Math lesson plan · 10th grade (Year 11 in England) · 60 minutes
Find domains of functions with roots and fractions
Algebra
CCSS HSF.IF.B.5CCSS HSF.IF.A.1England: A-level Pure Mathematics
Objective and success criteria
Students will: Find domains of functions with roots and fractions.
- 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; Solve linear inequalities
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 · 6 min
- Quick retrieval from earlier learning (Function notation; Solve linear inequalities). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- f(x) = 2x² − 6x + 6. Find f(1). → 2Prompt: Replace every x with 1.
- Solve: 7x − 3 > −24 (x > −2 / x > −3 / x > −21 / x < −3) → x > −3Prompt: Solve it like an equation, keeping the inequality sign.
- f(x) = −x + 3. For what value of x is f(x) = 3? → x = 0Prompt: Set the expression equal to the value.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find domains of functions with roots and fractions. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: What is the domain of f(x) = √(2 − x) (real numbers only)?
- Step 1: x ≤ 2
- Answer: x ≤ 2
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- What is the domain of f(x) = √(x + 5) (real numbers only)? (x ≠ −5 / x ≥ −5 / x ≤ −5 / x > −5) → x ≥ −5Prompt: You cannot square-root a negative number.
- What is the smallest x in the domain of f(x) = √(4x − 4)? → 1Prompt: The expression under the root must be at least 0.
You do: independent practice · 17 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 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- What is the domain of f(x) = 1/(x − 3) (real numbers only)? (x ≠ 3 / x ≥ 3 / x ≤ 3 / x > 3) → x ≠ 3Prompt: You cannot square-root a negative number.
- What is the smallest x in the domain of f(x) = √(4x + 4)? → -1Prompt: The expression under the root must be at least 0.
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-10.
Free lesson plan from eurekami.com/lesson-plan-builder