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Math lesson plan · 8th grade (Year 9 in England) · 45 minutes

Write numbers in scientific notation (standard form)

Number sense

CCSS 8.EE.A.3CCSS 8.EE.A.4England: KS3 NumberEngland: GCSE Foundation Number

Objective and success criteria

Students will: Write numbers in scientific notation (standard form).

  • 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 scientific notation as an ordinary number

Leads to: Compare and order numbers in scientific notation; Multiply and divide in scientific notation

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 (Write scientific notation as an ordinary number). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Write 3.8 × 10⁵ as an ordinary number. → 380000Prompt: 10 to the power 5 moves the digits 5 places to the left.
  2. Write 9.2 × 10⁻¹ as a decimal. → 0.92Prompt: A negative power of 10 makes the number small.
  3. A red blood cell is about 7.5 × 10⁻⁶ m. Write this number in full. → 0.0000075Prompt: Divide by 10 6 times.

Hook · 5 min

  • Show a number in the news or a price tag and ask what each digit is worth.
  • Share the objective: Write numbers in scientific notation (standard form). 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: Write 16 000 in scientific notation (like 4.5 × 10^6).
  • Step 1: Move the point 4 places: 1.6 × 10⁴
  • Answer: 1.6 × 10⁴
  • 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.
  1. Write 2 600 000 in scientific notation (like 4.5 × 10^6). → 2.6 × 10⁶Prompt: The first number must be at least 1 and less than 10.
  2. Write 0.076 in scientific notation. → 7.6 × 10⁻²Prompt: Move the decimal point to just after the first non-zero digit.

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.
  1. Write 0.0008 in scientific notation. → 8 × 10⁻⁴Prompt: Move the decimal point to just after the first non-zero digit.
  2. Ana writes 6 200 000 as 62 × 10⁵. Why is that not scientific notation? (62 is not between 1 and 10 / The power of 10 must be negative / The value is wrong / You cannot use decimals) → 62 is not between 1 and 10Prompt: Is the value correct? Check by multiplying out.

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 scientific notation as an ordinary number.
  • 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 and order numbers in scientific notation; Multiply and divide 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

eurekami

Write numbers in scientific notation (standard form)

Name

Date

Score/ 8

  1. Question 1

    Hiro writes 820 000 as 82 × 10⁴. Why is that not scientific notation?

    • A. The power of 10 must be negative
    • B. 82 is not between 1 and 10
    • C. You cannot use decimals
    • D. The value is wrong

  2. Question 2

    Write 20 000 in scientific notation (like 4.5 × 10^6).

    Answer

  3. Question 3

    Write 0.00088 in scientific notation.

    Answer

  4. Question 4

    Grace writes 330 000 as 33 × 10⁴. Why is that not scientific notation?

    • A. The value is wrong
    • B. The power of 10 must be negative
    • C. You cannot use decimals
    • D. 33 is not between 1 and 10

  5. Question 5

    Write 310 000 in scientific notation (like 4.5 × 10^6).

    Answer

  6. Question 6

    Write 0.00076 in scientific notation.

    Answer

  7. Question 7

    Jamal writes 7600 as 76 × 10². Why is that not scientific notation?

    • A. The power of 10 must be negative
    • B. The value is wrong
    • C. 76 is not between 1 and 10
    • D. You cannot use decimals

  8. Question 8

    Write 660 000 in scientific notation (like 4.5 × 10^6).

    Answer

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Answer key: Write numbers in scientific notation (standard form)

  1. 1. B. 82 is not between 1 and 10

  2. 2. 2 × 10⁴

  3. 3. 8.8 × 10⁻⁴

  4. 4. D. 33 is not between 1 and 10

  5. 5. 3.1 × 10⁵

  6. 6. 7.6 × 10⁻⁴

  7. 7. C. 76 is not between 1 and 10

  8. 8. 6.6 × 10⁵