NY Next Generation Math NY-8.F.5

Math8th GradeUse functions to model relationships between quantities.

The Standard

Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described in a real-world context.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What This Standard Means

What Students Need to Do

Students describe how two quantities change together by reading a graph. They identify intervals that increase, decrease, stay constant, or change linearly or nonlinearly and sketch graphs from contexts.

What Mastery Looks Like

The student narrates a graph interval by interval without inventing unsupported values. Given a situation, the student sketches the correct direction, flat sections, and changes in steepness.

Common Misconceptions

Students may treat graph height as speed instead of reading steepness and direction. They may connect every description with straight segments even when the rate changes gradually.

How to Assess It

Describe a tank filling steadily, pausing, then draining faster. Ask students to sketch volume versus time and label each interval.

Lesson moves

Ways to Teach It

  1. Walk in front of a motion sensor to create increasing, constant, and decreasing graph sections for classmates to describe.

  2. Ask students to describe what a flat segment means for both quantities in a stated context.

  3. Play graph-story match with increasing, decreasing, constant, linear, and curved intervals.

  4. Sketch and interpret graphs for temperature, distance, water level, or attendance changing over time.

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