Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
Evaluate and use piecewise functions
Algebra
CCSS HSF.IF.C.7.B
Objective and success criteria
Students will: Evaluate and use piecewise functions.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Function notation
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Function notation). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- f(x) = x² − 8. Find f(5). → 17Prompt: Replace every x with 5.
- f(x) = −2x − 2. For what value of x is f(x) = −20? → x = 9Prompt: Set the expression equal to the value.
- f(x) = 2x² − 3x − 8. Find f(−3). → 19Prompt: Replace every x with (−3).
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Evaluate and use piecewise functions. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: f(x) = x² − 4 when x < −1, and f(x) = −2x + 3 when x ≥ −1. Find f(−2).
- Step 1: −2 < −1: use x² − 4
- Step 2: f(−2) = 0
- Answer: 0
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- f(x) = x² + 1 when x < −1, and f(x) = −3x − 1 when x ≥ −1. Find f(−3). → 10Prompt: First decide which piece applies to this x.
- A phone plan costs $7 a month including 4 GB of data. Each extra GB costs $0.50. What is the bill for a month using 5 GB? Give the amount as a number. → 7.5Prompt: The rule changes once you go over the included data.
You do: independent practice · 7 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- f(x) = x² − 4 when x < 2, and f(x) = 2x + 3 when x ≥ 2. Find f(4). → 11Prompt: First decide which piece applies to this x.
- A phone plan costs $6 a month including 5 GB of data. Each extra GB costs $1.50. What is the bill for a month using 12 GB? Give the amount as a number. → 16.5Prompt: The rule changes once you go over the included data.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Function notation.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.
Free lesson plan from eurekami.com/lesson-plan-builder