Rate of Change and Slope from a Graph

What students learn

Students learn to count the rise and the run between two grid corners on a line, write the slope as rise over run in simplest form with the right sign, and give a rate of change with its units.

See inside

Watch out

A line rises 3 units for every 7 units it runs to the right. What is its slope?

The mistakes it targets

• Puts the run on top instead of the rise
• Drops the minus sign of a falling line
• Judges steepness by the sign of the slope instead of its size
• Mixes up a slope of 0 and an undefined slope

The interactive Teacher Deck (33 slides, PowerPoint)

• The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
• The worked example one slide per step (five steps), each with the reason for the step
• Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
• Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
• Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
• A completed deck PDF (19 pages) with every slide fully built, to print or post

The student packet (9 pages)

• Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
• Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
• Apply: one word problem, a reasoning prompt and one error analysis
• Assess: an exit ticket of four items, two per page, with an I-can self-rating
• Homework (page 5): eight new problems, two warm-up, four standard and two stretch
• Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
• Color and ink-saver editions of the whole packet