Key Features of Graphs
I can find the intercepts, the maximum or minimum, and where a graph rises, falls, and is positive or negative.
What students learn
Students learn to read a graph's intercepts and turning point as points, give a maximum or minimum value and where it occurs, and give the intervals where the graph increases, decreases, is positive and is negative.
See inside
The key rule
Read left to right; give each interval in x-values, with <. A maximum or minimum is a point; its value is its height.
max (a, b): value b, at x = a
A turn or a crossing is in neither interval, so use < at both ends.
Watch out
A graph's lowest point is (2, −3). Give the minimum value and where it occurs.
The mistake: the minimum is x = 2x = 2 is where it occurs, not its value.
The fix: minimum value −3, at x = 2The value is the y-coordinate of (2, −3).
The mistakes it targets
- Gives where a maximum or minimum occurs as its value
- Reads an interval from right to left
- Gives the interval below the x-axis as positive
- Mixes up the y-intercept and the x-intercept
The interactive Teacher Deck (31 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 (three 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
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.