Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Fractions as decimals
Number sense
CCSS 7.NS.A.2.DEngland: Y6 Fractions (including decimals)England: KS3 Number
Objective and success criteria
Students will: Fractions as decimals.
- 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: Divide decimals; Equivalent fractions
Leads to: Rational and irrational numbers; Recurring decimals to fractions; Terminating and repeating decimals from fractions
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 (Divide decimals; Equivalent fractions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 48.8 ÷ 8 = ? → 6.1Prompt: Divide as with whole numbers.
- 2.75 ÷ 0.25 = ? → 11Prompt: Make the divisor a whole number by multiplying both numbers by 10 (or 100).
- 27.2 ÷ 4 = ? → 6.8Prompt: Divide as with whole numbers.
Hook · 6 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Fractions as decimals. 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 7/25 as a decimal.
- Step 1: 7 ÷ 25 = 0.28
- Answer: 0.28
- 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 9/40 as a decimal. → 0.225Prompt: A fraction means numerator ÷ denominator: 9 ÷ 40.
- Does 11/25 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.
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.
- Does 1/6 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 7/25 as a decimal. → 0.28Prompt: A fraction means numerator ÷ denominator: 7 ÷ 25.
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: Divide 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: Rational and irrational numbers; Recurring decimals to fractions; Terminating and repeating decimals from 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