NY Next Generation Math NY-8.EE.5

Math8th GradeUnderstand the connections between proportional relationships, lines, and linear equations.

The Standard

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

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What This Standard Means

What Students Need to Do

Students graph proportional relationships and interpret the unit rate as the graph's slope. They compare proportional relationships shown as graphs, equations, tables, or descriptions.

What Mastery Looks Like

The student finds slope from a graph through the origin and states its unit-rate meaning. The student compares two relationships across different representations and supports the comparison with rates.

Common Misconceptions

Students may use one coordinate as the slope instead of the ratio of vertical change to horizontal change. They may compare visual steepness when graph scales differ.

How to Assess It

Show one cyclist's distance-time graph and another's equation d = 12t. Ask which cyclist is faster and require both unit rates.

Lesson moves

Ways to Teach It

  1. Build proportional graphs by stacking equal rise and run triangles along a taped coordinate grid.

  2. Ask students to explain why the slope of a proportional graph is also its output per one input.

  3. Play representation match with graphs, equations, tables, and unit-rate descriptions for proportional relationships.

  4. Compare two service prices shown by a cost graph and a price-per-unit advertisement.

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