South Carolina

DPSR Data, Probability, and Statistical Reasoning

• 7.DPSR.1 Analyze data sets to identify their statistical elements.

  • 7.DPSR.1.1 Create stem-and-leaf plots to represent numerical data sets in mathematical and real-world situations.

    • Create stem-and-leaf plots (7-GG.4)

  • 7.DPSR.1.2 Use the shape of the graph to select the measure of center (mean, median, or mode) that best describes the data set.

    • Interpret line plots (7-GG.2)
    • Interpret stem-and-leaf plots (7-GG.5)
    • Interpret bar graphs (7-GG.7)
    • Box plots (7-GG.13)

  • 7.DPSR.1.3 Calculate and interpret the measures of center (mean, median, mode) and spread (mean absolute deviation, interquartile range, range) in mathematical and real-world situations.

    • Calculate mean, median, mode, and range (7-HH.1)
    • Interpret charts and graphs to find mean, median, mode, and range (7-HH.2)
    • Changes in mean, median, mode, and range (7-HH.4)
    • Calculate mean absolute deviation (7-HH.5)
    • Calculate quartiles and interquartile range (7-HH.6)
    • Compare populations using measures of center and spread (7-HH.11)

  • 7.DPSR.1.4 Create histograms to represent data sets and interpret histograms to answer questions or draw conclusions about data sets.

    • Create histograms (7-GG.8)
    • Interpret histograms (7-GG.9)

  • Checkpoint opportunity

• 7.DPSR.2 Calculate and interpret probability.

  • 7.DPSR.2.1 Identify the sample space for a simple event.

    • Sample spaces of simple events (7-II.1)

  • 7.DPSR.2.2 Calculate and interpret the theoretical probability of a simple random event.

    • Probability of simple events (7-II.2)
    • Make predictions using theoretical probability (7-II.8)

  • 7.DPSR.2.3 Calculate and interpret the experimental probability of a random event related to a simple experiment.

    • Experimental probability (7-II.5)
    • Make predictions using experimental probability (7-II.6)
    • Use collected data to find probabilities and make predictions (7-II.7)

  • 7.DPSR.2.4 Compare and contrast the experimental and theoretical probabilities for a simple experiment.

  • Checkpoint opportunity

MGSR Measurement, Geometry, and Spatial Reasoning

• 7.MGSR.1 Determine the measurements of geometric figures.

  • 7.MGSR.1.1 Identify the parts of a circle. Limit the parts to center, radius, diameter, and chord.

    • Parts of a circle (7-Z.13)

  • 7.MGSR.1.2 Describe the relationship between the radius, diameter, and circumference of a circle.

    • Circumference of circles (7-BB.5)

  • 7.MGSR.1.3 Solve mathematical and real-world situations involving circumference or area of circles.

    • Area of circles (7-BB.6)
    • Circles: word problems (7-BB.7)

  • 7.MGSR.1.4 Determine if three given side lengths can form a triangle using the Triangle Inequality Theorem.

    • Triangle inequality (7-Z.3)

  • 7.MGSR.1.5 In mathematical and real-world situations, find the volume of right prisms and right pyramids having triangular or quadrilateral bases.

    • Volume of cubes and prisms (7-CC.5)
    • Volume of cubes and rectangular prisms: word problems (7-CC.6)
    • Volume of pyramids (7-CC.8)
    • Volume of cylinders (7-CC.9)
    • Volume of cones (7)

  • 7.MGSR.1.6 In mathematical and real-world situations, find the surface area of right prisms and right pyramids having triangular or quadrilateral bases.

    • Surface area of cubes and prisms (7-CC.1)
    • Surface area of pyramids (7-CC.2)

  • Checkpoint opportunity

    • Checkpoint: Area, circumference, surface area, and volume (7)

• 7.MGSR.2 Determine angle and/or side relationships.

  • 7.MGSR.2.1 Determine the measure of the third angle given the measure of the other two angles of a triangle using the Triangle Sum Theorem.

    • Find missing angles in triangles (7-Z.8)

  • 7.MGSR.2.2 Solve mathematical and real-world situations involving dimensions and areas of geometric figures including scale drawings and scale factors.

    • Scale drawings of polygons (7-DD.1)
    • Scale drawings: word problems (7-DD.2)
    • Scale drawings: scale factor word problems (7-DD.3)
    • Perimeter and area: changes in scale (7-DD.4)

  • 7.MGSR.2.3 Identify the relationships and measures among angles formed by two intersecting lines, given the measure of one angle. Limit to supplementary, complementary, vertical, and adjacent relationships.

    • Identify complementary, supplementary, vertical, and adjacent angles (7-Y.4)
    • Find measures of complementary, supplementary, vertical, and adjacent angles (7-Y.5)

  • 7.MGSR.2.4 Write and solve equations to solve mathematical and real-world situations involving the relationships among angles formed by two intersecting lines. Limit to supplementary, complementary, vertical, and adjacent relationships.

    • Write and solve equations using angle relationships (7-Y.6)

  • Checkpoint opportunity

    • Checkpoint: Scale drawings (7-DD.5)

• 7.MGSR.3 Graph on the coordinate plane.

  • 7.MGSR.3.1 Find distances between ordered pairs on the coordinate plane, limited to the same x-coordinate or the same y-coordinate.

    • Distance between two points (7-M.4)

NR Numerical Reasoning

• 7.NR.1 Translate among multiple representations of rational numbers.

  • 7.NR.1.1 Convert rational numbers into equivalent forms among fractions (including mixed numbers), decimals, and percentages. Exclude the conversion of repeating decimals to fractions.

    • What percentage is illustrated? (7-O.1)
    • Convert between percents, fractions, and decimals (7-O.2)

• 7.NR.2 Utilize rational numbers in mathematical and real-world situations.

  • 7.NR.2.1 Compare two rational numbers and write statements using is equal to (=), is not equal to (≠), is less than (<), is greater than (>), is greater than or equal to (≥), and/or is less than or equal to (≤) in mathematical and real-world situations.

    • Compare and order rational numbers using number lines (7)
    • Compare rational numbers (7-H.9)
    • Compare percents to fractions and decimals (7-O.3)

  • Checkpoint opportunity

PAFR Patterns, Algebra, and Functional Reasoning

• 7.PAFR.1 Use tables, graphs, verbal descriptions, or equations to represent a function.

  • 7.PAFR.1.1 Apply proportional reasoning to solve problems in mathematical and real-world situations involving ratios and percentages.

    • Percent of change (7-O.10)
    • Percent of change: word problems (7-O.11)
    • Percent of change: find the original amount word problems (7-O.12)
    • Percent error: word problems (7-O.13)
    • Unit prices with unit conversions (7-P.4)
    • Unit prices: find the total price (7-P.5)
    • Percent of a number: tax, discount, and more (7-P.6)
    • Which is the better coupon? (7-P.7)
    • Find the percent: tax, discount, and more (7-P.8)
    • Sale prices: find the original price (7-P.9)
    • Multi-step problems with percents (7-P.10)
    • Simple interest (7-P.12)

  • 7.PAFR.1.2 Create a model with functions that address a proportional relationship in real-world situations.

    • Identify proportional relationships by graphing (7-N.3)
    • Identify proportional relationships from graphs and equations (7-N.6)
    • Identify proportional relationships from tables (7-N.7)
    • Complete a table and graph a proportional relationship (7-N.8)
    • Graph a proportional relationship: word problems (7-N.9)

  • 7.PAFR.1.3 Identify the constant of proportionality within proportional relationships.

    • Find the constant of proportionality from a table (7-N.1)
    • Find the constant of proportionality from a graph (7-N.4)

  • Checkpoint opportunity

• 7.PAFR.2 Write, simplify, and evaluate algebraic expressions; write and solve algebraic equations and inequalities.

  • 7.PAFR.2.1 Write and solve multi-step equations and inequalities in one variable involving rational numbers in mathematical and real-world situations.

    • Model and solve equations using algebra tiles (7-T.4)
    • Solve two-step equations without parentheses (7-T.8)
    • Solve two-step equations with parentheses (7-T.9)
    • Solve two-step equations (7-T.10)
    • Choose two-step equations: word problems (7-T.12)
    • Solve two-step equations: word problems (7-T.13)
    • Solve equations involving like terms (7-T.14)
    • Solve equations: complete the solution (7-T.15)
    • Solve one-step inequalities (7-U.4)
    • One-step inequalities: word problems (7-U.6)
    • Solve two-step inequalities (7-U.7)

  • 7.PAFR.2.2 Write and evaluate expressions in one variable that model mathematical and real-world situations.

    • Write variable expressions: word problems (7-R.3)
    • Evaluate linear expressions (7-R.4)
    • Write one-variable expressions: one operation (7)

  • 7.PAFR.2.3 Compute unit rates, including those involving complex fractions with like or different units.

    • Unit rates (7-L.5)
    • Calculate unit rates with fractions (7-L.6)
    • Compare rates: word problems (7-L.9)

  • 7.PAFR.2.4 Use dimensional analysis to convert units between metric and customary systems.

    • Compare and convert customary units (7-Q.1)
    • Mixed customary units (7-Q.2)
    • Compare and convert metric units (7-Q.3)
    • Convert between customary and metric systems (7-Q.4)

  • Checkpoint opportunity

    • Checkpoint: Solve two-step equations (7-T.16)
    • Checkpoint: Solve two-step inequalities (7-U.9)
    • Checkpoint: Percents, ratios, and rates (7)

• 7.PAFR.3 Apply mathematical patterns, properties, and algorithms to the set of rational numbers to find sums, differences, products, and quotients and to write equivalent expressions.

  • 7.PAFR.3.1 Simplify numerical expressions that include integer exponents using the laws of exponents: the Product of Powers, Quotient of Powers, Power of a Power, Power of a Product, Power of a Quotient, Zero Power, and Negative Exponent.

    • Understanding exponents (7-J.1)
    • Evaluate powers (7-J.2)
    • Powers with negative bases (7-J.4)
    • Powers with decimal and fractional bases (7-J.5)
    • Powers of ten (7-J.6)
    • Evaluate numerical expressions involving exponents (7-J.7)
    • Multiplication with exponents (7)
    • Division with exponents (7)
    • Power rule (7)
    • Evaluate powers with negative or zero exponents (7)
    • Exponent rules: review (7)

  • 7.PAFR.3.2 Identify linear expressions that are equivalent.

    • Identify equivalent linear expressions using algebra tiles (7-S.11)
    • Identify equivalent linear expressions I (7-S.12)
    • Identify equivalent linear expressions II (7-S.13)

  • 7.PAFR.3.3 Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation.

    • Identify equivalent linear expressions: word problems (7-S.14)

  • 7.PAFR.3.4 Factor linear expressions with integer coefficients using the greatest common factor (GCF).

    • Factor linear expressions: area models (7-S.9)
    • Factors of linear expressions (7-S.10)

  • 7.PAFR.3.5 Apply all operations with rational numbers to solve problems in mathematical and real-world situations.

    • Evaluate numerical expressions involving integers (7-B.25)
    • Maps with decimal distances (7-D.11)
    • Evaluate numerical expressions involving decimals (7-D.12)
    • Maps with fractional distances (7-G.17)
    • Evaluate numerical expressions involving fractions (7-G.18)
    • Multi-step word problems with positive rational numbers (7-I.11)
    • Evaluate linear expressions (7-R.4)
    • Evaluate multi-variable expressions (7-R.5)
    • Evaluate nonlinear expressions (7-R.7)

  • Checkpoint opportunity

    • Checkpoint: Problem solving with rational numbers (7-I.14)