Piecewise, Step, and Absolute Value Functions
I can use the right piece of a piecewise, step, or absolute value function, and read its open and closed circles.
What students learn
Students learn to find the piece whose x-values hold an input and use only its rule, read open and closed circles at a break, and find the vertex and values of an absolute value function.
See inside
The key rule
Find the piece whose x-values hold your x, then use only that rule. At a break, the closed circle counts.
≤ ≥ included; < > left out
Which piece is drawn or written first does not matter; the circle does.
Watch out
g(x) = x + 4 for x < 2, and g(x) = 1 for x ≥ 2. Find g(2).
The mistake: g(2) = 2 + 4 = 6x + 4 is only for x < 2, and 2 is not less than 2.
The fix: 2 ≥ 2: g(2) = 1The ≥ piece holds x = 2: its closed circle counts.
The mistakes it targets
- Uses the wrong piece or the open circle at a break point
- Leaves the value of an absolute value negative
- Puts the vertex of |x + 2| at x = 2
- Reads under as including the boundary, or lets two pieces share an endpoint
The interactive Teacher Deck (32 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 (four 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.