Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Convert repeating decimals into fractions
Number sense
CCSS 8.NS.A.1England: KS3 NumberEngland: GCSE Higher Number
Objective and success criteria
Students will: Convert repeating decimals into 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: Terminating and repeating decimals from fractions
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 · 6 min
- Quick retrieval from earlier learning (Terminating and repeating decimals from fractions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Does 11/16 give a terminating or a repeating decimal? (Terminating / Repeating) → TerminatingPrompt: Write the fraction in simplest form and look at the denominator's prime factors.
- Write 27/40 as a decimal. → 0.675Prompt: Divide 27 by 40.
- Which decimal equals 8/9? (0.089 / 0.9… / 0.8 / 0.8889…) → 0.8889…Prompt: Divide 8 by 9.
Hook · 6 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Convert repeating decimals into fractions. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Write 0.333… (3 repeating) as a fraction in simplest form.
- Step 1: 10x − x = 3
- Step 2: 9x = 3
- Step 3: x = 3/9 = 1/3
- Answer: 1/3
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 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 0.444… (4 repeating) as a fraction in simplest form. → 4/9Prompt: Let x = the decimal. Multiply by 10.
- Write 0.626262… (“62” repeating) as a fraction in simplest form. → 62/99Prompt: Two digits repeat, so multiply by 100.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Write 0.767676… (“76” repeating) as a fraction in simplest form. → 76/99Prompt: Two digits repeat, so multiply by 100.
- Write 0.3222… (only the 2 repeats) as a fraction in simplest form. → 29/90Prompt: Let x = the decimal. Compare 100x and 10x.
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: Terminating and repeating decimals from fractions.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder