Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Compare real quantities in scientific notation
Number sense
CCSS 8.EE.A.3CCSS 8.EE.A.4England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Compare real quantities 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: Multiply and divide in scientific notation
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 · 5 min
- Quick retrieval from earlier learning (Multiply and divide in scientific notation). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Work out (2 × 10⁶) × (1 × 10⁸). Give the answer in scientific notation. → 2 × 10¹⁴Prompt: Multiply the front numbers.
- Work out (3 × 10⁶) × (6 × 10⁴). Give the answer in scientific notation. → 1.8 × 10¹¹Prompt: Multiply the front numbers and add the powers.
- Work out (1.2 × 10¹²) ÷ (3 × 10²). Give the answer in scientific notation. → 4 × 10⁹Prompt: Divide the front numbers.
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Compare real quantities in scientific notation. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A large hard drive holds 5 × 10⁵ bytes. A photo is 4 × 10³ bytes. How many photos fit on the drive?
- Step 1: 5 ÷ 4 = 1.25
- Step 2: 10⁵ ÷ 10³ = 10²
- Step 3: 125
- Answer: 125
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A large hard drive holds 8 × 10⁷ bytes. A photo is 2 × 10¹ bytes. How many photos fit on the drive? → 4000000Prompt: Divide the drive size by the photo size.
- How many times heavier or larger is an elephant (about 6 × 10³ kg) than a mouse (about 2 × 10⁻² kg)? → 300000Prompt: Divide the larger by the smaller.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Two cities have populations 2.4 × 10⁵ and 1.4 × 10⁵. What is their total population, in scientific notation? → 3.8 × 10⁵Prompt: The powers of 10 are the same, so add the front numbers.
- How many times heavier or larger is an elephant (about 6 × 10³ kg) than a mouse (about 2 × 10⁻² kg)? → 300000Prompt: Divide the larger by the smaller.
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: Multiply and divide in scientific notation.
- 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