Math lesson plan Β· 8th grade (Year 9 in England) Β· 45 minutes
Classify numbers as rational or irrational
Number sense
CCSS 8.NS.A.1England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Classify numbers as rational or irrational.
- 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: Rational and irrational numbers
Leads to: Order numbers including square roots and Ο
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 (Rational and irrational numbers). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Which of these numbers is irrational: 0.333β¦ (repeating) ; β5 ; β(9/4) ; β49? (β(9/4) / 0.333β¦ (repeating) / β49 / β5) β β5Prompt: A rational number can be written as a fraction of two integers.
- Is 0 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: β(9/4) ; β3 ; β16 ; 0.75? (β16 / 0.75 / β3 / β(9/4)) β β3Prompt: A rational number can be written as a fraction of two integers.
Hook Β· 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Classify numbers as rational or irrational. 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: Is β5 rational or irrational?
- Step 1: β5 can be written as a fraction: rational.
- Answer: Rational
- 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.
- Is 0.333β¦ rational or irrational? (Rational / Irrational) β RationalPrompt: Rational numbers can be written as a fraction of two integers.
- Which number is irrational? (0.25 / β16 / 3/7 / β10) β β10Prompt: Check each: can it be written as a fraction?
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.
- Which number is irrational? (β27 / 3/7 / β5 / 1.010010001β¦) β 1.010010001β¦Prompt: Check each: can it be written as a fraction?
- Is β33 rational or irrational? (Rational / Irrational) β IrrationalPrompt: Is the number under the root a perfect square?
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: Rational and irrational numbers.
- 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: Order numbers including square roots and Ο.
- 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