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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 4.2 × 10⁴ as an ordinary number. → 42000Prompt: 10 to the power 4 moves the digits 4 places to the left.
  2. Write 8.4 × 10⁻⁴ as a decimal. → 0.00084Prompt: 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 · 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 430 000 000 in scientific notation (like 4.5 × 10^6). → 4.3 × 10⁸Prompt: The first number must be at least 1 and less than 10.
  2. Write 0.0056 in scientific notation. → 5.6 × 10⁻³Prompt: 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. Sam writes 7400 as 74 × 10². Why is that not scientific notation? (74 is not between 1 and 10 / The power of 10 must be negative / You cannot use decimals / The value is wrong) → 74 is not between 1 and 10Prompt: Is the value correct? Check by multiplying out.
  2. Write 44 000 in scientific notation (like 4.5 × 10^6). → 4.4 × 10⁴Prompt: The first number must be at least 1 and less than 10.

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

    Write 810 000 in scientific notation (like 4.5 × 10^6).

    Answer

  2. Question 2

    Aisha writes 220 000 as 22 × 10⁴. Why is that not scientific notation?

    • A. The power of 10 must be negative
    • B. 22 is not between 1 and 10
    • C. You cannot use decimals
    • D. The value is wrong

  3. Question 3

    Write 0.00069 in scientific notation.

    Answer

  4. Question 4

    Write 28 000 000 in scientific notation (like 4.5 × 10^6).

    Answer

  5. Question 5

    Nia writes 640 as 64 × 10¹. Why is that not scientific notation?

    • A. The value is wrong
    • B. 64 is not between 1 and 10
    • C. The power of 10 must be negative
    • D. You cannot use decimals

  6. Question 6

    Write 0.0023 in scientific notation.

    Answer

  7. Question 7

    Write 2 800 000 000 in scientific notation (like 4.5 × 10^6).

    Answer

  8. Question 8

    Tariq writes 5700 as 57 × 10². Why is that not scientific notation?

    • A. You cannot use decimals
    • B. The value is wrong
    • C. The power of 10 must be negative
    • D. 57 is not between 1 and 10

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

  1. 1. 8.1 × 10⁵

  2. 2. B. 22 is not between 1 and 10

  3. 3. 6.9 × 10⁻⁴

  4. 4. 2.8 × 10⁷

  5. 5. B. 64 is not between 1 and 10

  6. 6. 2.3 × 10⁻³

  7. 7. 2.8 × 10⁹

  8. 8. D. 57 is not between 1 and 10