South Carolina

OS One Step Mathematical Operations

• Standards

  • Standard 1 Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations. (Limit to linear; quadratic.)

    • Add and subtract polynomials using algebra tiles (A1-W.3)
    • Add polynomials to find perimeter (A1-W.5)
    • Multiply a polynomial by a monomial (A1-W.6)
    • Multiply two binomials using algebra tiles (A1-W.7)
    • Multiply two binomials (A1-W.8)
    • Multiply two binomials: special cases (A1-W.9)
    • Multiply polynomials using area models (A1-W.10)
    • Multiply polynomials (A1-W.11)
    • Multiply polynomials to find area (A1-W.12)
    • Add and subtract polynomials (A1)

  • Standard 2 Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.

    • Does x satisfy the equation? (A1-C.2)
    • Which x satisfies an equation? (A1-C.3)
    • Properties of equality (A1-C.4)
    • Identify equivalent equations (A1-C.5)
    • Solve linear equations: complete the solution (A1-C.14)

• Competency Goals

  • 1 Add, subtract, multiply, and divide using whole numbers.

    • Add, subtract, multiply, or divide two whole numbers (7)

  • 2 Add and subtract using positive and negative numbers.

    • Add and subtract positive and negative decimals (7-I.1)
    • Add and subtract positive and negative fractions (7-I.2)
    • Add and subtract integers (A1)
    • Add and subtract rational numbers (A1-A.4)

  • 3 Change a quantity from one form to another using whole numbers, fractions, decimals, and percentages.

    • Convert between percents, fractions, and decimals (A1)
    • Convert between decimals and fractions (A1-A.3)

  • 4 Solve simple one step word problems in a systematic manner.

    • Add and subtract integers: word problems (8-A.6)
    • Add and subtract rational numbers: word problems (8-B.7)
    • Multiply and divide rational numbers: word problems (8-B.10)

  • 5 Demonstrate a mastery of measurement using a ruler and tape measure.

    • Measure using an inch ruler (5)
    • Measure using a centimeter ruler (5)

MS Multiple Step Problems (Reorder Information)

• Standards

  • Standard 1 Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (Limit to linear; quadratic; exponential.)

    • Domain and range of linear functions: graphs (A1-N.9)
    • Domain and range of linear functions: word problems (A1-N.10)
    • Domain and range of exponential functions: graphs (A1-V.5)
    • Domain and range of exponential functions: equations (A1-V.6)
    • Domain and range of quadratic functions: graphs (A1-Y.9)
    • Domain and range of quadratic functions: equations (A1-Y.10)

  • Standard 2 Analyze decisions and strategies using probability concepts.

    • Theoretical probability (A1-KK.1)
    • Experimental probability (A1-KK.2)
    • Find probabilities using two-way frequency tables (A1-KK.3)
    • Find conditional probabilities using two-way frequency tables (A1-KK.4)
    • Outcomes of compound events (A1-KK.5)
    • Identify independent and dependent events (A1-KK.6)
    • Probability of independent and dependent events (A1-KK.7)

• Competency Goals

  • 1 Reorder information and eliminate information to solve problems.

    • Word problems with extra or missing information (6)

  • 2 Calculate one-step conversion.

    • Convert between customary and metric systems (A1)
    • Convert between standard and scientific notation (A1-T.1)
    • Time units (6)
    • Convert customary units (6)
    • Convert metric units (6)

  • 3 One or two mathematical operations; addition, subtraction, multiplication, or division on positive or negative numbers.

    • Add three or more integers (7-B.5)
    • Complete addition and subtraction equations with integers (7-B.13)
    • Complete multiplication and division equations with integers (7-B.23)
    • Add, subtract, multiply, and divide integers (7-B.24)
    • Add and subtract positive and negative decimals (7-I.1)
    • Add and subtract positive and negative fractions (7-I.2)
    • Multiply and divide positive and negative decimals (7-I.6)
    • Multiply and divide positive and negative fractions (7-I.7)
    • Add, subtract, multiply, and divide rational numbers (7-I.10)
    • Add and subtract rational numbers (A1-A.4)
    • Multiply and divide rational numbers (A1-A.5)
    • Order of operations (6)

  • 4 Calculate averages, simple ratios, proportions, and rates using whole numbers and decimals.

    • Understanding ratios (A1)
    • Solve proportions: word problems (A1)
    • Estimate population size using proportions (A1)
    • Scale drawings: word problems (A1-E.1)
    • Calculate mean (8)
    • Identify equivalent ratios (A1)
    • Write an equivalent ratio (A1)
    • Unit rates (A1)
    • Unit prices (A1)
    • Solve proportions (A1)

  • 5 Add simple fractions, decimals, or percentages.

    • Add fractions with unlike denominators (5-L.3)
    • Add decimal numbers (5-AA.2)
    • Add fractions with like denominators (5)

  • 6 Read and draw simple graphs and diagrams.

    • Create line plots (A1-HH.1)
    • Interpret line plots (A1-HH.2)
    • Create bar graphs, line graphs, and histograms (A1-HH.5)
    • Interpret bar graphs, line graphs, and histograms (A1-HH.6)
    • Interpret circle graphs (A1-HH.7)
    • Interpret stem-and-leaf plots (A1-HH.8)
    • Interpret graphics I (A1-HH.10)
    • Interpret graphics II (A1-HH.11)

EI Multiple Step Problems (Extraneous Information)

• Standards

  • Standard 1 Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.

    • Rearrange multi-variable equations (A2-B.4)

  • Standard 2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

    • Convert a recursive formula to an explicit formula (A1-U.10)
    • Convert an explicit formula to a recursive formula (A1-U.11)
    • Find terms of an arithmetic sequence (A2-MM.1)
    • Find terms of a geometric sequence (A2-MM.2)
    • Evaluate explicit formulas for sequences (A2-MM.3)
    • Evaluate recursive formulas for sequences (A2-MM.4)
    • Write a formula for an arithmetic sequence (A2-MM.6)
    • Write a formula for a geometric sequence (A2-MM.7)
    • Write a formula for a recursive sequence (A2-MM.8)

  • Standard 3 Use units of measurement to guide the solution of multi-step tasks. Choose and interpret appropriate labels, units, and scales when constructing graphs and other data displays.

    • Convert rates and measurements: customary units (A1-E.2)
    • Convert rates and measurements: metric units (A1-E.3)
    • Unit prices with unit conversions (A1-E.4)
    • Multi-step problems with unit conversions (A1-E.5)
    • Convert rates and measurements (A1)

• Competency Goals

  • 1 Separate the important facts from the information.

    • Word problems with extra or missing information (6)

  • 2 Look up formulas and use them to perform one step conversions.

    • Convert between customary and metric systems (A1)
    • Convert customary units (6)
    • Convert metric units (6)

  • 3 Calculate using mixed units.

    • Convert mixed time units (4-DD.2)
    • Add and subtract mixed time units (5)
    • Convert mixed customary units (5-II.8)
    • Add and subtract mixed customary units (7)
    • Convert metric mixed units (5-JJ.6)
    • Add and subtract metric mixed units (5-JJ.7)
    • Multiply and divide mixed customary units (6-W.5)
    • Convert mixed time units: days, hours, minutes, and seconds (4)

  • 4 Calculate perimeter and areas.

    • Perimeter (A1)
    • Area (A1)
    • Area and perimeter: word problems (A1-D.1)

  • 5 Calculate percentage discounts or markups.

    • Find the percent: tax, discount, and more (A1)

  • 6 Complete a balance sheet or order form.

    • Keeping financial records (7)

  • 7 Calculate the best deal using one or two step calculations to compare costs.

    • Which is the better buy? (6)
    • Which is the better coupon? (7-P.7)
    • Unit prices (6)

PS Problem Solving

• Standards

  • Standard 1 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

    • Solve linear equations with variables on one side (A1-C.10)
    • Solve linear equations with variables on both sides (A1-C.12)
    • Solve linear equations: mixed review (A1-C.13)
    • Solve advanced linear inequalities (A1-F.10)
    • Graph solutions to advanced linear inequalities (A1-F.11)
    • Solve compound inequalities (A1-F.14)
    • Graph solutions to compound inequalities (A1-F.15)

  • Standard 2 Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.

    • Rearrange multi-variable equations (A2-B.4)

  • Standard 3 Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.

    • Properties of equality (A1-C.4)
    • Identify equivalent equations (A1-C.5)
    • Solve linear equations: complete the solution (A1-C.14)

• Competency Goals

  • 1 Solve complicated multiple step problems.

    • Maps with decimal distances (7-D.11)
    • Fractions: word problems with graphs and tables (7-F.4)
    • Maps with fractional distances (7-G.17)
    • Area of compound figures with rectangles and triangles (G)
    • Multi-step word problems (8-B.14)
    • Price lists (8-I.1)
    • Unit prices with unit conversions (8-I.3)
    • Unit prices: find the total price (8-I.4)
    • Multi-step problems with percents (A1)

  • 2 Calculate using negative numbers, fractions, ratios, percentages, and mixed numbers.

    • Evaluate numerical expressions involving integers (A1-A.2)
    • Evaluate numerical expressions involving rational numbers (A1-A.7)
    • Solve equations using order of operations (A1)

  • 3 Calculate multiple rates.

    • Rate of change: tables (A1-M.15)
    • Rate of change: graphs (A1-M.16)
    • Unit rates (A1)

  • 4 Compare ratios or use them to perform other calculations.

    • Word problems involving ratios (8)

  • 5 Find areas and volumes of rectangles.

    • Area of rectangles and squares (6-GG.2)
    • Volume of cubes and rectangular prisms (7)

  • 6 Calculate the best deal using the result in another problem.

    • Which is the better buy? (6)
    • Which is the better coupon? (7-P.7)

  • 7 Find mistakes in calculations.

    • Identify mistakes involving the order of operations (A1)

RS Reasoning Skills (Careful Reading)

• Standards

  • Standard 1 Explain the derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone. Apply these formulas to solve mathematical and real-world problems.

    • Area and circumference of circles (G-S.9)

  • Standard 2 Apply surface area and volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems and justify results. Include problems that involve algebraic expressions, composite figures, geometric probability, and real-world applications.

    • Surface area of prisms and cylinders (G-U.4)
    • Surface area of pyramids and cones (G-U.5)
    • Surface area of spheres (G-U.6)
    • Volume of prisms and cylinders (G-U.7)
    • Volume of pyramids and cones (G-U.8)
    • Volume of spheres (G-U.9)
    • Volume of compound figures (G-U.10)

• Competency Goals

  • 1 Do several steps of reasoning and multiple calculations.

    • Area of composite figures (8)
    • Volume of compound figures (G-U.10)

  • 2 Solve problems involving more than one unknown.

    • Area of composite figures (8)
    • Volume of compound figures (G-U.10)

  • 3 Calculate the percentage of change.

    • Percent of change (A1)
    • Percent of change: word problems (A1)

  • 4 Calculate multiple areas and volumes of sphere, cylinders, and cones.

    • Volume of cylinders (8-W.3)
    • Volume of cones (8-W.4)
    • Surface area of cylinders (8-W.5)
    • Surface area of cones (8-W.6)
    • Volume of spheres (8-W.7)
    • Surface area of spheres (8-W.8)

  • 5 Set up and manipulate complex ratios and proportions.

    • Calculate unit rates with fractions (7-L.6)
    • Scale drawings: word problems (G)
    • Similar triangles and indirect measurement (G-M.5)
    • Perimeters of similar figures (G-M.6)
    • Areas of similar figures (G-M.14)
    • Surface area and volume of similar solids (G-U.12)
    • Surface area and volume: changes in scale (G-U.13)
    • Convert rates and measurements: customary units (G-V.1)
    • Convert rates and measurements: metric units (G-V.2)
    • Convert square and cubic units of length (G-V.3)
    • Simplify complex fractions (7)

  • 6 Determine the best economic value of several alternatives.

    • Which is the better buy? (6)
    • Which is the better coupon? (7-P.7)

  • 7 Find mistakes in multiple step calculations.

    • Identify mistakes involving the order of operations (A1)