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Exponents, roots, big numbers: 8th grade math

Integer exponents, square and cube roots, scientific notation. A free 8th grade lesson plan, a question set with answers and a printable sheet with its key. Copy it and make it yours.

Lesson plan

Goal

  • Students can do this: integer exponents, square and cube roots, scientific notation.

Teach (10 min)

  • 2³ × 2⁴ means 2 × 2 × 2 and then 2 × 2 × 2 × 2: seven 2s in all. So 2³ × 2⁴ = 2⁷.
  • Same base, multiply: ADD the exponents. Same base, divide: SUBTRACT them.
  • Work one example on the board while students say each step aloud, then do one together.

Practise (15 min)

  • Students work the printable sheet in pairs, then alone.
  • Or practise it as a game with no sign-up: https://peabody.kids/math/sci.same?lesson=8-sci-same-1&at=8

Exit ticket (5 min)

  • Three questions on a slip:
  • 1. Find the missing exponent: 28 × 28 = 2?
  • 2. Find the missing exponent: 36 ÷ 32 = 3?
  • 3. Find the missing exponent: 104 × 103 = 10?

Question set

10 questions that read in words, easiest first. Questions that need a picture are on the printable sheet below.

  1. Find the missing exponent: 28 × 28 = 2?
  2. Find the missing exponent: 36 ÷ 32 = 3?
  3. Find the missing exponent: 104 × 103 = 10?
  4. Find the missing exponent: 28 × 27 = 2?
  5. Find the missing exponent: 105 × 104 = 10?
  6. Find the missing exponent: 76 × 77 = 7?
  7. Find the missing exponent: 106 × 104 = 10?
  8. Find the missing exponent: 104 ÷ 103 = 10?
  9. Find the missing exponent: 53 × 57 = 5?
  10. Find the missing exponent: 55 ÷ 54 = 5?
Answers
  1. 16
  2. 4
  3. 7
  4. 15
  5. 9
  6. 13
  7. 10
  8. 1
  9. 10
  10. 1

Printable sheet

Name: ____________________   Date: ____________

Exponents, roots, big numbers (8th grade)

  1. Find the missing exponent:
    107 ÷ 104 = 10?
  2. Find the missing exponent:
    57 ÷ 52 = 5?
  3. Find the missing exponent:
    36 ÷ 33 = 3?
  4. Find the missing exponent:
    32 × 38 = 3?
  5. Find the missing exponent:
    58 ÷ 57 = 5?
  6. Find the missing exponent:
    36 ÷ 32 = 3?
  7. Find the missing exponent:
    54 ÷ 52 = 5?
  8. Find the missing exponent:
    27 ÷ 26 = 2?
  9. Find the missing exponent:
    38 ÷ 36 = 3?
  10. Find the missing exponent:
    57 ÷ 52 = 5?
  11. Find the missing exponent:
    77 ÷ 75 = 7?
  12. Find the missing exponent:
    38 ÷ 36 = 3?
Key
  1. 3
  2. 5
  3. 3
  4. 10
  5. 1
  6. 4
  7. 2
  8. 1
  9. 2
  10. 5
  11. 2
  12. 2

Written by Peabody from its own skill pages. Free, no ads, no sign-in. Children can practise this on Peabody. More from teachers: teacher-shared resources.