SOUTH CAROLINA MATHEMATICS CURRICULUM STANDARDS 2000

GRADES 6-8

CORRELATED TO

AGS BASIC MATH SKILLS

1

SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS NUMBER AND OPERATIONS I. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. A. Work flexibly with fractions, decimals, and percents to solve problems. Grade 6 *1. Show the relationship among fractions, decimals, and percents.

Fractions: Pp. 54-83, 111, 118-19, 121-27, 131-32, 136, 156, 272-79, 319 Decimals: Pp. 84-113, 124-25, 131-55, 185, 190, 193-94, 197, 227-32 Percents: Pp. 128-57

Grade 7 1. Write and use the appropriate equivalent forms of whole numbers, fractions, decimals, and percents.

Pp. 109-13, 131-37, 148-49

Grade 8 1. Solve real world problems involving fractions, decimals, and percents.

Pp. 67, 69-70, 72, 74, 80-81, 88, 92, 94, 96, 99, 103, 105, 107, 110, 121, 123, 125, 135-36, 140, 145, 147, 149, 154

B. Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line. Grade 6 1. Use order symbols to compare two fractions, two decimals, or two percents.

Pp. 56-57, 89-92, 118-19, 121-27

Grade 7 1. Identify, represent, and find the approximate location of fractions, decimals, percents, and square roots of perfect squares on a number line and justify the reasoning used.

2. Use order symbols to compare fractions, decimals, percents, and square roots of perfect squares and justify the reasoning used.

Pp. 56-57, 89-92, 118-19, 121-27

Grade 8 1. Compare and order rational and irrational numbers and find their approximate locations on a number line.

C. Develop meaning for percents greater than 100 and less than 1. Grade 6 1. Use models to represent percents greater than 100% and solve problems involving them.

Pp. 131-33

2

NUMBERS AND OPERATIONS, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS Grade 7 1. Use models to represent percents less than 1% and solve problems involving them.

Pp. 132-33, 136, 139, 141, 146

Grade 8 1. Solve real-world problems involving the use of percents greater than 100% or less than 1%.

Pp. 131-33, 136, 139, 141, 146

D. Understand and use ratios and proportions to represent quantitative relationships. Grade 6 1. Connect the concept of ratio and fractions by determining the equivalence of two ratios.

Pp. 116-25

Grade 7 *1. Create and write ratios and proportions from applied situations and explain the reasoning used.

Pp. 115, 117, 121, 123-27

E. Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation. Grade 6 1. Evaluate powers of ten up to 10 to the 6th power.

Pp. 100-01

Grade 7 1. Translate a number written in exponential form, in scientific notation, and in calculator notation to standard form.

Pp. 100-01

Grade 8 1. Use scientific notation to write very large numbers and numbers less than one.

Pp. 100-01

F. Use factors, multiples, prime factorization, and relatively prime numbers to solve problems. Grade 6 1. Solve problems using prime factorization, common multiples, and common factors, and explain the reasoning used.

Pp. 36-41, 46-53, 65

3

NUMBERS AND OPERATIONS, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS Grade 7 1. Apply primes, composites, factors, multiples, and relatively prime numbers in a variety of applied and mathematical situations and explain the reasoning used.

Pp. 36-41, 46-53, 65

G. Develop meaning for integers and represent and compare quantities with them. Grade 6 1. Use integers to describe real world phenomena in order to develop their meaning.

Pp. 282-92, 296-97

Grade 7 1. Compare and order integers.

Pp. 282-92, 296-97

II. Understand meanings of operations and how they relate to one another. A. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers. Grade 6 1. Explain the meaning and effects of adding, subtracting, multiplying and dividing.

Addition: Meaning and effects of: Pp. 7-9. Added practice: Pp. 32-33, 41-43, 53, 71-74, 93-94, 150-55, 179, 183, 207-12, 215, 223, 233-34, 239, 275, 277, 283-95, 300-03, 315 Subtraction: Meaning and effects of: Pp. 10-13. Added practice: Pp. 32-33, 75-83, 95-96, 148-49, 153, 207-08, 222, 233-37, 239, 283-90, 300, 302, 316 Multiplication: Meaning and effects of: Pp. 14-19. Added practice: Pp. 32-33, 36-38, 57-61, 64-70, 83, 93-94, 97-99, 118-20, 124-25, 132, 139-40, 146-58, 185, 188, 190, 197, 202-03, 208-09, 227-32, 272-79, 293-95, 291-92, 316-17 Division: Meaning and effects of: Pp. 20-26. Added practice: Pp. 32-33, 42-47, 59, 62, 65-69, 102-08, 124, 137, 143-45, 152, 202-03, 206, 209, 268-71, 296-97, 304-07, 312, 317

4

NUMBERS AND OPERATIONS, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS Grade 7 1. Explain the meaning and effects of arithmetic operations with integers.

Pp. 282-92, 296-97

B. Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals. Grade 6 1. Apply the commutative, associative, and distributive properties to simplify computations with whole numbers, fractions, and decimals.

Pp. 293-95

Grade 7 1. Apply the associative, commutative, and distributive properties for operations on integers, fractions, and decimals.

Pp. 293-97

Grade 8 1. Apply the associative, commutative, and distributive properties to simplify expressions.

Pp. 293-97

C. Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems. Grade 7 1. Using models and numbers, explain the inverse relationships between squaring and finding square roots of perfect squares.

Grade 8 1. Approximate to the nearest tenth the square root of a number that falls between two perfect squares.

5

NUMBERS AND OPERATIONS, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS III. Compute fluently and make reasonable estimates. A. Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods. Grade 6 1. Select appropriate methods and tools to solve problems requiring the addition and subtraction of fractions and decimals.

Fractions: Pp. 55-57, 71-81 Decimals: Pp. 93-96, 148-51, 153, 155, 183

Grade 7 1. Select appropriate methods and tools to solve problems applying all operations to fractions, decimals and integers.

Fractions: Pp. 25, 55-83, 109-11, 118-37, 156, 272-79, 319 Decimals: Pp. 85-113, 124-25, 131-55, 185, 190, 193-94, 197, 227-32 Integers: Pp. 282-89, 296-97

Grade 8 1. Select appropriate methods and tools to solve problems requiring the use of rational numbers.

B. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use. Grade 6 1. Divide commonly used fractions (including decimals) using models.

Pp. 68-69, 102-08, 124, 143-45, 148, 152

*2. Use models and numbers to develop and analyze algorithms with fractions and decimals.

Fractions: Pp. 54-83, 114-27, 133-37, 156, 272-79, 319 Decimals: Pp. 84-113, 124, 131-32, 143-44, 148-55, 185, 188, 190, 193-94, 197, 227-32

*3. Add, subtract, multiply and divide fractions (including decimals) to solve a variety of applied and mathematical problem situations.

Pp. 54-137, 143-44, 148-156, 272-79, 319

6

NUMBERS AND OPERATIONS, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS Grade 7 *1. Use models and numbers to develop and analyze the algorithms for computing with integers.

Pp. 288-92, 296-97

*2. Add, subtract, multiply and divide integers to solve a variety of applied and mathematical problem situations.

Pp. 288-92, 296-97

Grade 8 *1. Compute with rational numbers to solve a variety of applied and mathematical problem situations.

C. Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results. Grade 6 1. Estimate the sums and differences of fractions, describe the method used, and determine the reasonableness of results.

The opportunity to estimate sums and differences of fractions can be found on pp. 55-57, 71-81.

Grade 7 1. Estimate the products and quotients of fractions and decimals, describe the method used, and determine the reasonableness of results.

The opportunity to estimate products and quotients of fractions and decimals can be found on pp. Pp. 58, 64-65, 68-69, 83, 97-99, 102-08, 111-13, 124-25, 139-40, 143-45, 148, 150, 152-55, 185, 188, 190, 193-94, 197, 227-32, 272-79.

2. Estimate the sums and differences of integers, describe the method used, and determine the reasonableness of results.

The opportunity to estimate sums and differences of integers can be found on pp. 282-90.

Grade 8 1. Justify the reasonableness of an estimate of rational number computations.

D. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios. Grade 7 1. Explain the equivalent ratio method of solving problems involving proportions.

Pp. 116-23

7

NUMBERS AND OPERATIONS, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS Grade 8 *1. Analyze and explain each method for solving a proportion (equivalent ratios, unit rates, and cross-multiplying.

Pp. 118-27, 146-47, 268-75

*2. Use proportional reasoning to solve applied problems and justify the solution. Pp. 118-27, 146-47, 268-75 * FOCUS STANDARDS

8

SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS ALGEBRA I. Understand patterns, relations, and functions. A. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules. Grade 6 *1. Describe, extend, and write rules for a wide variety of patterns.

Pp. 35-53, 240-65

Grade 7 1. Describe, extend, analyze, and create a wide variety of patterns to investigate relationships and to solve problems.

Pp. 35-53, 240-65

B. Relate and compare different forms of representations for a relationship. Grade 7 1. Use different forms of representing information (e.g., graphical, symbolic and tabular).

Charts and Tables: Pp. 2, 123-24, 136, 151, 153, 168, 178-79, 181-82, 184, 187, 192, 194, 196, 202-04, 206, 233, 242-47, 250-59, 268-69. Graphs: Pp. 241-65

Grade 8 1. Describe the merits and limitations of graphical, symbolic and tabular representations.

Pp. 241-65

C. Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. Grade 7 1. Examine tables and graphs to determine if there is a constant rate of change between the quantities.

Pp. 241-65

Grade 8 1. Examine tables, graphs, or simple equations to classify relationships as linear or non- linear.

9

ALGEBRA, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS II. Represent and analyze mathematical situations and structures using algebraic symbols. A. Develop an initial conceptual understanding of different uses of variables. Grade 6 *1. Use order of operations to evaluate numerical expressions.

Pp. 31, 291-95, 318

Grade 7 1. Explain the use of a variable as a quantity that can change its value, as a quantity on which other values depend, and as generalization of patterns.

Pp. 298-311

Grade 8 *1. Evaluate simple algebraic expressions for given values of variables by using the substitution principle and the rules for order of operations.

Pp. 300-13

B. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope. Grade 6 1. Write simple equations and inequalities accurately to represent relationships.

P. 303

Grade 7 1. Analyze quantitative changes by comparing and contrasting numerical patterns in tables with their respective graphs in the coordinate plane.

2. State the coordinates of the x and y intercepts from a graph. P. 299 Grade 8 1. Explain the impact of coefficients and constants on linear equations as they reflect simple applications.

C. Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships. Grade 7 1. Use variables to describe numerical expressions and relationships.

Pp. 120-26, 268-74, 298-313

10

ALGEBRA, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS Grade 8 1. Write or model a linear equation to solve a simple applied problem.

D. Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations. Grade 6 1. Use commutative, associative and distributive properties to examine equivalence of a variety of simple algebraic expressions.

Pp. 293-95, 300-13

Grade 7 1. Recognize and apply the additive and multiplicative inverses.

Pp. 308-09

2. Use models and numbers to solve one-step linear equations and inequalities in one variable.

Grade 8 *1. Simplify a variety of algebraic expressions using properties of real numbers and rules for order of operations.

Pp. 295, 300-13

*2. Solve one- and two-step linear equations and inequalities in one variable using strategies that involve inverse operations.

III. Use mathematical models to represent and understand quantitative relationships. A. Model and solve contextualized problems using various representations, such as graphs, tables, and equations. Grade 6 1. Use graphs and tables to solve applied problems.

Pp. 241-65, 344

Grade 7 *1. Use graphs, tables, and equations to solve applied problems involving tips, discounts, sales tax and simple interest.

Pp. 151, 153

11

ALGEBRA, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS Grade 8 *1. Use one or more representations to model and to analyze the relationship in applied problems to determine if it is linear or non-linear.

IV. Analyze change in various contexts. A. Use graphs to analyze the nature of changes in quantities in linear relationships. Grade 7 1. Describe a linear relationship as positive or negative from a graph.

Grade 8 1. Use tables and graphs to model and analyze linear relationships between variables.

*FOCUS STANDARDS

12

SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS GEOMETRY I. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. A. Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties. Grade 6 1. Compare and contrast prisms, cylinders and pyramids with the polygons or circles that constitutes their faces.

Pp.168-73

Grade 7 1. Classify polygon as regular or non-regular and investigate relationships between the number of diagonals and the number of sides of a regular polygon.

Polygons: Pp. 168-73

Grade 8 1. Identify the necessary and sufficient properties that characterize quadrilaterals.

Pp. 168, 170-71

B. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects. Grade 6 1. Describe relationships among angles, side lengths, perimeters, and areas of similar polygons.

Pp. 168-71, 183-86, 210-18

Grade 7 *1. Describe relationships between the edge lengths, and volume of similar prisms.

Pp. 219-23

Grade 8 *1. Describe how a change in the edge length affects the angle measures, perimeters and areas of similar regular polygons.

Pp. 168-71, 183-86, 210-23

C. Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. Grade 6 1. Identify and describe point and line symmetry in two-dimensional shapes.

P. 161

13

GEOMETRY, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS 2. Distinguish between similarity and congruence. Grade 7 *1. Compare and contrast attributes of similar figures and the attributes of congruent figures.

Grade 8 1. Given the length of 3 segments, determine and explain whether or not they can form a triangle.

Pp. 168-71, 216-17, 221

2. Apply the Pythagorean relationship to determine if a triangle is a right triangle. *3. Apply the Pythagorean Theorem to find the missing length of a side of a right triangle.

II. Specify locations and describe spatial relationships using coordinate geometry and other representational systems. A. Use coordinate geometry to represent and examine the properties of geometric shapes. Grade 6 1. Given the coordinates of three vertices of a rectangle or square oriented horizontally or vertically, use the first quadrant of the rectangular coordinate system to locate the other vertex.

Grade 7 1. Identify and graph ordered pairs in the four quadrants of a coordinate plane.

P. 299

Grade 8 *1. Given the coordinates of a vertex and the length of adjacent sides of a polygon, use the rectangular coordinate system to locate other vertices with a square, rectangle or right triangle.

14

GEOMETRY, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS B. Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides Grade 6 1. Plot the vertices of squares and rectangles and determine the relationship among the coordinates.

Grade 7 *1. State relationships among the coordinates of the vertices of rectangles, squares, parallelograms, trapezoids, and rhombuses oriented horizontally.

III. Apply transformations and use symmetry to analyze mathematical situations. A. Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling. Grade 6 1. Describe the transformation used to move a polygon from one location to another in the first quadrant.

Grade 7 1. Describe the transformation used to move a polygon in one quadrant to another quadrant in the coordinate plane.

Grade 8 1. Apply dilations and describe their results.

B. Examine the congruence, similarity, and line or rotational symmetry of objects using transformations. Grade 6 *1. Apply a transformation to a polygon and describe how it has changed.

Grade 7 1. Determine the type of symmetry (point or line) found in a reflection or a rotation.

15

GEOMETRY, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS Grade 8 1. Determine the equivalence, if any, between multiple applications of one transformation and the application of a different transformation.

IV. Use visualization, spatial reasoning, and geometry modeling to solve problems. A. Draw geometric objects with specified properties, such as side lengths or angle measures. Grade 6 1. Use symbols for parallel lines and perpendicular lines to describe polygons and figures where appropriate.

P. 171

Grade 7 *1. Draw two-dimensional objects from a geometric description and write a description of geometric properties for a given object.

Grade 8 1. Identify the congruent and supplementary relationships of the angles formed by parallel lines and a transversal.

B. Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume. Grade 6 *1. Given the top, side, and front views, construct a 3-dimensional model using cubes.

Grade 7 1. Construct nets for 3-dimensional figures.

Teacher’s Edition: P. 173

2. Compare and contrast the number of faces, vertices, and edges of 3-dimensional figures.

Pp. 172-73, 188-89

Grade 8 1. Use isometric drawings of three-dimensional figures to build the model with cubes.

16

GEOMETRY, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS *2. Determine the changes in volume and surface area of 3-dimensional figures that can be built with cubes when one or more measurements are changed.

C. Use visual tools such as networks to represent and solve problems. Grade 7 1. Given a network with up to six vertices, determine the number of paths.

Grade 8 1. Construct a network to solve a problem situation.

D. Use geometric models to represent and explain numerical and algebraic relationships. Grade 8 1. Use an area model to analyze probability.

E. Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life. Grade 6 1. Identify and apply geometric concepts in a variety of practical contexts.

Student Edition: P. 159 Teacher’s Edition: Pp. 7, 159, 163, 165, 166, 173, 220, 230

Grade 7 1. Identify transformations in tessellations, use transformations to draw tessellations, and describe relationships among figures that tessellate.

Grade 8 1. Identify applications of transformations, such as tiling, fabric design, art, and scaling.

* FOCUS STANDARDS

17

SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS MEASUREMENT I. Understand measurable attributes of objects and the units, systems, and processes of measurement. A. Understand both metric and customary systems of measurement. Grade 7 1. Explain the relationship between the metric system and the base ten number system.

Pp. 176-83

B. Understand relationships among units and convert from one unit to another within the same system. Grade 7 1. Compare and convert units of measure for length, weight/mass, and volume within the U.S. customary system and within the metric system.

U.S. Customary: Pp. 204-06, 213, 219-21, 231-32 Metric: Pp. 179-84, 187-90, 195-97

2. Add and subtract mixed units of measure and express answers in appropriate form. Grade 8 1. Use dimensional analysis to convert from one unit to another.

C. Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. Grade 6 1. Estimate angle measure using 45 degrees, 90 degrees, 180 degrees, 270 degrees, and 360 degrees as referents and use the appropriate tools to measure any angle.

Pp. 162-67

2. Use appropriate units of measure to label angles, perimeter, area. Pp. 162-67, 183-86, 210-18, 229-30 Grade 7 1. Use appropriate units of measure to label surface area and volume.

Pp. 184-90, 213-17, 219-21, 225-32

18

MEASUREMENT, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS II. Apply appropriate techniques, tools, and formulas to determine measurements. A. Use common benchmarks to select appropriate methods for estimating measurements. Grade 6 *1. Estimate and then determine length, weight/mass, area, and volume/capacity, using standard and nonstandard units of measure.

Pp. 179-84, 187-90, 195-97, 204-06, 213, 219-21, 231-32

2. Estimate and justify estimates of perimeter and area of irregular shapes. Pp. 211-12 Grade 7 1. Use appropriate methods to approximate the surface area and volume of an irregular figure.

Pp. 184-90, 213-17, 219-21, 225-32

B. Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision. Grade 6 1. Select and use appropriate tools and units to measure to the degree of accuracy required in a particular situation.

Pp. 179-90, 204-06, 213-15, 219-21, 229-32

Grade 7 1. Analyze a variety of measurement situations to determine the necessary degree of accuracy and precision.

Pp. 179-90, 204-06, 213-15, 219-21, 229-32

C. Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes Grade 6 1. Investigate and describe the relationship between areas of rectangles and triangles or other quadrilaterals.

Pp. 184-86, 213-18

*2. Develop and apply the formulas for the area of triangles and parallelograms. Pp. 184-86, 216-18

19

MEASUREMENT, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS Grade 7 1. Use measurements and formulas to solve real-world and mathematical problems.

Pp. 184-91, 193-94, 197, 213-21, 225-32

2. Using concrete materials or computer models, derive approximations for pi from measurements for circumference and diameter.

Pp. 226-32

*3. Create and solve problems by finding the circumference and/or area of a circle when given the diameter or radius.

Pp. 228-33

Grade 8 *1. Find the area of irregular shapes.

2. Find the area of a trapezoid using the formula. D. Develop strategies to determine the surface area and volume of selected prisms, and cylinders. Grade 7 *1. Investigate and describe the relationship between the area of the base and the volume of a prism, pyramid or cylinder.

Pp. 216-21

Grade 8 1. Investigate and describe the relationship between the area of the faces and surface area of prisms, pyramids and cylinders.

E. Solve problems involving scale factors, using ratio and proportion. Grade 6 1. Use a scale to find distance.

Pp. 277-79

Grade 7 *1. Determine the unit rate.

Pp. 267-79

Grade 8 *1. Use the properties of similar figures to determine the length of a missing side.

Pp. 267-79

20

MEASUREMENT, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS F. Solve simple problems involving rates and derived measurements for such attributes as velocity and density. Grade 7 1. Apply rates to solve problems in real world situations.

Pp. 138-55

Grade 8 1. Use measurements and formulas to solve real-world and mathematical problems.

Formulas: Pp. 148-52, 184-86, 213-18, 227-30

* FOCUS STANDARDS

21

SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS DATA ANALYSIS AND PROBABILITY I. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. A. Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population. Grade 6 1. Given a problem situation involving one population, collect, analyze, and interpret data.

Pp. 248-50, 253, 256, 259

Grade 7 1. Given a problem situation involving two populations, collect, analyze and interpret data.

Pp. 248-50, 253, 256, 259

B. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter plots. Grade 6 1. Organize and display data in a variety of ways including frequency tables, histograms, and stem-and-leaf plots.

Pictographs, bar graphs, double bar graphs, divided bar graphs, line graphs, circle graphs, multiple bar graphs: Pp. 241-63

Grade 7 1. Organize, display and interpret data in a variety of ways including box-and-whisker plots.

Pictographs, bar graphs, double bar graphs, divided bar graphs, line graphs, circle graphs, multiple bar graphs: Pp. 241-63

2. Construct circle graphs and interpret the meaning. Pp. 257-59 Grade 8 1. Use a matrix to organize and describe data.

2. Create and use a scatter plot and estimate its line of fit. 3. Explain what type of graph would be appropriate for a given data set. Pp. 241-63

22

DATA ANALYSIS AND PROBABILITY, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS II. Select and use appropriate statistical methods to analyze data. A. Find, use, and interpret measures of center and spread, including mean and interquartile range. Grade 6 1. Create and solve problems involving the mean, median, mode, and range of a set of data.

Grade 7 1. Compute, describe, and interpret the interquartile range.

Grade 8 1. Determine which measure of center is the most appropriate for a given situation and explain the reasoning used.

B. Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots. Grade 6 1. Interpret histograms and stem-and-leaf plots.

*2. Describe the relationship between a data set and its corresponding histogram or stem-and-leaf plot.

Grade 7 *1. Describe the relationship between a data set and its corresponding box plot or circle graph.

Pp. 257-59

Grade 8 1. Explain how different graphical representations of data can bias the interpretation of this data.

Pp. 260-63

23

DATA ANALYSIS AND PROBABILITY, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS III. Develop and evaluate inferences and predictions that are based on data. A. Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken. Grade 6 1. Analyze and list the differences between two data sets.

Pp. 241-63

Grade 7 1. Make inferences and predictions based on the analysis of sample data.

Pp. 241-63

B. Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit. Grade 8 *1. Use a scatter plot and its line of fit to determine if a positive, negative, or no relationship exists between two sets of data and to make predictions.

C. Use conjectures to formulate new questions and plan new studies to answer them. Grade 8 1. Formulate a hypothesis, then design and carry out an experiment to test it.

2. Formulate new areas of investigation based on the results of prior experiments. IV. Understand and apply basic concepts of probability. A. Understand and use appropriate terminology to describe complementary and mutually exclusive events. Grade 6 1. Identify and describe complementary events.

Grade 7 1. Identify and describe mutually exclusive events.

24

DATA ANALYSIS AND PROBABILITY, continued SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 AGS BASIC MATH SKILLS B. Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations. Grade 6 1. Create a sample space for one- or two-stage events and represent it in the form of a list, chart, picture, or tree diagram.

*2. Determine and interpret the probability of an event occurring from a given sample space.

Grade 7 1. Investigate and describe the difference between the probability of an event found through simulation versus the theoretical probability of that same event.

Grade 8 1. Make inferences and convincing arguments based on analysis of theoretical or experimental probability.

C. Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models. Grade 6 1. Determine the number of possible outcomes in two-stage events, making a tree diagram, or using models.

Grade 7 1. Determine the number of possible outcomes in a multi-stage event using the fundamental counting principle or other techniques.

*2. Compute the probability of two independent events. Grade 8 *1. Compute the probability of two dependent events.

2. Determine the odds of a given event. * FOCUS STANDARDS

25