Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Recurring decimals to fractions
Number sense
CCSS 8.NS.A.1England: GCSE Higher Number
Objective and success criteria
Students will: Recurring decimals to fractions.
- 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: Fractions as decimals; One-step equations
Leads to: the next skill in this area.
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 (Fractions as decimals; One-step equations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write 3/20 as a decimal. → 0.15Prompt: A fraction means numerator ÷ denominator: 3 ÷ 20.
- Does 3/5 give a terminating or a repeating (recurring) decimal? (Terminating / Repeating) → TerminatingPrompt: Write the fraction in simplest form and look at the prime factors of the denominator.
- Write 7/25 as a decimal. → 0.28Prompt: A fraction means numerator ÷ denominator: 7 ÷ 25.
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Recurring decimals to fractions. 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: Write 0.939393… as a fraction in simplest form.
- Step 1: 100x − x = 93
- Step 2: 99x = 93
- Step 3: x = 93/99 = 31/33
- Answer: 31/33
- 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.
- Write 0.171717… as a fraction in simplest form. → 17/99Prompt: Let x = 0.171717…. Multiply by 100 to shift one repeating block.
- Write 0.727272… as a fraction in simplest form. → 8/11Prompt: Let x = 0.727272…. Multiply by 100 to shift one repeating block.
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 0.22222… as a fraction in simplest form. → 2/9Prompt: Let x = 0.22222…. Multiply by 10 to shift one repeating block.
- Write 0.161616… as a fraction in simplest form. → 16/99Prompt: Let x = 0.161616…. Multiply by 100 to shift one repeating block.
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: Fractions as decimals.
- 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
- 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