7.PAR.4Proportional Relationships

Expectations

• 7.PAR.4.1

  Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units presented in realistic problems.

• 7.PAR.4.2

  Determine the unit rate (constant of proportionality) in tables, graphs (1, r), equations, diagrams, and verbal descriptions of proportional relationships to solve realistic problems.

• 7.PAR.4.3

  Determine whether two quantities presented in authentic problems are in a proportional relationship.

• 7.PAR.4.4

  Identify, represent, and use proportional relationships.

• 7.PAR.4.5

  Use context to 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.PAR.4.6

  Solve everyday problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

• 7.PAR.4.7

  Use similar triangles to explain why the slope, m, is the same between any two distinct points on a nonvertical line in the coordinate plane.

• 7.PAR.4.8

  Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

• 7.PAR.4.9

  Use proportional relationships to solve multi-step ratio and percent problems presented in applicable situations.

• 7.PAR.4.10

  Predict characteristics of a population by examining the characteristics of a representative sample. Recognize the potential limitations and scope of the sample to the population.

• 7.PAR.4.11

  Analyze sampling methods and conclude that random sampling produces and supports valid inferences.

• 7.PAR.4.12

  Use data from repeated random samples to evaluate how much a sample mean is expected to vary from a population mean. Simulate multiple samples of the same size.

Georgia Milestones coverage

• Mathematics Grade 7 (EOG) · Patterning & Algebraic Reasoning

  Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.

  about 28% of the test · 16 points

What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

Beginning

Calculate a unit rate from a verbal description. Given a graph, identify whether the relationship shown is proportional. Determine the missing side in a pair of scale drawings of geometric figures. Make a prediction about a population from the data in a representative sample.

Developing

Identify and calculate the unit rate from a realistic problem. Given a set of values described by a graph/table or a relevant context, determine whether the values are in a proportional relationship. Create a scale drawing of a geometric figure. Graph a proportional relationship from the slope or unit rate. Solve relevant ratio and percentage problems. Explain potential limitations to making predictions about a population from a representative sample. Recognize the sampling method that would best support a conclusion about a population.

Proficient

Determine the unit rate or constant of proportionality by extracting data from a table, graph, equation, diagram, or verbal description. Determine whether two quantities presented in authentic problems are in a proportional relationship. Explain the properties of proportional relationships to solve relevant problems. Explain what a coordinate point (x, y) means in the graph of a proportional relationship and relate it to the unit rate. Solve a multi-step, relevant problem involving scale drawings. Given the graph of a proportional relationship, use similar triangles to explain why the slope is the same between any two points. Compare two different proportional relationships represented in different ways. Solve multi-step, relevant ratio and percentage problems. Make a prediction about a population from repeated random samples.

Distinguished

Explain the key features of proportional relationships in equations, tables, and graphs to explain the relationships in context. Solve a multi-step, everyday problem involving scale drawings, including computing lengths and areas and explaining relationships in the context of the problem. Solve multi-step, relevant problems involving proportional relationships in different forms, explaining the solution in the context of the problem. Analyze and interpret how data is collected to solve statistical questions and compare multiple data sets to solve complex, relevant problems.

The same standard across grades

1. Grade 2 · 2.PAR.4

   Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns.

2. Grade 7 · 7.PAR.4 (this standard)

   Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.

3. Grade 8 · 8.PAR.4

   Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.