Math lesson plan · 7th grade (Year 8 in England) · 30 minutes
Terminating and repeating decimals from fractions
Number sense
CCSS 7.NS.A.2.DEngland: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Terminating and repeating decimals from 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
Leads to: Convert repeating decimals into fractions
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Fractions as decimals). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write 9/40 as a decimal. → 0.225Prompt: A fraction means numerator ÷ denominator: 9 ÷ 40.
- Does 4/9 give a terminating or a repeating (recurring) decimal? (Terminating / Repeating) → RepeatingPrompt: Write the fraction in simplest form and look at the prime factors of the denominator.
- Write 13/20 as a decimal. → 0.65Prompt: A fraction means numerator ÷ denominator: 13 ÷ 20.
Hook · 3 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Terminating and repeating decimals from fractions. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Does 2/3 give a terminating or a repeating decimal?
- Step 1: 3 = 3 → another prime factor: repeating
- Step 2: 2 ÷ 3 = 0.666666…
- Answer: Repeating
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Does 13/40 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 3/8 as a decimal. → 0.375Prompt: Divide 3 by 8.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Does 23/40 give a terminating or a repeating decimal? (Terminating / Repeating) → TerminatingPrompt: Write the fraction in simplest form and look at the denominator's prime factors.
- Which decimal equals 1/3? (0.3333… / 0.013 / 0.5… / 0.1667…) → 0.3333…Prompt: Divide 1 by 3.
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
- Move on to: Convert repeating decimals into fractions.
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder