Mathematics Competency Assurance Documents

7th 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

7^th Grade Number/Computation Standards

NC7.1 Show number sense by modeling, communicating and applying multiple representations and equivalent relationships of real numbers (fractions, decimals, percents, integers, pi, etc.)

NC7.2 Use models and real world investigations to read, write, compare, order, and apply operations for computation involving fractions, decimals, percents and ratios.

NC7.3 Use order of operations including ( )’s to solve problems with rational numbers (fractions, decimals, percents, integers).

NC7.4 Apply ratios, percents, and proportional reasoning to solve problems dealing with rates, scaling (scale factor), similarity and a constant change factor.

Skills, Concepts & Relationships

• Use estimation to determine the reasonableness of answers (G2 ch1) (DU) (CP)
• Use order of operations with ( )’s (G2 ch1)
• Round to the required or appropriate degree of precision (G2 ch2.2&2.8)
• Determine the effect multiplying or dividing by a decimal has on the product or quotient (10x10 grids, base 10 blocks) (estimate reasonable answers then check with or without a calculator) (G2 ch2.7) (BP2)
• Explore exponents (cubic numbers: 1, 8, 27, 64, 125) (G2 ch1,2, 9&10)
• Introduce scientific notation (G2 ch2&7) (DU Inv4)
• Review applications of fraction and decimal computation in real world situations (G2 ch2&5) (BP2 Inv1&6) (DU)
• Review divisibility rules (G2 ch4&5)
• Convert fractions/mixed numbers to repeating/terminating decimals (G2 ch4.7)
• Add & subtract commonly encountered (cooking, stock market, ruler, etc.) fractions and mixed numbers with and without common denominators (estimate sums and differences then check with or without a calculator) (tangrams, pattern blocks, fraction circles, geoboards) (G2 ch5.3&5.4) (BP2 Inv3&4)
• Determine the effect multiplying or dividing by commonly encountered fractions less than one or mixed numbers greater than one have on the product or quotient (tangrams, pattern blocks, fraction circles, geoboards, etc.) (G2 ch5.5,5.9&5.10) (BP2 Inv5)
• Develop recognizing and using properties: Commutative, Associative, Distributive, Inverse, and Identity of zero and one (G2 ch5)
• Explore an approximation of pi as an example of an irrational number (G2 ch5.7&9.8)
• Determine the opposite of an integer (absolute value, number line, positive-negative, have money-owe money, etc.) (G2 ch7) (AN Inv1)
• Add & subtract integers (integer chips, number line, algeblock mat, etc.) (G2 ch7) (AN Inv1&2)
• Develop multiplying & dividing integers (look for patterns) (G2 ch7) (AN Inv3&4)
• Develop finding and approximating square roots using a calculator (recognize perfect squares to 169) (G2 ch9.1&9.2)
• Compare, order, and convert among decimals, fractions, and percents (10x10 grids, base 10 blocks, etc.) (G2 ch11) (BP2)
• Recognize and define ratio, proportion, and percent (10x10grids, base 10 blocks)(G2 ch11) (CP) (BP2)
• Apply ratios and proportional reasoning to solve problems dealing with rates, scaling, similarity and a constant change factor (G2 ch11.2-11.5) (CP Inv6)
• Solve percent problems using proportions (G2 ch12.4) (CP) (BP2)
• Determine percent of change in real world problems (G2 ch12.7) (BP2)
• Calculate sale price, simple interest, discounts and commission (G2 ch12.8&12.9) (CP) (BP2)
• Develop use of calculators to explore exponents (G2 ch1), order of operations (G2 ch1), reciprocal (inverse) key, number patterns (G2 ch4.3), pi key (G2 ch5), square roots (G2 ch9), and scientific notation (G2 ch2&7)
• Develop use of a spreadsheet to perform calculations (G2 ch1.9,4.1&12.9)

G2--Glencoe Course 2; Connected Math: BP2--Bits & Pieces II, CP--Comparing & Scaling, AN--Accentuate the Negative, DU--Data Around Us

7th 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

7^th Grade Geometry/Measurement Standards

GM7.1 Describe, draw, classify, and analyze regular and irregular two-dimensional figures; recognize translations & reflections; and recognize proportional relationships in similar figures.

GM7.2 Apply the concepts of perimeter and area to two-dimensional shapes: using the formula for the area of rectangles, determine and use formulas for perimeter and area of triangles, parallelograms and trapezoids; determine the area and perimeter of irregular shapes by subdivision using manipulatives; and determine with manipulatives formulas for circumference and area of circles to apply in problem situations.

GM7.3 Recognize the following relationships: the sum of measures of the angles of a triangle equals 180 degrees, and the sum of measures of the angles of a quadrilateral equals 360 degrees.

Skills, Concepts & Relationships

• Review basic geometric terms: point, line, line segment, ray, plane (supplement)
• Review conversions within the same measurement system(G2 ch2.9&6.6)
• Matching congruent figures and parts of figures (G2 ch8.1) (SD)
• Introduce angle pair classification: supplementary, complementary, etc. (supplement)
• Classify polygons; special quadrilaterals: square, rectangle, rhombus, trapezoid, parallelogram; special triangles: acute, right, obtuse, scalene, isosceles, equilateral (G2 ch8.2,8.3) (SD)
• Use a compass and an angle ruler (G2 ch8.2,8.4) (SD)
• Introduce 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)(G2 ch8)
• Recognize the following relationships: the sum of measures of the angles of a triangle is 180 degrees and that the sum of the measures of the angles of a quadrilateral is 360 degrees (tear edges to form straight line-180, or circle-360) (G2 ch8.2) (SD Inv4)
• Translate and reflect figures (slide, flip) (MIRA, patty paper)(G2 ch8.7&8.8) (CS)
• Find perimeter and area of special triangles and special quadrilaterals (color tiles, graph paper)(G2 ch9)(CS Inv5&6)
• Determine and use formulas for area of triangles, parallelograms, and trapezoids and recognize how they are related to the formula for the area of a rectangle (geoboards, graph paper) (G2 ch9.7)(CS Inv5&6)
• Find area of regular and irregular shapes (over-estimate, under-estimate, use graph paper) (G2 ch9.6)(CS Inv2)
• Determine circle measurements (circumference, area, radius, diameter) and relationships among them (develop formulas through investigations with string, graph paper, etc.) (G2 ch5.7&9.8) (CS Inv7)
• Use square units correctly (G2 ch9) (CS)
• Introduce volume and surface area of cubes, prisms, and cylinders(cubes, pentomino "open-top boxes", nets, isometric dot paper drawings) (G2 ch10) (FW Inv1&2)
• Review geometric solids and their terms: base, vertices, edges, faces, cubes, rectangular prisms, triangular prisms, cylinders, cones, pyramids, and spheres (G2 ch10&supplement) (FW)
• Recognize measures of similar figures have equal ratios (expand, contract) (G2 11.4) (SS Inv2&3)

G2--Glencoe Course 2; Connected Math: SS--Stretching & Shrinking Inv2&3, CS—Covering & Surrounding Inv5-7, SD--Shapes & Designs, FW--Filling & Wrapping Inv1&2

7th 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

7^th Grade Probability/Statistics Standards

PS7.1 Collect, compile, compare and display data (multiple line graph, double bar graph, line plot, stem and leaf plot, circle graph, histogram) to analyze and interpret situations.

PS7.2 Make predictions and evaluate conclusions based on statistical analysis (misleading statistics & graphs).

PS7.3 Determine probabilities by constructing sample space and conducting probability experiments.

Skills, Concepts & Relationships

• Develop organizing information on a spreadsheet and making appropriate computer generated graphs (G2 ch1.9)
• Review choosing appropriate scales and intervals when graphing (G2 ch3.3)
• Review applications of measures of central tendency (G2 ch3.5&3.7)
• Recognize misleading representations of statistics (validity/bias) (G2 ch3.8)
• Develop outliers effect on mean and median (dispersion/variance) (G2 ch3.4)
• Construct and interpret: line plots, stem and leaf plots, multiple line graphs, double bar graphs, circle graphs, histograms (G2 ch3.4,3.6,12.6&supplement) (WD Inv1-4)
• Develop accessing information from a database (G2 ch3.2)
• Construct tree diagrams and area models to analyze theoretical probability (G2 ch9.9&13.1) (WD Inv1-4)
• Recognize and use the Fundamental Counting Principle (multiply number of choices for each item to get total possible outcomes) (G2 ch13.3)
• Determine theoretical and experimental probability (G2 ch13.3) (WD Inv1-4)
• Express probability as a fraction, decimal and percent (G2 ch13&supplement) (WD1-4)
• Determine probability by designing and conducting experiments (spinners, number cubes, cards, coins, counters, etc.) (G2 ch13.4&supplement) (WD Inv1-4)
• Predict and draw conclusions from experiments and statistics (fair and unfair games)(G2 ch13.1&13.5) (WD Inv1-4)
• Design a statistical study to investigate a problem, conduct the study and interpret and communicate the outcomes (supplement)
• Introduce Law of Large Numbers (more experimental trials should get closer to theoretical probability) (supplement) (WD Inv1-4)
• Gather, organize, represent, analyze, and interpret large sets of data (G2 ch13.5 & supplement)
• Determine the probability of two independent events (G2 13.6) (WD Inv1-4)
• Introduce graphing calculator for line graphs and histograms (supplement)
• Develop sampling techniques (supplement)
• Introduce box and whisker plots (supplement)

G2--Glencoe Course 2; Connected Math: WD—What Do You Expect? Inv. 1-4

7th 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

7^th Grade Algebraic Ideas Standards

AI7.1 Recognize, create, continue and generalize numeric and geometric patterns by giving the rule for any term in the pattern.

AI7.2 Solve one-step equations with whole numbers, and simple decimals, fractions and percents using concrete, pictorial, and abstract methods (variables).

AI7.3 Translate from concrete, pictorial and verbal expressions to algebraic expressions and vice versa.

Skills, Concepts & Relationships

• Recognize, define, and use the concepts of variables, expressions, and equations (open sentences, cups and counters, balance scale, "Hands-On" equations, etc.) (G2 ch1.8,6.4&6.5) (VP)
• Develop simplifying expressions (combining like terms) (G2 ch1.8&7.7) (MS)
• Recognize number patterns (sequences, square numbers, triangular numbers, etc.) (G2 ch4.3) (VP) (MS)
• Solve one-step equations with simple fractions, decimals, and percents using models and symbolically (balance scale, open sentences, algebra tiles, cups and counters, "Hands-On equations, algeblocks, etc.) (G2 ch6.1,6.2&6.3) (MS Inv4)
• Introduce solving simple two-step equations with both models and symbols (balance scale, open sentences, algebra tiles, cups and counters, etc.) (G2 ch6.3&14.2) (MS Inv4)
• Graph using the Cartesian coordinate system (4-quadrants, x/y coordinates, plot ordered pairs) (G2 ch7.3) (VP) (MS) (SS Inv2&3) (AN Inv5)
• Introduce graphing calculator to represent linear patterns (use "table" or "list" to make scatterplots, positive or negative correlations) (G2 ch1.8&ch7.3) (VP Inv5)
• Introduce patterns in Pascal’s Triangle (G2 ch7.6&supplement)
• Solve problems involving formulas (A=pr² , A=1/2bh) (G2 ch9)
• Develop using spreadsheet formulas to represent patterns (G2 ch12.9) (VP Inv3&4)
• Generalize patterns by determining the rule for any term in linear patterns (G2 ch14.5) (VP)
• Develop representing and interpreting relationships among narrative, tables, graphs, verbal rules, and equations (G2 ch14.4&14.5) (VP)

G2--Glencoe Course 2; Connected Math: VP—Variables & Patterns Inv1-5, MS—Moving Straight Ahead Inv1-5, SS--Stretching & Shrinking Inv2&3, AN--Accentuate the Negative Inv5