Mathematics Competency Assurance Documents

8th Grade Mathematics Standards

Number/Computation

MIDDLE SCHOOL MATHEMATICS EXIT PERFORMANCE STANDARD 1: Student will consistently and accurately apply number sense and order relationships in problem solving situations to perform estimations and/or calculations involving different kinds and forms of rational numbers (fractions, decimals, percents, integers, exponents, square roots, ratios, proportions, etc.) with and without calculators and will communicate the reasoning used in solving these problems.

Based on Kentucky’s Core Content for Mathematics Assessment, the Kentucky Program of Studies, and Academic Expectations: 1.5-1.9 Mathematical Communication & Reasoning, 1.16 Technology, 2.7 Number, 2.8 Procedures, 2.11 Change, 2.12 Structure; Goal 5 Think & Solve Problems; & Goal 6 Connect & Integrate Knowledge

8^th Grade Number/Computation Standards

NC8.1 Show number sense by interpreting, modeling and using appropriate mathematical notation (%,!,/, pi, square roots, exponents, scientific notation) for real numbers and by comparing and contrasting various subsets of the real number system (counting numbers, whole numbers, integers, rational numbers, irrational numbers).

NC8.2 Use order of operations including ( )’s and exponents, and properties (commutative, associative, distributive, inverse, identity, equality) to solve problems with rational numbers (fractions, decimals, percents, & integers).

Skills, Concepts & Relationships

• Use order of operations with ( )’s and exponents (G3 ch2)(GP ch1.2&4.2)(SI Inv1)
• Determine absolute value (number line) (G3 ch3) (GP ch2.1-2.3)
• Review adding & subtracting integers (integer chips, number line, algeblock mats) (G3 ch3)(GP ch2.4-2.5)
• Multiply & divide integers (look for patterns) (G3 ch3)(GP ch2.7-2.8)
• Determine scientific notation (G3 ch6.11)(GP ch6.9)
• Introduce negative exponents (G3 ch6.11)(GP ch4.9)
• Recognize, use, & apply properties (commutative, associative, distributive, inverse, identity, equality) to solve problems with fractions, decimals, percents, integers, using algebraic equations (G3 ch7)(GP ch1.4-1.5,5.3)(SI Inv1-3)
• Develop the concept of infinite progressions (arithmetic & geometric sequences) (G3 ch7.6)(GP5.9&6.8)
• Find and approximate square roots using a calculator (recognize perfect squares to 169)(G3 ch8) (GP ch13.1)(LP Inv1-5)
• Show number sense by comparing and contrasting various subsets of the real number system (counting numbers, whole numbers, integers, rationals, irrationals) (G3 ch8.3) (GP ch13.3)
• Review applications of fraction, decimal, and percent computations in real world situations (G3 ch7&10) (GP ch5,6&9) (CP)
• Review using percents to calculate sale price, discounts, simple interest, and commission (G3 ch10&supplement) (GP ch9&supplement) (CP)
• Introduce compound interest with a graphing calculator (Banker’s rule of 72) (supplement)
• Solve percent problems using proportions and equations (G3 ch10) (GP ch9)
• Find percent one number is of another, and find number when percent is known (G3 ch10) (GP ch9) (CP)
• Find an approximation for pi as an example of an irrational number (G3 ch12) (GP ch12.2)
• Determine number relationships in Pascal’s Triangle, Fibonacci Sequence & the Golden Ratio (G3 ch7,9&13) (GP ch2.6,5.9,9.1,14.2,&15) (LP)
• Use calculators to solve problems with exponents, order of operations, reciprocals (inverse), pi, square roots, and number patterns & sequences. (Caution: different calculators handle order of operations differently) (SI)
• Develop use of spreadsheets to perform calculations (G3 ch3.5,9.3,10.9&10.10) (GP ch4.8,5.3&9.9)

G3--Glencoe Course 3, GP--Glencoe Pre-Algebra; Connected Math: SI—Say It With Symbols, LP—Looking For Pythagoras, CP--Comparing and Scaling

8th Grade Mathematics Standards

Geometry/Measurement

MIDDLE SCHOOL MATHEMATICS EXIT PERFORMANCE STANDARD 2: Student will apply properties of measurement (perimeter and area of triangles, quadrilaterals, circles, polygons, and irregular shapes; volume and surface area of prisms and cylinders; weight; temperature, etc.) and will use geometric concepts, properties and relationships (proportionality of similar figures, sum of triangle measures equals 180 degrees, transformations in the coordinate plane, etc.) in problem solving situations and communicate the reasoning used in solving these problems.

Based on Kentucky’s Core Content for Mathematics Assessment, the Kentucky Program of Studies, and Academic Expectations: 1.5-1.9 Mathematical Communication & Reasoning, 1.16 Technology, 2.8 Procedures, 2.9 Space and Dimensionality, 2.10 Measurement, 2.11 Change, 2.12 Structure; Goal 5 Think & Solve Problems; & Goal 6 Connect & Integrate Knowledge

8^th Grade Geometry/Measurement Standards

GM8.1 Classify, analyze, and draw visual representations (scale drawings, isometric dot paper drawings, etc.) of two-dimensional and three-dimensional figures.

GM8.2 Recognize, describe, and draw transformations in a four-quadrant coordinate plane.

GM8.3 Determine and apply the formulas for volume and surface area of prisms and cylinders.

GM8.4 Determine and apply the Pythagorean Theorem.

Skills, Concepts & Relationships

• Classify angles and angle pairs: adjacent, vertical, corresponding, interior, exterior, complementary, supplementary, etc. (G3 ch2.3&supplement) (GP ch11.3&supplement)
• Develop proving triangle similarity and congruence (SSS,SAS,ASA) (G3 ch5.6) (GP ch11.5-11.7) (SS Inv5)
• Generate, describe and analyze transformations: translations (slide), reflections (flip), rotations (turn), and dilations (expand & contract) in the coordinate plane (MIRA, patty paper)(G3 ch5.6,9.8,11.8-11.10)(GP 11.8-11.9)(KH)
• Develop performing simple constructions (construct congruent lines and angles, angle bisectors, perpendicular bisector of a segment, circle with given radius, perpendicular line through a point on or off a given line, construct regular polygons,etc.) (compass, patty paper) (G3 ch5) (GP ch11)
• Determine and use the Pythagorean Theorem (geoboards, tangrams, graph paper)(G3 ch8.5&8.6)(GP ch 13.4)(LP Inv3&4)
• Calculate indirect measurement (height of flagpole, mirror method, etc.) with similar triangles (G3 ch9.6)(GP 11.6) (SS Inv4&5)
• Construct scale representations of 2D and 3D objects using proportional reasoning about similar figures (G3 ch9.7)(GP ch12.8) (SS Inv4) (FW Inv6)
• Introduce right triangle ratios (tangent, sine, and cosine) (G3 ch9.9&9.10)(GP ch13.5-13.6)
• Review development of formulas for perimeter (circumference) & areas of circles, triangles, trapezoids, parallelograms, etc. (geoboards, graph paper, etc.) (G3 ch12.1)(GP ch7.4,12.1-12.2)(FW Inv3-5)
• Review classifying geometric solids and their terms: base, vertices, edges, faces, prisms, pyramids, cylinders, cones, & spheres) (G3 ch12&supplement) (GP ch12&supplement) (FW Inv3-5)
• Introduce 5 regular platonic solids: tetrahedron (4 equilateral triangles), cube (6 squares), octahedron (8 equilateral triangles), dodecahedron (10 regular pentagons), and icosahedron (20 equilateral triangles)
• (supplement)
• Introduce investigations of counting techniques with various paths (networks, circuits, Euler's formula: F+V-E=2, etc.) (supplement) (CC Inv3)
• Visualize and draw different representations of 3D geometric figures (multilink cubes, isometric dot paper) (G3 ch12.3) (GP ch12&supplement) (FW) (RM Inv4)
• Derive and apply formulas for surface area and volume of prisms and cylinders (cubes, pentomino "open-top boxes", nets) (G3 ch12) (GP ch12)(FW Inv3-5) (SI Inv5)
• Introduce volume and surface area of pyramids and cones (G3 ch12) (GP ch12)(FW Inv3-5) (SI Inv5)
• Use cubic units correctly (G3 ch12) (GP ch12) (FW Inv3-5)

G3--Glencoe Course 3, GP--Glencoe Pre-Algebra; Connected Math: FW—Filling & Wrapping Inv3-5, LP—Looking for Pythagoras Inv3&4, KH—Kaleidoscopes, Hubcaps, & Mirrors Inv1-4, CC—Clever Counting Inv3, SS--Stretching & Shrinking Inv4&5, SI--Say It With Symbols Inv5, RM--Ruins of Montarek Inv4

8th Grade Mathematics Standards

Probability/Statistics

MIDDLE SCHOOL MATHEMATICS EXIT PERFORMANCE STANDARD 3: Student will use data collection & analysis, graphing (multiple line and bar graphs, circle graphs, stem and leaf plots, box and whisker plots, etc.), statistics (mean, median, mode, range, outliers, quartiles, etc.), and experimental & theoretical probabilities to solve real world problems and communicate the reasoning used in solving these problems.

Based on Kentucky’s Core Content for Mathematics Assessment, the Kentucky Program of Studies, and Academic Expectations: 1.5-1.9 Mathematical Communication & Reasoning, 1.16 Technology, 2.7 Number, 2.8 Procedures, 2.11 Change, 2.12 Structure, 2.13 Probability & Statistics; Goal 5 Think & Solve Problems; & Goal 6 Integrate Knowledge

8^th Grade Probability/Statistics Standards

PS8.1 Collect, compile, interpret, compare, and display data (histogram, stem and leaf plot, box and whisker plot, scatterplot, etc.) to analyze, interpret, and support real-life situations.

PS8.2 Analyze odds and probabilities (experimental and theoretical) to make decisions involving real-world situations.

Skills, Concepts & Relationships

• Organize information on a spreadsheet and make appropriate computer generated graphs (G3 ch1.8,4.5,13.7) (GP ch4.8&9.9)
• Access information from a database (G3 ch4.1) (GP supplement)
• Construct and interpret: histograms, line plots, stem and leaf plots, circle graphs, box and whisker plots, scatterplots (G3 ch4) (GP ch8.2,10&11.2)(SP)
• Determine outliers effect on mean and median (G3 ch 4) (GP ch10&supplement) (SP)
• Develop concepts of dispersion and variance (quartile, interquartile, range, clusters, gaps, outliers) (G3 ch4) (GP ch10) (SP)
• Evaluate misleading graphs and statistics (G3 ch4.9) (GP ch10.4) (SP)
• Develop graphing calculator skills: enter data into a list; determine statistics: mean, median, mode, quartiles; make a stat plot: box and whisker plot, histogram, scatterplot; collect, analyze, and represent data (G3 4.6-4.7&supplement) (GP ch6.6,8.2,9.3,10.2,10.3,10.8,10.9)
• Recognize and use the Fundamental Counting Principle (multiply number of choices for each item to get total possible outcomes) (G3 ch13.1) (GP ch10.5)
• Introduce and explore permutations and combinations (factorials) (G3 ch13.3) (GP ch10.6) (CC)
• Determine the probability of independent and dependent (conditional) events (G3 ch13.5) (GP ch9.3,10.9&10.10) (WD Inv4-7)
• Construct tree diagrams and area models to analyze theoretical probability (G3 ch13) (GP ch10.5&12.3) (WD Inv3)
• Use Pascal's triangle to determine theoretical probability of binomial situations (G3 ch13.4) (WD Inv7)
• Make predictions, draw conclusions, and verify results from statistical and probability experiments (G3 ch13.6&supplement) (GP ch9.6&10.8)(WD Inv5-7)
• Analyze situations (games of chance, board games, basketball shooter) to make predictions using knowledge of probability (supplement) (WD Inv6&final project)
• Recognize the Law of Large Numbers (more experimental trials should get closer to theoretical probability) (supplement) (WD Inv5-7)
• Design a statistical study to investigate a problem, conduct the study and interpret and communicate the outcomes (supplement) (SP)
• Differentiate "odds" and "probability" (analyze gambling: horse races) (G3 supplement) (GP ch10.7)
• Use appropriate sampling techniques (supplement) (SP Inv3)

G3--Glencoe Course 3, GP--Glencoe Pre-Algebra; Connected Math: SP—Samples & Populations, WD—What Do You Expect? Inv3-7, CC-Clever Counting

8th Grade Mathematics Standards

Algebraic Ideas

MIDDLE SCHOOL MATHEMATICS EXIT PERFORMANCE STANDARD 4: Student will discover, explore, describe, and generalize patterns (linear, exponential and simple quadratic), represent and analyze algebraic relationships using tables, graphs in the coordinate plane, variables, expressions and equations in problem solving situations and communicate the reasoning used in solving these problems.

8^th Grade Algebraic Ideas Standards

AI8.1 Recognize, create, continue and generalize patterns (linear, exponential, and simple quadratic) by giving the rule for the nth term and defend the generalization.

AI8.2 Solve two-step equations with fractions, decimals, percents and integers using concrete, pictorial and abstract methods (variables).

AI8.3 Recognize and analyze algebraic relationships (functions) using tables, graphs in the coordinate plane, variables, expressions and equations in problem solving situations.

Skills, Concepts & Relationships

• Simplify algebraic expressions (combining like terms) (algebra tiles, cups & counters, etc.) (G3 ch14.1-14.2) (GP ch1.5,2.4-2.5) (SI Inv1-4) (MS Inv4)
• Solve linear equations using concrete, informal and formal methods (inverse operations) (balance scale, open sentences, algebra tiles, algeblocks, cups and counters, algeblocks) (G3 ch2.3,2.4,&11.4) (GP ch1.6,1.8,3,5.6,6.7)(SI Inv1-4) (MS Inv4)
• Solve two-step equations (balance scale, open sentences, algebra tiles, algeblocks, cups and counters, algeblocks) (G3 ch2.7) (GP ch7.2-7.3)(SI Inv2-4) (MS Inv4)
• Develop solving equations with variables on both sides (balance scale, open sentences, algebra tiles, algeblocks, cups and counters) (G3 supplement) (GP ch7.5)(SI Inv2-4)
• Graph inequalities with one variable on a number line (G3 ch2.10) (GP ch1.9,3.6-3.7)
• Introduce writing and solving simple inequalities (positive coefficients only) (G3 ch2.10)(GP ch3.6-3.7,5.7,6.7,7.6-7.7)
• Use variables and graphs to describe numerical patterns to the nth term in linear, exponential and simple quadratic patterns (painted cube problem) (G3 ch11.1&11.2) (GP ch5.9&6.8) (MS)(TM)(GG)(FF)
• Investigate non-linear relationships with concrete and informal methods (simple quadratic and exponential) (G3 ch11.2&11.7) (GP ch8.3B) (TM)(GG)(FF)
• Represent situations with tables, graphs, and equations, and recognize the interrelationship of these (how change in one variable affects change in another variable) (G3 ch11.2) (GP ch8.1-8.4)(MS)(TM)(SI)
• Introduce the concept of slope and the equation of a line (y=mx+b where m=rise/run and b=y-intercept) (G3 ch11.4&11.8) (GP ch8.6-8.7&11.3)(MS Inv5)(TM Inv1)(LP Inv6)
• Graph a line on a coordinate grid (graphing calculator, table of values) (G3 ch11.4) (GP ch8.3-8.4&8.7)(MS Inv3&6)(TM Inv1)
• Solve problems involving formulas with substitutions (V=pr²h, SA=6s²) (G3 ch12) (GPch7&12)
• Develop graphing calculator skills: linear equations, enter function in "Y=" form, set and evaluate table, window, trace, zoom, make scatterplots, positive or negative correlation; and evaluate expressions (G3 ch2.1,11.4&supplement) (GP ch8.2-8.4&8.7)(TM) (MS Inv3)
• Develop using spreadsheets formulas to represent patterns (G3 ch7.5&7.7) (GP ch4.8) (supplement)

G3--Glencoe Course 3, GP--Glencoe Pre-Algebra; Connected Math: MS--Moving Straight Ahead, TM—Thinking With Mathematical Models, SI—Say It With Symbols, LP—Looking For Pythagoras, GG—Growing, Growing, Growing, FF—Frogs, Fleas, & Painted Cubes