Printable Rate of Change Worksheet | Grade 9 Algebra I

This worksheet teaches students to calculate and interpret average rate of change from tables, equations, and a graph. Across 16 tasks, learners attach units to every rate, respect domains, and explain what a slope means in real situations such as pay, draining tanks, and battery life.

At a Glance

• Grade: 9 · Subject: Algebra I
• Standard: HSF-IF.B.6 — Calculate and interpret average rate of change over an interval from tables, equations, graphs
• Skill Focus: Average rate of change with units and domains
• Format: 5 pages · 16 problems · Answer key included · PDF
• Best For: Practice after slope instruction
• Time: 40–50 minutes

What's Inside

The worksheet has three parts: Foundation (Items 1–4), Core (Items 5–12), and Challenge (Items 13–16). Task types include data tables, two multiple-choice items, a cyclist distance graph, equation models, and error-analysis prompts. A conventions box states the rate formula and the unit and domain rules. A 3-page answer key is included.

Skill Progression

• Guided practice (Items 1–4): four problems with the rate formula in the conventions box and friendly numbers.
• Supported practice (Items 5–12): eight context problems with tables, one graph, and unit and domain prompts.
• Independent practice (Items 13–16): four challenge tasks that require written justification.

The sequence follows gradual release: I do, we do, you do.

Standards Alignment

HSF-IF.B.6 — Calculate and interpret the average rate of change of a function, presented symbolically or as a table, over a specified interval, and estimate it from a graph. This standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.

How to Use It

• After direct instruction on slope: assign Parts A and B as guided classwork.
• As a formative check or homework: assign Part C to see who can justify a rate.

While students work, watch for missing units and rates computed over the wrong interval. Item 8 exposes the average-of-segment-rates error. Expect 40–50 minutes for the full set.

Who It's For

Grade 9 Algebra I students working on slope and rate of change. Assign Part A alone for extra support, or Part C for extension. Pair it with a slope-formula anchor chart or a direct instruction lesson on interpreting rates.

HSF-IF.B.6 asks students to calculate and interpret the average rate of change of a function over a specified interval, using tables, equations, and graphs. This Grade 9 Algebra I worksheet turns that expectation into 16 tasks that move from computing slope to explaining rates with units, domains, and error analysis. Students find rates for tutoring pay, a draining tank, a cyclist's graph, and a projectile, then justify why average rates differ from segment averages. Fisher & Frey (2014) describe gradual release of responsibility, in which teachers shift from modeling to guided practice to independent work, as a structure that supports durable learning; the three labeled parts of this worksheet follow that sequence. The 5-page packet includes a 3-page answer key, making it suitable for classwork, homework, or formative checks within a slope and rate of change unit.