31

Basic Geometric Concepts, Frank Schaeffer Pub., p. 80

Pre-Algebra with Pizzazz, Steve & Janis Marcy, Book CC

Assessment Suggestions:

Suggestions for Integration:

.
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Objective:

8.7 The student will investigate and solve practical problems involving volume and surface area of rectangular solids (prisms), cylinders, cones, and pyramids.

Text Resources:

11.3, 11.4, 11.5, 11.6

AIMS Resources:

The Sky's the Limit: "Bernoulli Was a Bird Brain"

Suggested Manipulatives:

Technology and Web Resources:

Exploring Similarity Using Scale Drawings

Other Resources:

Introduction to Geometry, Frank Schaeffer Pub., pp. 86, 92, 94

Middle School Math with Pizzazz, Frank & Janis Marcy, Book D, pp. 64-70

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

.
Back to top.

Objective:

8.8 The student will apply transformations (rotate or turn, reflect or flip, translate or slide, and dilate or scale) to geometric figures represented on graph paper. The student will identify applications of transformations, such as tiling, fabric design, art, and scaling.

Text Resources:

5.4, 5.7, 8.10, 10.7-10.9

AIMS Resources:

Pieces and Patterns: "Inside Job"

Suggested Manipulatives:

Technology and Web Resources:

The Challenge of the Unknown film "Sun Sculpture" , "Giant Egg"

More Paper-Cutting Patterns

Other Resources:

Cooperative Informal Geometry, Wade H. Sherard, III, pp. 30-36

Introduction to Geometry Robyn Silby, pp. 49-50

National Teacher Training Institute folder, p. 249

Pre-Algebra, Frank Schaeffer Pub.

Basic Geometric Concepts,Frank Schaeffer Pub., pp 64-65

Introduction to Geometry, Robyn Silby

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

.
Back to top.

Objective:

8.9 The student will construct a three-dimensional model, given the top, side, and/or bottom views.

Text Resources:

11.2

AIMS Resources:

Vol. X, No. 4, Nov. '95, "Working out the Wiggles", p. 38

Historical Connections in Mathematics Vol. III: "Box It Up"

Historical Connections in Mathematics Vol. II: "White-Faced Cubes"

Suggested Manipulatives:

Ruler, Protractor

Technology and Web Resources:

Water To the Max

Other Resources:

Introduction to Geometry, Robyn Silby, pp. 26-31; pp. 81-83

Basic Geometric Concepts, Frank Schaeffer Pub., pp. 26-31; pp. 81-83

Build Your Own Polyhedra, Dale Seymour

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

.
Back to top.

Objective:

8.10 The student will

(a) verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement; and

(b) apply the Pythagorean Theorem to find the missing length of a side of a right triangle when given the lengths of the other two sides.

Text Resources:

9.1, 9.4, 9.5

AIMS Resources:

Pieces and Patterns: "Probably Pythagorean"

Historical Connections in Mathematics Vol. I: "The Pythagorean Puzzle"

Historical Connections in Mathematics Vol. II: "Make a Square Puzzle," "Smart Shadows"

Through the Eyes of the Explorers: "Sizing Up Shadows"

Suggested Manipulatives:

Calculator

Technology and Web Resources:

The Challenge of the Unknown, "Wind Prospecting"

Pythagorean Theorem

Other Resources:

Introduction to Geometry, pp. 77-80

Pre-Algebra Step by Step, p. 52

Pre-Algebra with Pizzazz, Book CC, p. 51-55

Middle School Math with Pizzazz, pp. 73-76

Assessment Suggestions:

Suggestions for Integration:

.
Back to top.

Objective:

8.11 The student will analyze problem situations, including games of chance, board games, or grading scales, and make predictions, using the knowledge of probability.

Text Resources:

6.6

AIMS Resources:

Find Your Bearings: "Surf 'n Sand"

What's Next? Vol. 1: "The End of the World," "Pascal Wins the World's Series"

Suggested Manipulatives:

Technology and Web Resources:

Other Resources:

The Challenge of the Unknown, "Dinosaurs," "Locks"

Thinking with Mathematical Models

Fantasy Baseball

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

Back to top.

Objective:

8.12 The student will make comparisons, predictions, and inferences, using information displayed in frequency distributions; box-and-whisker plots; scattergrams; line, bar, circle, and picture graphs; and histograms.

Text Resources:

4.1, 4.2

AIMS Resources:

 

Mostly Magnets: "Fish and Clips, " "What's the Attraction," "Magnets Apart"

Find Your Bearings: "Surf 'n Sand", "Forecast for Today"

Pieces and Patterns: "Jellybean Lab," " M&M's Lab"

Floaters and Sinkers: "What's In a BB?"

Jawbreakers and Heart Thumpers: "By Golly, By Gum," "By Golly, By Gum, By Time"

Machine Shop: "Watt Power"

Historical Connections in Mathematics Vol. II: "Paper Folding a Parabola"

Suggested Manipulatives:

Technology and Web Resources:

SMILE METRIC STYLE

Other Resources:

Middle School Math with Pizzazz, Book E E40-E48

Developing Skills in Tables and Graphs

Pre-Algebra with Pizzazz, Book CC pp. 60-67

Thinking with Mathematical Models

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

.
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Objective:

8.13 The student will use a matrix to organize and describe data.

Text Resources:

2.6

AIMS Resources:

 

Fun with Foods

Pieces and Patterns

Historical Connections in Mathematics Vol. II: "Magic Flexagons"

Historical Connections in Mathematics Vol. III: "The Locker Problem," "A New Kind of Arithmetic," "Who's In Charge"

What's Next? Vol. 2: "Figurate Family"

Suggested Manipulatives:

calculator

graphing calculator

Technology and Web Resources:

Other Resources:

Adventures with Logic, pp. 31, 36-41

Assessment Suggestions:

Suggestions for Integration:

Back to top.

Objective:

8.14 The student will

(a) describe and represent relations and functions, using tables, graphs, and rules; and

(b) relate and compare tables, graphs, and rules as different forms of representation for relationships.

Text Resources:

10.1, 10.4

AIMS Resources:

Looking at Lines

Historical Connections in Mathematics Vol. II: "Diagonal Challenge," "Region Revenge"

What's Next? Vol. 1: "Busy Intersections"

What's Next? Vol. 3: ""Pick the Pocket," "What Symmetry"

Mostly Magnets: "What's the Attraction?", "Magnets Apart"

Machine Shop: "Designer Gears," "Clever Lever 1"

Suggested Manipulatives:

Technology and Web Resources:

Naming Polygons

The Challenge of the Unknown, "Dinosaurs"

Other Resources:

Math For Smarty Pants, p. 44-45

Aims Patchwork and Pieces

National Teacher Training Institute Folder

What's My Rule? Using Problem Solving Strategies

Assessment Suggestions:

Suggestions for Integration:

.
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Objective:

8.15 The student will solve two-step equations and inequalities in one variable, using concrete materials, pictorial representations, and paper and pencil.

Text Resources:

1.4-1.7, 1.9, 2.9, 7.9, 7.10

AIMS Resources:

Machine Shop: "Meet the Equalizer," "Clever Lever 1,", Clever Lever 2," "Clever Lever 3," "The Great Catapult Caper"

Suggested Manipulatives:

Technology and Web Resources:

Other Resources:

Algebra with Pizzazz, Book A pp. 40-48

Middle School Math with Pizzazz, Book E p. 76

Algebra by Design, pp. 7-8

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

Back to top.

Objective:

8.16 The student will graph a linear equation in two variables, in the coordinate plane, using a table of ordered pairs.

Text Resources:

2.10, 10.2, 10.3, 10.4

AIMS Resources:

Brick Layers: "Dial a Gear," "Turn Around," "Threads of Time," "Effort-Less," "Fiddling with Fulcrums"

Mostly Magnets: "What's the Attraction?", "Magnets Apart"

Machine Shop: "Penny Weight"

Suggested Manipulatives:

graphing calculator

Technology and Web Resources:

A Functional Housing Market

Other Resources:

Estimation by Design, pp. 74-80

Pre-Algebra with Pizzazz, Book DD pp. 58-65

Assessment Suggestions:

Suggestions for Integration:

.
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8.17 The student will create and solve problems, using proportions, formulas, and functions.

Text Resources:

1.8, 3.3, 3.4, 8.1, 8.2, 8.6

AIMS Resources:

Looking at Lines

Proportional Reasoning

Mostly Magnets: "What's the Attraction?", "Magnets Apart"

Machine Shop: "Designer Gears," ""Meet the Equalizer"

Brick Layers: "Gear Guessing"

Math + Science: A Solution: "Rubber Band Stretch," "Rubber Band Shoot"

Suggested Manipulatives:

Technology and Web Resources:

The Challenge of the Unknown, "Dinosaurs," "Locks," "Ski Bus," "Canoe Building"

The Internet Pizza Server

Other Resources:

Assessment Suggestions:

Stanford 9 test objective

Suggestions for Integration:

.
Back to top.

 

Objective:

8.18 The student will use the following algebraic terms appropriately: domain, range, independent variable, and dependent variable.

Text Resources:

10.1

AIMS Resources:

 

Pieces and Patterns: "Trying Triangles," "See How They Roll," "Probably Pythagorean"

Suggested Manipulatives:

Technology and Web Resources:

Other Resources:

Assessment Suggestions:

Suggestions for Integration:

.
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