Math lesson plan · 8th grade (Year 9 in England) · 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 · 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 √49? → 7Prompt: Which number multiplied by itself gives this?
- Write 3/16 as a decimal. → 0.1875Prompt: A fraction means numerator ÷ denominator: 3 ÷ 16.
- √149 lies between which two whole numbers? (13 and 14 / 10 and 11 / 12 and 13 / 11 and 12) → 12 and 13Prompt: List the square numbers near it.
Hook · 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 · 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: √16 ; √49 ; √2 ; 1.25?
- Step 1: √2 cannot be written as a fraction: its decimal goes on forever without repeating.
- 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.
- Which of these numbers is irrational: √2 ; −8 ; 1.25 ; 22/7? (22/7 / −8 / 1.25 / √2) → √2Prompt: A rational number can be written as a fraction of two integers.
- Is √0.5 rational or irrational? (Rational / Irrational) → IrrationalPrompt: Can it be written as a fraction a/b with integers a and b?
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.
- Which of these numbers is irrational: √16 ; 3/7 ; √10 ; 0.333… (repeating)? (0.333… (repeating) / 3/7 / √16 / √10) → √10Prompt: A rational number can be written as a fraction of two integers.
- Is 5/9 rational or irrational? (Rational / Irrational) → RationalPrompt: Can it be written as a fraction a/b with integers a and b?
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