NY Next Generation Math NY-8.EE.5
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
Build proportional graphs by stacking equal rise and run triangles along a taped coordinate grid.
Ask students to explain why the slope of a proportional graph is also its output per one input.
Play representation match with graphs, equations, tables, and unit-rate descriptions for proportional relationships.
Compare two service prices shown by a cost graph and a price-per-unit advertisement.
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Printable NY-8.EE.5 Worksheet
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Related Standards
- NY-7.RP.2.b
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- NY-7.RP.2.a
Decide whether two quantities are in a proportional relationship.
- NY-7.RP.2.c
Represent a proportional relationship using an equation.
- NY-7.RP.2
Recognize and represent proportional relationships between quantities.
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