Math lesson plan · 9th grade (Year 10 in England) · 45 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 · 5 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 6x + 7x. → 13xPrompt: These are like terms: they both have x.
- Simplify 8x + 8 + 4x − 2. → 12x+6Prompt: Group the x terms together and the numbers together.
- Simplify 2x + 3y − 2x − 6y. → -3yPrompt: x terms and y terms are different kinds; collect each kind separately.
Hook · 5 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 · 10 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 · 10 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 3x − 4x² + 1? → 2Prompt: The degree is the highest power of x.
- Which name describes −5x³ + 3x² − 7? (quartic binomial / cubic binomial / quartic trinomial / cubic trinomial) → cubic trinomialPrompt: Count the terms: 1 monomial, 2 binomial, 3 trinomial.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Write −3x − 4 − 6x⁴ in standard form (highest power first). What is the leading coefficient? → -6Prompt: Order the terms from the highest power of x to the lowest.
- Which name describes 5x³ + 3x? (quadratic binomial / quartic monomial / cubic binomial / cubic trinomial) → cubic binomialPrompt: Count the terms: 1 monomial, 2 binomial, 3 trinomial.
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