Greenup County School District 8 th Grade Mathematics Curriculum Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources/Activities Unit 1 Ratios/ Proportional / Number Sense Ratios/Proportional 7.RP.A.2 Recognize and represent proportional relationships between quantities. 7.RP.A.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.A.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.A.2.c Represent proportional relationships by equations. 7.RP.A.2.d Explain what a point (x, y) on the graph of a proportional relationship means in terms of Ratios/Proportional Simplify fractions Compute unit rates Identify the unit rate given a graph or table Use dimensional (unit) analysis for unit conversion Identify equivalent ratios Identify proportional relationships by testing for equivalent ratios Identify the constant of proportionality Use proportional relationships to solve ratio and percent problems Calculate percent decrease, percent increase and percent error Make calculations based on percentages, e.g. simple interest, tax, gratuities and commissions Number Sense Define irrational numbers Show that the decimal expansion of rational numbers repeats eventually. Convert a decimal expansion which repeats eventually into a rational number. Time Frame: August September Ratios/Proportional Ratio, Equivalent Ratios, Rate, Scale, Unit rate, Proportion, Proportional, Non-Proportional, Cross Products, Scale Drawing, Scale Model, Rate of Change, Compound Interest, Interest, Percent of Change, Percent of Decrease, Percent of Increase, Percent, Discount, Principal, Percent Proportion, Markup, Number Sense Factors, Greatest Common Factors, Rational, Irrational, Ratios/Proportional Analyze proportional relationship and use them to solve real world and mathematical problems Number Sense Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers Knowledge Ratios/Proportional 15 days Number Sense 20 days Learning Checks Target Quizzes Short Cycle Unit Automaticity Exit Slips Fractions number strips Fraction, decimal, percent cards(rummy concept) FAL: rational and irrational numbers Integer cards Number lines Turnover cards http://www.engageny.org/ http://www.kutasoftware.com/ http://www.map.mathshell.org/
the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Number Sense 8.NS.A.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. Show informally that every number has a decimal expansion. Approximate irrational numbers as rational numbers. Approximately locate irrational numbers on a number line. Estimate the value of expressions involving irrational numbers using rational approximations. Reduce fractions Recognize fractions in lowest terms Recognize equivalent fractions Order and place on a number line combinations of numbers including rational, irrational, and decimal. Least Common Multiple, Square Root, Terminating Decimal, Repeating Decimal, Pi, Radical Sign, Exponent, Greater Than, Equal To, Expression, Equivalent, Fraction, Denominator, Numerator, Decimal Expansion, Number Line, Estimate, Truncating, Prime, Composite, Relatively Prime 8.NS.A.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., π²).
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources/Activities Unit 2 Exponents and Radicals Unit 3 Expressions and Equations Unit 4 Unit 5 (Systems of Equations) Unit 6 Modeling Exponents and Radicals 8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. 8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. 8.EE.A.3 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.EE.A.4 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. Expressions and Equations 8.EE.C.7 Exponents and Radicals Evaluate expressions with integer exponents Use exponent properties to simplify basic expressions including negative exponents Identify basic squares and cubes Use square roots and cube roots to solve simple equations Express and interpret numbers using scientific notation Perform operations using scientific notations Expressions and Equations Evaluate expressions Solve one step equations Solve two step equations Solve equations using the distributive property Solve equations that involve combining like terms Check answers to equations by substituting Understand answers that include no real answer and all real answers Recognize equivalent fractions Solve proportions Time Frame: October-November-December Exponents Radicals Exponent, Square root, Cube root, Scientific Notation, Expanded form, Standard form Expressions and Equations and Algebraic Expression, Algebraic Equation, Equation, Variable, Inverse Operations, Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, Division Property of Equality, Like Terms, Solve, Simplify, Coefficient, Equivalent Equations Slope Formula, Rate of Change, Y Intercept, Slope intercept form, Vertical, Horizontal Function Slope Slope of a Line Exponents and Radicals Work with radical and integer exponents Knowledge Expressions and Equations Analyze and solve linear equations and pairs of simultaneous linear equations Knowledge Understand the connections between proportional relationship, lines, and linear equations (Systems of Equations) Analyze and solve linear equations and pairs of simultaneous linear equations Knowledge Modeling Exponents and Radicals 10 days Expressions and Equations 20 days 15 days (Systems of Equations) 20 days Modeling 15 days Learning Checks Target Quizzes Short Cycle Unit Automaticity Exit Slips Exponents and Radicals Turnover cards FAL: Comparing Investments http://www.map.mathshell.org/ million dollar mission activity http://www.kutasoftware.com/ http://www.engageny.org/ Expressions and Equations Turnover cards http://www.map.mathshell.org/ http://www.kutasoftware.com/ Algebra 1 Game: Exploring Multi-S Equations Functions: Walk-a-thon and five activities Coordinate Plane Dry Eraser Boar http://www.engageny.org/ Lines(Function Turnover cards http://www.map.mathshell.org/ http://www.kutasoftware.com/ Slope-Intercept Form Line Art Stained Glass Window Project Functions: Walk-a-thon and five activities Pumpkin Lab Graphs Coordinate Plane Dry Eraser Boar http://www.engageny.org/ (Systems of Equations Turnover cards http://www.map.mathshell.org/ http://www.kutasoftware.com/ Functions: Walk-a-thon and five activities Coordinate Plane Dry Eraser Boar http://www.engageny.org/
Solve linear equations in one variable. 8.EE.C.7.a 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.EE.C.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. 8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical 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. (Systems of Equations) 8.EE.C.8 Calculate a rate of change from two points Understand that a constant rate of change is shown on a graph through the slope of a line. Use similar triangles to show the slope of a line Graph a line starting at the origin and using slope to find a second point Graph a line starting at a y intercept and using slope to find a second point Be led to discover y=mx+b as Slope Intercept form for a line. Graph vertical and horizontal lines. Determine an equation of a line from its graph (Systems of Equations) Solve a system of linear equations algebraically Estimate a solution of a system of linear equations by graphing Solve a system of linear equations in a real world context Understand that a solution to a system of linear equations is the point of intersections of the two graphs. Modeling Use input and output tables to describe functions Use rate of change comparisons from (Systems of Equations) Solution to a system Elimination Method Substitution Method System of Equations Modeling Rate of Change, Input, Output, Function,, Non-linear, Function rule Function Discrete Data Nonlinear Function Parabola Proportional Relationship Quadratic Function Increasing Decreasing Define, evaluate, and compare functions. Knowledge Use functions to model relationships between quantities. Modeling Turnover cards http://www.map.mathshell.org/ http://www.kutasoftware.com/ Functions: Walk-a-thon and five activities Coordinate Plane Dry Eraser Boar http://www.engageny.org/
Analyze and solve pairs of simultaneous linear equations. 8.EE.C.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 8.EE.C.8.b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. 8.EE.C.8.c Solve real-world and mathematical problems leading to two linear equations in two variables. multiple representations of functions Model linear functions as tables, graphs and equations Compare functions that are not linear Create a rule for a function from a table or graph Write linear function rules from word descriptions and use them to solve problems Match nonlinear functions with word descriptions Sketch graphs of nonlinear functions from word descriptions Analyze a graph to determine if it is increasing, decreasing, or constant Modeling 8.F.A.1 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.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 8.F.A.3 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.F.B.4
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 a linear function in terms of the situation it models, and in terms of its graph or a table of values. 8.F.B.5 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.
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources/Activities Unit 7 Congruence and Similarity Through Angle Unit 8 Congruence and Similarity Through Unit 9 Theorem Unit 10 Volume of Solids Similarity Through Angle 8.G.A.1.a Lines are taken to lines, and line segments to line segments of the same length. 8.G.A.1.b Angles are taken to angles of the same measure. 8.G.A.1.c Parallel lines are taken to parallel lines. 8.G.A.5 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. Similarity Through 8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations: 8.G.A.2 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.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.A.4 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, Similarity Through Angle Determine angle sums for triangles including interior and exterior Determine angle properties from parallel lines cut by a transversal Use angle-angle criterion to show similarity of triangles Similarity Through Perform reflections, rotations, and translations of different Geometric shapes Determine congruence from transformations Perform dilations of Geometric shapes Theorem Explain a proof of the Theorem and its converse Determine if Theorem can be used to solve a problem Use the Theorem in 2 and 3 dimensions Use the Theorem in the coordinate plane for distance Lead students to the discovery of basic triples including 3-4-5 and 5-12-13 Volume of Solids Identify radius, height, and base Time Frame: January-February Similarity Through Angle Exterior Angles, Interior Angles, Transversal, Parallel, Alternate Exterior Angles, Alternate Interior Angles, Adjacent Angles, Complementary, Congruent Angles, Congruent Polygons, Corresponding Angles, Perpendicular Lines, Similar Figures, Similar Polygons, Supplementary, Vertical Angles, Similarity Through Reflection, Rotation, Translation, Dilation, Ratio, Line of Reflection, Angle of Rotation, Transformation, Image, Pre-Image, Enlargement, Reduction, Scale Factor, Similarity Through Angle Understand congruence/similarity using physical models, transparencies, or geometry software Similarity Through Understand congruence/similarity using physical models, transparencies, or geometry software Theorem Understand and apply the theorem. Knowledge Volume of Solids Similarity Through Angle 10 days Similarity Through 10 days Theorem 10 days Volume of Solids 10 days Learning Checks Target Quizzes Short Cycle Unit Automaticity Exit Slips Similarity Through Ang Turnover cards http://www.engageny.org/ http://www.kutasoftware.com/ http://www.map.mathshell.org/ Similarity Through Turnover cards http://www.engageny.org/ http://www.kutasoftware.com/ http://www.map.mathshell.org/ Theorem Turnover cards http://www.engageny.org/ http://www.kutasoftware.com/ http://www.map.mathshell.org/ Fire in Pythagoreville Activity Volume of Solids Turnover cards http://www.engageny.org/ http://www.kutasoftware.com/ http://www.map.mathshell.org/
translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them. Theorem 8.G.B.6 Explain a proof of the Theorem and its converse. 8.G.B.7 Apply the Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.B.8 Apply the Theorem to find the distance between two points in a coordinate system. Volume of Solids 8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems Identify cones, cylinders, and spheres Know formulas for the volumes of cones, cylinders, and spheres Use formulas for the volumes of cones, cylinders, and spheres Center of Rotation, Line of Symmetry, Reflectional, Symmetry, Rotational Symmetry, Theorem Theorem, Triples Hypotenuse, Legs, Sides a, b, and c, Right Triangle Distance Formula, Converse of the Theorem, Absolute Value, Coordinate Plane, Ordered Pair, Origin, Quadrants, Triangle Inequality Theorem, x-axis, x-coordinate, y-axis, y-coordinate, Solve real world and mathematical problems involving volume of cylinders, cones, and spheres. Volume of Solids Volume, Solids, Cone, Cylinder, Sphere, Pi, Radius, Area, Base, Height, Polyhedron, Prism, Pyramid, Similar Solids,
Skew Lines,
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources/Activities Unit 11 Statistics and Probability Statistics and Probability 8.SP.A.1 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.SP.A.2 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.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Statistics and Probability Create a scatter plot from a set of bivariate data Describe the pattern of a scatter plot. Create a line of best fit to a scatter plot Determine an equation of a line of best fit and use it to make a prediction within the context of the data Make inferences based on data using relative frequencies in a two way table Time Frame: March-April-May Statistics and Probability Bivariate Data, Clustering, Association, Correlation, Relative Frequency, Scatter Plot, Line of Best Fit, Frequency, Negative Association, No Association, Outlier, Positive Association, Trend Line, Two-Way Table Statistics and Probability Investigate patterns of associations in bivariate data. Statistics and Probability 20 days Learning Checks Target Quizzes Short Cycle Unit Automaticity Exit Slips Statistics and Probability Turnover cards http://www.engageny.org/ http://www.kutasoftware.com/ http://www.map.mathshell.org/ Pumpkin Lab graph 8.SP.A.4 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.