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1 Angle Relationships, Parallel Lines Angle Relationships, Interior/Exterior angles 8G2 8M8 Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal. Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor. Angles, Elevation and Depression 8M7 Apply proportional reasoning to solve problems involving indirect measurements or rates. Parallel Lines cut by a transversal ml ** Computer Application Animated tutorial on using a protractor/recognizing special angles Area and Perimeter (twodimensional shapes) Box and Whisker Plots 8M9 Demonstrate understanding of the concepts of Area and Perimeter perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and **Computer Application volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.) 8P8 Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve 8D1 Use, create and interpret scatterplots and other types of graphs as appropriate. 8D4 8D9 Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). Construct convincing arguments based on analysis of data and interpretation of graphs. Create & Analyze Box Plots and ** Computer Application Data Analysis and Probability/ various virtual manipulatives matti.usu.edu/nlvm/nav/category_g_3_t_5.html Comparing and Ordering Fractions & Decimals 8N6 Estimate, compute and solve problems involving Compass Constructions 8G2 Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 1

2 Congruence 8G3 Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures). Coordinate Plane Create a human coordinate plane Data Analysis, Constructing Arguments 8M6 Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs. Lesson Plan "Comparative Costs: The Early 19th Century and Today" ** requires minimal computer usage 8D1 Use, create and interpret scatterplots and other types of graphs as appropriate. 8D2 Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose; e.g., line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants. 8D9 Construct convincing arguments based on analysis of data and interpretation of graphs. Decimal Operations Distance and Midpoint Formulas (Coordinate Plane) 8N3 Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. 8G4 Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex. 8P8 Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve 8P13 Compute and interpret slope, midpoint and distance given a set of ordered pairs. Worksheet finding distance between two points **Scroll down until you find sample worksheets Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 2

3 Divisibility and Factors Equations, Variables on both sides 8P9 Solve linear equations and inequalities graphically, Using Pascal's triangle for divisibility www. shodor.org/interactivate/activities/pascal1.html and www. shodor.org/interactivate/activities/pascal2.html ** Computer Application Equations, Multi-Step Equations, One-Step (whole #'s, fractions, decimals, integers) 8P8 Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve 8P9 Solve linear equations and inequalities graphically, 8N4 Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations. 8N5 Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. Website with 40 different printable Solving Equations worksheets with answer keys worksheetoutline.htm Website with 40 different printable Solving Equations worksheets with answer keys worksheetoutline.htm Worksheet/ Basic Equations/ change the number of problems 8N6 Estimate, compute and solve problems involving Using algebra tiles works well for students to actually see the equation solving process. 8P4 Extend the uses of variables to include covariants where y depends on x. EX. x + 1 = 3 Equations, Solving by graphing 8P3 Identify functions as linear or nonlinear based on information given in a table, graph or equation. = Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 3

4 8P9 Solve linear equations and inequalities graphically, 8D6 8D9 Make conjectures about possible relationship in a scatterplot and approximate line of best fit. Construct convincing arguments based on analysis of data and interpretation of graphs. Equations, Systems 8P3 Identify functions as linear or nonlinear based on information given in a table, graph or equation. Solve systems of equations using graphing, substitution, and linear combination to see who wins the race between the tortoise and the hare. Go to and go under algebra for lesson plans and worksheets that go with it 8P10 Solve 2 by 2 systems of linear equations graphically and by simple substitution. 8P14 Differentiate and explain types of changes in variation vs. inverse variation. 8D9 Construct convincing arguments based on analysis of data and interpretation of graphs. Equations, Two variables 8P1 Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. 8P3 Identify functions as linear or nonlinear based on information given in a table, graph or equation. 8P4 Extend the uses of variables to include covariants where y depends on x. 8P14 Differentiate and explain types of changes in variation vs. inverse variation. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 4

5 Equations, Two-step 8P15 Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. 8P5 Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial. 8P7 8P9 Use symbolic algebra (equations and inequalities), Solve linear equations and inequalities graphically, Equations, Writing Exponential Growth and Decay 8P9 Solve linear equations and inequalities graphically, 8N3 Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. 8P14 Differentiate and explain types of changes in variation vs inverse variation 8P16 Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. Use M&Ms and paper folding to explore exponential models p/rhinos/rhinos_procedure.shtm Exponents 8N3 Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. Expressions 8P8 Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve 8P5 Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial. Interactive Exponent Tutorial and practice Worksheet for evaluating simple algebraic expressions wwww.cool-emath.com/evalexpress3.htm Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 5

6 Formulas 8M2 Use proportional relationships and formulas to convert units from one measurement system to another; e.g., degrees Fahrenheit to degrees Celsius 8P8 Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve Fraction Operations Various computer activities with fractions Fractions, Decimals, and Percents (Conversions) Frequency Tables, Histogram 8N6 8D3 8D9 Estimate, compute and solve problems involving Differentiate between discrete and continuous data and appropriate ways to represent each. Construct convincing arguments based on analysis of data and interpretation of graphs. Print off conversion worksheet ml Data Analysis and Probability/ various virtual manipulatives matti.usu.edu/nlvm/nav/category_g_3_t_5.html Graphing, Inequalities (Coordinate Plane) Graphing, Linear Equations 8P3 Identify functions as linear or nonlinear based on information given in a table, graph or equation. 8P7 8P9 8P14 Use symbolic algebra (equations and inequalities), Solve linear equations and inequalities graphically, Differentiate and explain types of changes in variation vs. inverse variation. 8P3 Identify functions as linear or nonlinear based on information given in a table, graph or equation. Match graphs to equations act.html Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 6

7 Graphing, Nonlinear functions 8P1 8P3 Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. Identify functions as linear or nonlinear based on information given in a table, graph or equation. Inequalities, graphing on a number line 8P8 Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve 8P14 Differentiate and explain types of changes in variation vs. inverse variation. 8N4 Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations. 8P7 8P9 8D1 Use symbolic algebra (equations and inequalities), Solve linear equations and inequalities graphically, Use, create and interpret scatterplots and other types of graphs as appropriate. Inequalities, Solving One-Step and Two-step Integers (operations) and Absolute Value 8P9 Solve linear equations and inequalities graphically, 8N2 Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system. Print-offs for rules 8N6 Estimate, compute and solve problems involving Irrational Numbers 8N2 Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 7

8 Line Plots (Graphs) 8D3 8D9 Differentiate between discrete and continuous data and appropriate ways to represent each. Construct convincing arguments based on analysis of data and interpretation of graphs. Data Analysis and Probability/ various virtual manipulatives matti.usu.edu/nlvm/nav/category_g_3_t_5.html Linear Functions, writing Rules 8P3 Identify functions as linear or nonlinear based on information given in a table, graph or equation. Activity in which students have to match graphs, descriptions, table of values db=cs.fp5&-lay=web&-format=lesson.html&-recid=47&-find Mean, Median, Mode 8P9 Solve linear equations and inequalities graphically, 8P14 Differentiate and explain types of changes in variation vs inverse variation 8D4 Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). 8D5 Explain the mean's sensitivity to extremes and its use in comparison with the median and mode. "Mystery Data Game" Given certain criteria, students must come up with a data set to match a mean, median, mode, etc. db=cs.fp5&-lay=web&-format=lesson.html&-recid=79&-find Metric System 8M1 Compare and order the relative size of common Print off worksheet with rules included U.S. customary units and metric units; e.g., mile and kilometer, gallon and liter, pound and kilogram. Order of Operations 8N3 Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. To help kids remember : Please Excuse My Dear Aunt Sally Patterns and Sequences 8P2 Generalize patterns and sequences by describing how to find the nth term. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 8

9 Percent, % of Change, Markup/Discount, Equations Several activities for Consumer Math (percent markup, discount, etc.) Look under Consumer Math Topic. Permutations and Combinations 8D10 Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important. Points, Lines, Planes 8G2 Recognize the angles formed and the relationship between the angles when two lines intersect and Polygons, Classifying Polynomials, Monomials, Binomials (Adding, Subtracting, Multiplying) 8M8 8G1 when parallel lines are cut by a transversal Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor. Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects. 8P5 Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial. Powers of Products and Quotients 8N3 Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. Prime Factorizations, GCF and LCM 8P1 Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. Find polygons in triangle grid **Computer application When multiplying binomials, F.O.I.L.; multiply the first, outside, inside, and last numbers. Ex. (x +1) (x +2) = (F) x 2 + (O)2x + (I)1x + (L) 2 Print-off crossnumber worksheet Probability (Counting Outcomes, theoretical, experimental, independent and dependent events) Data Analysis and Probability/ various virtual manipulatives matti.usu.edu/nlvm/nav/category_g_3_t_5.html 8D10 Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 9

10 8D11 Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities. Problem Solving Strategies 8N5 Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. Problem Solving Web Unit (Can use material off web too) gouchercenter.edu/jcampf/searching_for_solutions.htm 8P1 Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. Properties of Numbers 8N4 Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations. Proportions 8M7 Apply proportional reasoning to solve problems involving indirect measurements or rates. Matching number sentences with terms or/archive/ html "How much do you weigh in outerspace?" Pythagorean Theorem 8G3 Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures). 8N3 Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. 8N4 Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations. Find the Missing Side pyth2/index.html **Computer Application Proving the Pythagorean theorem using Euclid's method and Dept/mdm/pyth.html ** Computer Demonstrations Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 10

11 8N7 Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., the square root of 130 is between 11 and 12. 8P12 Solve simple quadratic equations graphically; e.g., y = x Rational Numbers 8N2 Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system. Ratios and Unit Rates Relations and Functions Rotations, Translations, Symmetry, and Reflections Rounding and Estimating 8M6 Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs. Write ratios in lowest terms 8P1 Relate the various representations of a Guess the Function relationship; i.e., relate a table to graph, description and symbolic form. **Computer Application 8G4 Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex. 8G5 Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations. 8N5 Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. Computer Game with Pythagoras as host oom.html Computer game hosted by Pythagoras and Hypatia that rounds numbers using significant digits /roundoff.html Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 11

12 8M3 Use appropriate levels of precision when calculating with measurements. Samples and Surveys, Random Scatter Plots 8D7 Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample. 8D8 Describe how the relative size of a sample compared to the target population affects the validity of predictions 8P14 Differentiate and explain types of changes in variation vs. inverse variation. 8D1 Use, create and interpret scatterplots and other types of graphs as appropriate. Data Analysis and Probability/ various virtual manipulatives matti.usu.edu/nlvm/nav/category_g_3_t_5.html 8D3 Differentiate between discrete and continuous data and appropriate ways to represent each. Use measurement and data collection from class to figure out Shaquille O'Neill's hand span Scientific Notation 8D6 Make conjectures about possible relationship in a scatterplot and approximate line of best fit. 8N1 Use scientific notation to express large numbers and small numbers between 0 and 1. Practice Problems dosxx.colorado.edu/~atlas/math/problems/problems1.html Similar Figures and Scale Drawing 8N8 Add, subtract, multiply, divide and compare numbers written in scientific notation. Create a scale model of a balsa wood plane. Website for guide regentsprep.org/regents/math/scale/tdino.htm They use a dinosaur model, but a plane works well. 8M3 Use appropriate levels of precision when calculating with measurements. 8M7 Apply proportional reasoning to solve problems involving indirect measurements or rates. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 12

13 Simple and Compound Interest 8G3 Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures). Simple Interest Worksheet 8P16 Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. Simplifying Fractions Create your own worksheet to practice simplifying Sine, Cosine, and Tangent Ratios 8M7 Apply proportional reasoning to solve problems involving indirect measurements or rates. Slope and y-intercept 8P6 Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world 8P13 Compute and interpret slope, midpoint and distance given a set of ordered pairs. "Walking the Plank" Collect data through an experiment to see the relationship between distance and a weight 8P14 Differentiate and explain types of changes in variation vs. inverse variation. Square Roots 8P15 Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. 8N3 Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 13

14 Stem and Leaf Plots 8N4 Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations. 8N7 Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., the square root of 130 is between 11 and 12 8D1 Use, create and interpret scatterplots and other Create & Analyze Stem and Leaf Plots types of graphs as appropriate. **Computer Application 8D4 Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). 8D9 Construct convincing arguments based on analysis of data and interpretation of graphs. Surface Area 8M4 Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find: 8M5 Determine surface area for pyramids by analyzing their parts. Collect cereal boxes, boxes, paper towel rolls, etc. and have students create a 3D model and compute surface area and volume. 8M9 Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.) 8M10 Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision. Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 14

15 Three-dimensional Shapes (Polyhedra) Transforming Formulas 8M9 Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.) A net is the "skin" of a 3D shape. EX. 8G6 8M2 Draw nets for a variety of prisms, pyramids, cylinders and cones. Use proportional relationships and formulas to convert units from one measurement system to another; e.g., degrees Fahrenheit to degrees Celsius 8P4 Extend the uses of variables to include covariants where y depends on x. 8P8 Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve U.S. Customary Measurement 8M1 Compare and order the relative size of common Print off worksheet with rules included U.S. customary units and metric units; e.g., mile and kilometer, gallon and liter, pound and kilogram. Volume 8M4 Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find: 8M9 Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.) "Million Dollar Giveaway" Computer Demonstration Shows Surface Area& Volume Adapted from Prentice Hall Courses Trumbull County Educational Service Center Page 15