Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Multiply and divide in scientific notation
Number sense
CCSS 8.EE.A.4England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Multiply and divide in scientific notation.
- 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: Write numbers in scientific notation (standard form); Multiply powers with the same base
Leads to: Compare real quantities in scientific notation
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 (Write numbers in scientific notation (standard form); Multiply powers with the same base). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write 5 300 000 000 in scientific notation (like 4.5 × 10^6). → 5.3 × 10⁹Prompt: The first number must be at least 1 and less than 10.
- 3⁵ × 3⁷ = 3ⁿ. What is n? → 12Prompt: Write it out: 5 lots of 3, then 7 more lots of 3.
- Write 0.0000053 in scientific notation. → 5.3 × 10⁻⁶Prompt: Move the decimal point to just after the first non-zero digit.
Hook · 3 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Multiply and divide in scientific notation. 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: Work out (4 × 10⁷) × (1 × 10³). Give the answer in scientific notation.
- Step 1: 4 × 1 = 4
- Step 2: 10⁷ × 10³ = 10¹⁰
- Step 3: 4 × 10¹⁰
- Answer: 4 × 10¹⁰
- 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.
- Work out (1 × 10⁶) × (2 × 10⁶). Give the answer in scientific notation. → 2 × 10¹²Prompt: Multiply the front numbers.
- Work out (6 × 10⁷) × (8 × 10⁶). Give the answer in scientific notation. → 4.8 × 10¹⁴Prompt: Multiply the front numbers and add the powers.
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.
- Work out (8 × 10³) × (3 × 10²). Give the answer in scientific notation. → 2.4 × 10⁶Prompt: Multiply the front numbers and add the powers.
- Work out (2.1 × 10⁷) ÷ (3 × 10³). Give the answer in scientific notation. → 7 × 10³Prompt: Divide the front numbers.
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: Write numbers in scientific notation (standard form).
- 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: Compare real quantities in scientific notation.
- 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