SOUTH CAROLINA MATHEMATICS CURRICULUM …
SOUTH CAROLINA MATHEMATICS CURRICULUM STANDARDS 2000
GRADES 6-8
CORRELATED TO
AGS BASIC MATH SKILLS
|SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 |AGS BASIC MATH SKILLS |
|NUMBER AND OPERATIONS | |
|Understand numbers, ways of representing numbers, relationships among | |
|numbers, and number systems. |Fractions: Pp. 54-83, 111, 118-19, 121-27, 131-32, 136, 156, |
| |272-79, 319 |
|Work flexibly with fractions, decimals, and percents to solve problems. |Decimals: Pp. 84-113, 124-25, 131-55, 185, 190, 193-94, 197, |
|Grade 6 |227-32 |
|*1. Show the relationship among fractions, decimals, and percents. |Percents: Pp. 128-57 |
|Grade 7 | |
|Write and use the appropriate equivalent forms of whole numbers, fractions, |Pp. 109-13, 131-37, 148-49 |
|decimals, and percents. | |
|Grade 8 |Pp. 67, 69-70, 72, 74, 80-81, 88, 92, 94, 96, 99, 103, 105, 107, |
|1. Solve real world problems involving fractions, decimals, and percents. |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 |Pp. 56-57, 89-92, 118-19, 121-27 |
|perfect squares and justify the reasoning used. | |
|Grade 8 | |
|1. Compare and order rational and irrational numbers and find their approximate | |
|locations on a number line. | |
|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 |Pp. 131-33 |
|them. | |
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 |Pp. 131-33, 136, 139, 141, 146 |
|than 1%. | |
|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 |Pp. 116-25 |
|ratios. | |
|Grade 7 | |
|*1. Create and write ratios and proportions from applied situations and explain the |Pp. 115, 117, 121, 123-27 |
|reasoning used. | |
|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 |Pp. 100-01 |
|calculator notation to standard form. | |
|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, |Pp. 36-41, 46-53, 65 |
|and explain the reasoning used. | |
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 |Pp. 36-41, 46-53, 65 |
|variety of applied and mathematical situations and explain the reasoning used. | |
|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. |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, |
|A. Understand the meaning and effects of arithmetic operations with fractions, decimals, |215, 223, 233-34, 239, 275, 277, 283-95, 300-03, 315 |
|and integers. |Subtraction: Meaning and effects of: Pp. 10-13. Added |
|Grade 6 |practice: Pp. 32-33, 75-83, 95-96, 148-49, 153, 207-08, 222, |
|1. Explain the meaning and effects of adding, subtracting, multiplying and dividing. |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 |
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 |Pp. 293-95 |
|computations with whole numbers, fractions, and decimals. | |
|Grade 7 | |
|Apply the associative, commutative, and distributive properties for operations on |Pp. 293-97 |
|integers, fractions, and decimals. | |
|Grade 8 | |
|1. Apply the associative, commutative, and distributive properties to simplify |Pp. 293-97 |
|expressions. | |
|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. | |
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 |Fractions: Pp. 55-57, 71-81 |
|1. Select appropriate methods and tools to solve problems requiring the addition and |Decimals: Pp. 93-96, 148-51, 153, 155, 183 |
|subtraction of fractions and decimals. | |
|Grade 7 |Fractions: Pp. 25, 55-83, 109-11, 118-37, 156, 272-79, 319 |
|1. Select appropriate methods and tools to solve problems applying all operations to |Decimals: Pp. 85-113, 124-25, 131-55, 185, 190, 193-94, 197, |
|fractions, decimals and integers. |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 |Fractions: Pp. 54-83, 114-27, 133-37, 156, 272-79, 319 |
|decimals. |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 |Pp. 54-137, 143-44, 148-156, 272-79, 319 |
|of applied and mathematical problem situations. | |
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 |Pp. 288-92, 296-97 |
|integers. | |
|*2. Add, subtract, multiply and divide integers to solve a variety of applied and |Pp. 288-92, 296-97 |
|mathematical problem situations. | |
|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 |The opportunity to estimate sums and differences of fractions can|
|1. Estimate the sums and differences of fractions, describe the method used, and |be found on pp. |
|determine the reasonableness of results. |55-57, 71-81. |
|Grade 7 |The opportunity to estimate products and quotients of fractions |
|1. Estimate the products and quotients of fractions and decimals, describe the method |and decimals can be found on pp. Pp. 58, 64-65, 68-69, 83, 97-99,|
|used, and determine the reasonableness of results. |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 |The opportunity to estimate sums and differences of integers can |
|determine the reasonableness of results. |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 |
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 |Pp. 118-27, 146-47, 268-75 |
|rates, and cross-multiplying. | |
|*2. Use proportional reasoning to solve applied problems and justify the solution. |Pp. 118-27, 146-47, 268-75 |
* FOCUS STANDARDS
|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 |Pp. 35-53, 240-65 |
|relationships and to solve problems. | |
|Relate and compare different forms of representations for a relationship. |Charts and Tables: Pp. 2, 123-24, 136, 151, 153, 168, 178-79, |
|Grade 7 |181-82, 184, 187, 192, 194, 196, 202-04, 206, 233, 242-47, |
|1. Use different forms of representing information (e.g., graphical, symbolic and |250-59, 268-69. |
|tabular). |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 |Pp. 241-65 |
|the quantities. | |
|Grade 8 | |
|1. Examine tables, graphs, or simple equations to classify relationships as linear or non- | |
|linear. | |
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 |Pp. 298-311 |
|which other values depend, and as generalization of patterns. | |
|Grade 8 | |
|*1. Evaluate simple algebraic expressions for given values of variables by using the |Pp. 300-13 |
|substitution principle and the rules for order of operations. | |
|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 |
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 |Pp. 293-95, 300-13 |
|variety of simple algebraic expressions. | |
|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 |Pp. 295, 300-13 |
|rules for order of operations. | |
|*2. Solve one- and two-step linear equations and inequalities in one variable using | |
|strategies that involve inverse operations. | |
|Use mathematical models to represent and understand quantitative | |
|relationships. | |
| | |
|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, |Pp. 151, 153 |
|discounts, sales tax and simple interest. | |
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. | |
| 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
|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 |Pp.168-73 |
|that constitutes their faces. | |
|Grade 7 | |
|1. Classify polygon as regular or non-regular and investigate relationships between the |Polygons: Pp. 168-73 |
|number of diagonals and the number of sides of a regular polygon. | |
|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 |Pp. 168-71, 183-86, 210-18 |
|polygons. | |
|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 |Pp. 168-71, 183-86, 210-23 |
|areas of similar regular polygons. | |
|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 |
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 |Pp. 168-71, 216-17, 221 |
|triangle. | |
|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. | |
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. | |
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 |P. 171 |
|figures where appropriate. | |
|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 |Pp. 172-73, 188-89 |
|figures. | |
|Grade 8 | |
|1. Use isometric drawings of three-dimensional figures to build the model with cubes. | |
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. |Student Edition: P. 159 |
|Grade 6 |Teacher’s Edition: Pp. 7, 159, 163, 165, 166, 173, 220, 230 |
|1. Identify and apply geometric concepts in a variety of practical contexts. | |
|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
|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 |U.S. Customary: Pp. 204-06, 213, 219-21, 231-32 |
|1. Compare and convert units of measure for length, weight/mass, and volume within |Metric: Pp. 179-84, 187-90, 195-97 |
|the U.S. customary system and within the metric system. | |
|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 |Pp. 162-67 |
|360 degrees as referents and use the appropriate tools to measure any angle. | |
|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 |
MEASUREMENT, continued
|SC MATHEMATICS CURRICULUM STANDARDS – GRADES 6-8 |AGS BASIC MATH SKILLS |
|II. Apply appropriate techniques, tools, and formulas to determine measurements. | |
| | |
|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 |Pp. 179-84, 187-90, 195-97, 204-06, 213, 219-21, 231-32 |
|standard and nonstandard units of measure. | |
|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 |Pp. 184-90, 213-17, 219-21, 225-32 |
|figure. | |
|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 |Pp. 179-90, 204-06, 213-15, 219-21, 229-32 |
|required in a particular situation. | |
|Grade 7 | |
|Analyze a variety of measurement situations to determine the necessary degree of |Pp. 179-90, 204-06, 213-15, 219-21, 229-32 |
|accuracy and precision. | |
|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 |Pp. 184-86, 213-18 |
|other quadrilaterals. | |
|*2. Develop and apply the formulas for the area of triangles and parallelograms. |Pp. 184-86, 216-18 |
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 |Pp. 226-32 |
|measurements for circumference and diameter. | |
|*3. Create and solve problems by finding the circumference and/or area of a circle when |Pp. 228-33 |
|given the diameter or radius. | |
|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 |Pp. 216-21 |
|volume of a prism, pyramid or cylinder. | |
|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 |
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 |Formulas: Pp. 148-52, 184-86, 213-18, 227-30 |
|1. Use measurements and formulas to solve real-world and mathematical problems. | |
* FOCUS STANDARDS
|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 |Pp. 248-50, 253, 256, 259 |
|data. | |
|Grade 7 | |
|1. Given a problem situation involving two populations, collect, analyze and interpret |Pp. 248-50, 253, 256, 259 |
|data. | |
|B. Select, create, and use appropriate graphical representations of data, including | |
|histograms, box plots, and scatter plots. | |
|Grade 6 |Pictographs, bar graphs, double bar graphs, divided bar graphs, |
|1. Organize and display data in a variety of ways including frequency tables, histograms, |line graphs, circle graphs, multiple bar graphs: Pp. 241-63 |
|and stem-and-leaf plots. | |
|Grade 7 |Pictographs, bar graphs, double bar graphs, divided bar graphs, |
|1. Organize, display and interpret data in a variety of ways including box-and-whisker |line graphs, circle graphs, multiple bar graphs: Pp. 241-63 |
|plots. | |
|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 |
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. | |
|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 |Pp. 257-59 |
|graph. | |
|Grade 8 | |
|1. Explain how different graphical representations of data can bias the interpretation of |Pp. 260-63 |
|this data. | |
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 |Pp. 241-63 |
|conjectures about the populations from which the samples were taken. | |
|Grade 6 | |
|1. Analyze and list the differences between two data sets. | |
|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. | |
| 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. | |
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 | |
|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
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