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Math lesson plan · 8th grade (Year 9 in England) · 60 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 · 6 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 7.8 × 10⁵ as an ordinary number. → 780000Prompt: 10 to the power 5 moves the digits 5 places to the left.
  2. Write 1.2 × 10⁻⁵ as a decimal. → 0.000012Prompt: A negative power of 10 makes the number small.
  3. The distance from Earth to the Sun is about 1.5 × 10⁸ km. Write this number in full. → 150000000Prompt: Multiply by 10 8 times.

Hook · 6 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 · 12 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 · 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.
  1. Write 550 000 000 in scientific notation (like 4.5 × 10^6). → 5.5 × 10⁸Prompt: The first number must be at least 1 and less than 10.
  2. Write 0.00087 in scientific notation. → 8.7 × 10⁻⁴Prompt: Move the decimal point to just after the first non-zero digit.

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.
  1. Write 41 000 in scientific notation (like 4.5 × 10^6). → 4.1 × 10⁴Prompt: The first number must be at least 1 and less than 10.
  2. Write 0.008 in scientific notation. → 8 × 10⁻³Prompt: Move the decimal point to just after the first non-zero digit.

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

    Arjun writes 180 000 as 18 × 10⁴. Why is that not scientific notation?

    • A. The power of 10 must be negative
    • B. The value is wrong
    • C. You cannot use decimals
    • D. 18 is not between 1 and 10

  2. Question 2

    Write 9 400 000 in scientific notation (like 4.5 × 10^6).

    Answer

  3. Question 3

    Write 0.0062 in scientific notation.

    Answer

  4. Question 4

    Luis writes 950 as 95 × 10¹. Why is that not scientific notation?

    • A. The power of 10 must be negative
    • B. The value is wrong
    • C. 95 is not between 1 and 10
    • D. You cannot use decimals

  5. Question 5

    Write 7500 in scientific notation (like 4.5 × 10^6).

    Answer

  6. Question 6

    Write 0.0000039 in scientific notation.

    Answer

  7. Question 7

    Fatima writes 8 400 000 as 84 × 10⁵. Why is that not scientific notation?

    • A. 84 is not between 1 and 10
    • B. The value is wrong
    • C. The power of 10 must be negative
    • D. You cannot use decimals

  8. Question 8

    Write 9 200 000 000 in scientific notation (like 4.5 × 10^6).

    Answer

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

  1. 1. D. 18 is not between 1 and 10

  2. 2. 9.4 × 10⁶

  3. 3. 6.2 × 10⁻³

  4. 4. C. 95 is not between 1 and 10

  5. 5. 7.5 × 10³

  6. 6. 3.9 × 10⁻⁶

  7. 7. A. 84 is not between 1 and 10

  8. 8. 9.2 × 10⁹