The Common Core in Pennsylvania

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Skills available for Pennsylvania seventh-grade math standards

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7.M07.C-G Geometry

7.M07.C-G.1 Demonstrate an understanding of geometric figures and their properties.
- 7.M07.C-G.1.1 Describe and apply properties of geometric figures.
  - 7.M07.C-G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area.
  - 7.M07.C-G.1.1.2 Identify or describe the properties of all types of triangles based on angle and side measures.
    - Classify triangles (7-W.3)
  - 7.M07.C-G.1.1.3 Use and apply the triangle inequality theorem.
    - Triangle Inequality Theorem (G-M.5)
  - 7.M07.C-G.1.1.4 Describe the two-dimensional figures that result from slicing three-dimensional figures.
    - Bases of three-dimensional figures (7-X.1)
    - Front, side, and top view (7-X.3)
7.M07.C-G.2 Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume.
- 7.M07.C-G.2.1 Identify, use, and describe properties of angles and their measures.
  - 7.M07.C-G.2.1.1 Identify and use properties of supplementary, complementary, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
    - Identify complementary, supplementary, vertical, and adjacent angles (7-W.16)
    - Find measures of complementary, supplementary, vertical, and adjacent angles (7-W.17)
  - 7.M07.C-G.2.1.2 Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding).
- 7.M07.C-G.2.2 Determine circumference, area, surface area, and volume.
  - 7.M07.C-G.2.2.1 Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided.
  - 7.M07.C-G.2.2.2 Solve real-world and mathematical problems involving area, volume, and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided.

7.M07.D-S Statistics and Probability

7.M07.D-S.1 Use random sampling to draw inferences about a population.
- 7.M07.D-S.1.1 Use random samples.
  - 7.M07.D-S.1.1.1 Determine whether a sample is a random sample given a real-world situation.
    - Identify representative, random, and biased samples (7-DD.8)
  - 7.M07.D-S.1.1.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.
    - Estimate population size using proportions (7-J.13)
7.M07.D-S.2 Draw comparative inferences about populations.
- 7.M07.D-S.2.1 Use statistical measures to compare two numerical data distributions.
  - 7.M07.D-S.2.1.1 Compare two numerical data distributions using measures of center and variability.
7.M07.D-S.3 Investigate chance processes and develop, use, and evaluate probability models.
- 7.M07.D-S.3.1 Predict or determine the likelihood of outcomes.
  - 7.M07.D-S.3.1.1 Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (i.e., a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event).
- 7.M07.D-S.3.2 Use probability to predict outcomes.
  - 7.M07.D-S.3.2.1 Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability.
    - Experimental probability (7-EE.4)
    - Make predictions using theoretical probability (7-EE.7)
  - 7.M07.D-S.3.2.2 Find the probability of a simple event, including the probability of a simple event not occurring.
    - Probability of simple events (7-EE.1)
    - Probability of simple events and opposite events (7-EE.2)
  - 7.M07.D-S.3.2.3 Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation.

The Common Core in Pennsylvania

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7.M07.A-N The Number System

7.M07.A-N.1 Apply and extend previous understandings of operations to add, subtract, multiply, and divide rational numbers.

7.M07.A-N.1.1 Solve real-world and mathematical problems involving the four operations with rational numbers.

7.M07.A-N.1.1.1 Apply properties of operations to add and subtract rational numbers, including real-world contexts.

7.M07.A-N.1.1.2 Represent addition and subtraction on a horizontal or vertical number line.

7.M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.

7.M07.A-R Ratios and Proportional Relationships

7.M07.A-R.1 Demonstrate an understanding of proportional relationships.

7.M07.A-R.1.1 Analyze, recognize, and represent proportional relationships and use them to solve real-world and mathematical problems.

7.M07.A-R.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

7.M07.A-R.1.1.2 Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

7.M07.A-R.1.1.3 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.M07.A-R.1.1.4 Represent proportional relationships by equations.

7.M07.A-R.1.1.5 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.

7.M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems.

7.M07.B-E Expressions and Equations

7.M07.B-E.1 Represent expressions in equivalent forms.

7.M07.B-E.1.1 Use properties of operations to generate equivalent expressions.

7.M07.B-E.1.1.1 Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.

7.M07.B-E.2 Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

7.M07.B-E.2.1 Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers.

7.M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.

7.M07.B-E.2.2 Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems.

7.M07.B-E.2.2.1 Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.

7.M07.B-E.2.2.2 Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality.

7.M07.B-E.2.3 Determine the reasonableness of the answer(s) in problem-solving situations.

7.M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem.

7.M07.C-G Geometry

7.M07.C-G.1 Demonstrate an understanding of geometric figures and their properties.

7.M07.C-G.1.1 Describe and apply properties of geometric figures.

7.M07.C-G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area.

7.M07.C-G.1.1.2 Identify or describe the properties of all types of triangles based on angle and side measures.

7.M07.C-G.1.1.3 Use and apply the triangle inequality theorem.

7.M07.C-G.1.1.4 Describe the two-dimensional figures that result from slicing three-dimensional figures.

7.M07.C-G.2 Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume.

7.M07.C-G.2.1 Identify, use, and describe properties of angles and their measures.

7.M07.C-G.2.1.1 Identify and use properties of supplementary, complementary, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

7.M07.C-G.2.1.2 Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding).

7.M07.C-G.2.2 Determine circumference, area, surface area, and volume.

7.M07.C-G.2.2.1 Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided.

7.M07.C-G.2.2.2 Solve real-world and mathematical problems involving area, volume, and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided.

7.M07.D-S Statistics and Probability

7.M07.D-S.1 Use random sampling to draw inferences about a population.

7.M07.D-S.1.1 Use random samples.

7.M07.D-S.1.1.1 Determine whether a sample is a random sample given a real-world situation.

7.M07.D-S.1.1.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

7.M07.D-S.2 Draw comparative inferences about populations.

7.M07.D-S.2.1 Use statistical measures to compare two numerical data distributions.

7.M07.D-S.2.1.1 Compare two numerical data distributions using measures of center and variability.

7.M07.D-S.3 Investigate chance processes and develop, use, and evaluate probability models.

7.M07.D-S.3.1 Predict or determine the likelihood of outcomes.

7.M07.D-S.3.2 Use probability to predict outcomes.

7.M07.D-S.3.2.1 Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability.

7.M07.D-S.3.2.2 Find the probability of a simple event, including the probability of a simple event not occurring.

7.M07.D-S.3.2.3 Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation.