Math lesson plan Β· 8th grade (Year 9 in England) Β· 45 minutes
Rational and irrational numbers
Number sense
CCSS 8.NS.A.1CCSS 8.NS.A.2England: GCSE Higher Number
Objective and success criteria
Students will: Rational and irrational numbers.
- 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: Square roots and cube roots; Fractions as decimals
Leads to: Classify numbers as rational or irrational
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up Β· 5 min
- Quick retrieval from earlier learning (Square roots and cube roots; Fractions as decimals). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is β729? β 9Prompt: Which number, used three times in a multiplication, gives this?
- Write 9/40 as a decimal. β 0.225Prompt: A fraction means numerator Γ· denominator: 9 Γ· 40.
- β31 lies between which two whole numbers? (3 and 4 / 4 and 5 / 6 and 7 / 5 and 6) β 5 and 6Prompt: List the square numbers near it.
Hook Β· 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Rational and irrational numbers. Read the success criteria together.
I do: model it Β· 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Which of these numbers is irrational: β16 ; β49 ; β2 ; 1.25?
- Step 1: β2 cannot be written as a fraction: its decimal goes on forever without repeating.
- Answer: β2
- Pause after each step and ask a student to say what comes next.
We do: guided practice Β· 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.
- Which of these numbers is irrational: 0.333β¦ (repeating) ; β7 ; 3/7 ; 1.25? (β7 / 0.333β¦ (repeating) / 3/7 / 1.25) β β7Prompt: A rational number can be written as a fraction of two integers.
- Is β36 rational or irrational? (Rational / Irrational) β RationalPrompt: Can it be written as a fraction a/b with integers a and b?
You do: independent practice Β· 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 Β· 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Is β(1/4) rational or irrational? (Rational / Irrational) β RationalPrompt: Can it be written as a fraction a/b with integers a and b?
- Which of these numbers is irrational: β16 ; 0.333β¦ (repeating) ; β2 + 1 ; 0.75? (β16 / 0.333β¦ (repeating) / 0.75 / β2 + 1) β β2 + 1Prompt: A rational number can be written as a fraction of two integers.
Watch out for
- Reading 1,045 as one thousand four hundred five: point to each place and say its value.
- Thinking a longer number is always bigger, even with decimals (0.45 vs 0.5).
Support and stretch
Support
- Review first: Square roots and cube roots.
- Use concrete materials: place value chart.
- 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: Classify numbers as rational or irrational.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder