Mathematics Competency Assurance Documents

6th 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

6^th Grade Number/Computation Standards

NC6.1 Show number sense by explaining, demonstrating, and modeling positional value of fractions and decimals (place value, number line).

NC6.2 Understand and apply number theory concepts to solve problems (factors, primes, multiples, divisibility).

NC6.3 Use models and real-world investigations to develop operations (+,-,x,/) for fractions and decimals.

NC6.4 Compute using estimation or mental math when method is appropriate (e.g. add ½ + 5/6 mentally or on paper but may opt to add 13/24 + 57/68 on a calculator).

Skills, Concepts & Relationships

• Use mental math: computation/estimation skills(clustering/front end/break apart/rounding/compatible numbers)(G1ch1)
• Develop order of operations with whole numbers (x,/,+,-) (24 Game) (G1 ch1)
• Determine place value of large and small numbers (expanded notation) (G1 ch2.1, 3,5)
• Read, write, identify, & round decimals to the 10,000ths (place value, 10x10 grids, base 10 blocks) (G1 ch3) (BP1)
• Locate & plot decimals to the 10,000ths on number line (G1 ch3) (BP1)
• Use a 4-function calculator (+,-,x,/) to solve problems with large numbers, fractions, and decimals in problem solving (supplement) (BP1)
• Develop and use Commutative, Associative, Distributive, and Identity properties (zero and one) (G1 ch4 & supplement)
• Review multiplying 3-digit by 2-digit whole numbers in real-world problems (estimate reasonable products, then check with or without a calculator) (G1 ch4)
• Determine the effect that multiplying by a decimal has on the product (10x10 grids, base 10 blocks) (G1 ch4) (BP1)
• Introduce positive exponents (G1 ch4)
• Recognize, use & understand square numbers (G1 ch4 & supplement) (CS) (PT)
• Introduce square roots of perfect squares through 169 & calculator use to compute square roots (G1 ch4 & supplement)
• Review division with 2-digit whole number divisors in real world problems (estimate reasonable quotients then check with or without a calculator) (G1 ch5)
• Introduce/determine the effect dividing by a decimal (to the 100ths) has on the quotient (10x10 grids, base 10 blocks) (G1 ch5) (BP1)
• Review generating equivalent fractions, writing fractions in the simplest form, determining equal ratios, and changing improper fractions to mixed numbers (G1 ch1,6&10)(BP1)
• Find factors and the Greatest Common Factor-GCF (use divisibility rules) (G1 ch6, PT)
• Find multiples and the Least Common Multiple-LCM (use multiplication tables) (G1 ch6)(PT)
• Find prime factorization (primes, composites) (tree model, repeated addition, etc.) (G1 ch6)(PT)
• Develop converting fractions/mixed numbers to repeating/terminating decimals using a calculator (G1 ch6) (BP1)
• Develop comparing and ordering rational numbers (whole numbers, fractions, decimals, integers) using relations of equality and inequality (< > =, order on a number line) (G1 ch6) (BP1)
• Add & subtract commonly encountered (cooking, stock market, ruler, etc.) fractions with and without common denominators (add 1/2 +5/6 mentally or on paper but may opt to add 13/24 + 57/68 on a calculator) (tangrams, pattern blocks, fraction strips) (G1 ch7) (BP1)
• Introduce adding & subtracting commonly encountered (cooking, stock market, ruler, etc.) mixed numbers (estimate reasonable sums or differences then check with or without calculator) (G1 ch7) (BP1)
• Use models to solve real world problems using fractions & decimals (10x10 grids, base 10 blocks, tangrams, pattern blocks, fraction circles, fraction strips, geoboards, etc.) (G1 ch7,8) (BP1)
• Develop determining the effect multiplying or dividing commonly encountered fractions less than one or mixed numbers greater than one have on the product or quotient (tangrams, pattern blocks, fraction strips, fractions circles, geoboards, etc.) (G1 ch8) (BP1)
• Introduce basic concept of percent (one out of one hundred) (one hundred bead circles, 10x10 grids) (G1 ch10) (BP1)
• Introduce integers and their opposites (number line, thermometer, loss - gain, etc.) (G1 ch12)

G1--Glencoe Course 1; Connected Math: PT--Prime Time, BP1--Bits & Pieces I, CS--Covering & Surrounding

6th 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

6^th Grade Geometry/Measurement Standards

GM6.1 Determine whether estimation or accurate measurement is appropriate for a task and select the appropriate standard or non-standard tools to use.

GM6.2 Recognize & use symmetry, including sketching plane figures with multiple lines of symmetry.

GM6.3 Use metric & customary tools to measure length, perimeter, area, weight, and temperature.

GM6.4 Recognize and classify line segments, rays, planes, points, special quadrilaterals, special triangles, and regular polygons.

Skills, Concepts & Relationships

• Review basic geometric terms: point, line, line segment, ray, plane (SD)
• Read measurement tools: ruler, scale, etc. (G1 ch3.3) (CS)
• Measure length in Metric units to the nearest mm (G1 ch3.3) (CS)
• Review calculating perimeter of regular and irregular polygons (G1 ch3.10&4.6) (CS Inv1&2)
• Define circles and their terms: center, radius, diameter, chord (G1 ch4.9) (SD)
• Use Metric units to measure mass and capacity (liters, grams, ml) (G1 ch5.5)
• Convert Metric units to Metric units (kilo, hecto, deka, basic unit, deci, cent, milli) (G1 ch5.6)
• Recognize relationships in constant perimeter and area problems (G1 ch6.2) (CS Inv3&4)
• Measure length in U.S. Customary units to the nearest 16th of an inch (G1 ch6.7)
• Convert U.S. Customary units to U.S. Customary units (inch to feet to yard, fl. oz. to cup to pint to quarts to gallons, etc.) (G1 ch8.8)
• Use U.S. Customary units to measure mass & capacity (oz., lb., ton, tsp., fl. oz., cup, etc.) (G1 ch8.8)
• Review defining angles & their terms: vertex, side, degree, ray (G1 ch9.1) (SD)
• Use a protractor or angle ruler to measure and draw angles (G1 ch9.1) (SD)
• Classify angles: acute, obtuse, right, straight (G1 ch9.1) (SD)
• Develop the following relationships: the sum of measures of the angles of a triangle equals 180 degrees, and sum of measure of the angles of a quadrilateral equals 360 degrees (tear edges to form straight line-180, or circle 360)(supplement) (SD Inv4)
• Review characteristics of lines: parallel, perpendicular (G1 ch9.5&supplement)
• Classify polygons; special quadrilaterals: square, rectangle, rhombus, trapezoid, parallelogram; special triangles: acute, right, obtuse, scalene, isosceles, equilateral (pattern blocks, tangrams, polystrips, alphashapes) (G1 ch9.5&supplement) (SD)
• Create and use Venn Diagrams to solve problems (G1 ch9.6)
• Sketch multiple lines of symmetry (use MIRA, patty paper)(G1 ch9.7) (SD) (RM Inv3)
• Slide figures in a plane (translations) (G1 ch9.8) (SD)
• Tile a figure or pattern across a plane (tesselations) (G1 ch9) (SD Inv4) (CS)
• Review finding area of squares, rectangles, and triangles (use pentominoes, tangrams, color tiles, graph paper, etc.) (G1 ch4.6,11.1&11.2) (CS Inv1-6)
• Develop finding area of irregular shapes (over-estimate, under-estimate, use graph paper) (G1 ch11.1) (CS Inv1&2)
• Define geometric solids and their terms: cubes, rectangular and triangular prisms, cylinders, cones, pyramids, spheres, bases, vertices, edges, faces, etc. (G1 ch11.4&supplement)

G1--Glencoe Course 1; Connected Math: SD--Shapes and Designs, CS--Covering & Surrounding Inv1-6, RM--Ruins of Montarek

6th 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

6^th Grade Probability/Statistics Standards

PS6.1 Collect, compile, compare, and display data (line graph, bar graph, line plot) to interpret situations.

PS6.2 Apply range and measures of central tendency (mean, median, mode) to solve real life problems.

Skills, Concepts & Relationships

• Organize data into tables and construct graphs of data (G1 ch2) (DA)
• Construct and interpret: tables, charts, pictographs, bar graphs, line graphs, line plots (G1 ch2&supplement) (DA)
• Develop interpreting relationship between tables and graphs (G1 ch2.3) (DA)
• Choose appropriate scales and intervals when making graphs (G1 ch2.4) (DA)
• Make predictions and draw conclusions from data and graphs of data (G1 ch2.6&2.8) (DA)
• Select an appropriate graph to represent given data (supplement) (DA)
• Gather, organize, and interpret large sets of data (supplement) (DA)
• Apply mean, median, mode and range to solve problems (G1 ch2.4&2.7) (DA)
• Introduce organizing information on a spreadsheet and making appropriate computer generated graphs.(G1 ch2.3&4.5)
• Introduce accessing information from electronic sources (internet, CD Rom, etc.) (supplement)
• Introduce basic circle graphs (use 360 bead circles, angle rulers) (G1 ch11.3) (DA)
• Review conducting simple probability experiments (games of chance, fair games) (spinners, number cubes, cards, coins, counters, etc.)(G1 ch14) (HL)
• Develop using fractions and decimals to describe the probability of an event (0=impossible and 1=certain) (G1 ch14) (HL)

G1--Glencoe Course 1; Connected Math: DA--Data About Us, HL--How Likely Is It?

6th 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.

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, 2.9 Space and Dimensionality, 2.11 Change, 2.12 Structure; Goal 5 Think & Solve Problems; & Goal 6 Connect & Integrate Knowledge

6^th Grade Algebraic Ideas Standards

AI6.1 Recognize, create, and continue geometric and numeric patterns (give an informal description for the continuance of the pattern and/or generalize patterns through a verbal rule).

AI6.2 Solve one-step equations informally with concrete and/or pictorial methods.

Skills, Concepts & Relationships

• Develop the concepts of variables, expressions, and equations (G1 ch1.7)
• Solve problems involving simple formulas (A=lw , P=2l+2w) (G1 ch4.7)
• Explore number patterns on the calculator using the constant key (G1, ch6)
• Use diagrams and or manipulatives to recognize, create, continue and generalize patterns (Pattern Block Trains) (G1 ch9.6,13.4&supplement) (CS Inv3&4) (SD Inv4) (RM Inv3)
• Develop coordinate graphing (4 quadrants, x/y coordinates, plot ordered pairs) (G1 ch12.8) (DA Inv4)
• Solve one-step algebraic equations using addition, subtraction, multiplication, & division with whole numbers (balance scale, open sentences, "Hands-On" equations, algebra tiles, cups & counters) (G1 ch13.1&13.2)
• Use input-output tables and function machines to generalize number patterns (G1 ch13.4)
• Introduce using spreadsheet formulas to represent patterns (G1 ch13.4)

G1--Glencoe Course 1; Connected Math: SD--Shapes and Designs Inv4, CS--Covering and Surrounding Inv3&4, RM--Ruins of Montarek Inv3, DA—Data About Us Inv4