Math lesson plan · 9th grade (Year 10 in England) · 30 minutes
Name polynomials by degree and number of terms
Algebra
CCSS HSA.SSE.A.1.A
Objective and success criteria
Students will: Name polynomials by degree and number of terms.
- 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: Simplify expressions: like terms
Leads to: Add and subtract polynomials
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 (Simplify expressions: like terms). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify 5x − 4x. → xPrompt: These are like terms: they both have x.
- Simplify 8x − 2 + x + 3. → 9x+1Prompt: Group the x terms together and the numbers together.
- Simplify 2x + 2y − 2x + y. → 3yPrompt: x terms and y terms are different kinds; collect each kind separately.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Name polynomials by degree and number of terms. 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: What is the degree of the polynomial −3x² + 6x + 8?
- Step 1: Highest power: x²
- Step 2: 2
- Answer: 2
- 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.
- What is the degree of the polynomial 9x⁵ − 9x⁴ − 2x³? → 5Prompt: The degree is the highest power of x.
- Which name describes −9x? (quadratic binomial / linear monomial / quadratic monomial / linear binomial) → linear monomialPrompt: Count the terms: 1 monomial, 2 binomial, 3 trinomial.
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.
- Which name describes −7x⁴ + 6? (quartic trinomial / cubic binomial / quadratic monomial / quartic binomial) → quartic binomialPrompt: Count the terms: 1 monomial, 2 binomial, 3 trinomial.
- Write 2x + x² − 4x³ in standard form (highest power first). What is the leading coefficient? → -4Prompt: Order the terms from the highest power of x to the lowest.
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: Simplify expressions: like terms.
- 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
- Move on to: Add and subtract polynomials.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder