Math lesson plan · 6th grade (Year 7 in England) · 60 minutes
Square and cube fractions and decimals
Number sense
CCSS 6.EE.A.1England: KS3 Number
Objective and success criteria
Students will: Square and cube fractions and 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: Use exponent notation for repeated multiplication; Multiply fractions; Multiply decimals
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 (Use exponent notation for repeated multiplication; Multiply fractions; Multiply decimals). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write 10 × 10 × 10 × 10 × 10 × 10 as a power (for example 4^3). → 10⁶Prompt: The base is the number being multiplied.
- 1.7 × 5 = ? → 8.5Prompt: Multiply 17 × 5 as whole numbers first.
- Write 6 × 6 × 6 × 6 as a power (for example 4^3). → 6⁴Prompt: The base is the number being multiplied.
Hook · 6 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Square and cube fractions and 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: Work out (4/7)². Give a fraction.
- Step 1: (4/7)² = 4/7 × 4/7
- Step 2: = 16/49
- Answer: 16/49
- 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.
- Work out (2/9)². Give a fraction. → 4/81Prompt: Squaring means multiplying the fraction by itself.
- Work out 0.05². → 0.0025Prompt: 0.05² = 0.05 × 0.05.
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.
- Mei says (1/3)³ = 3/9. Find the correct value of (1/3)³. → 1/27Prompt: The exponent tells you how many times to multiply, not what to multiply by.
- Work out 0.1². → 0.01Prompt: 0.1² = 0.1 × 0.1.
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: Use exponent notation for repeated multiplication.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder