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Irrational numbers: 8th grade math

Irrational numbers; decimal approximations. 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: irrational numbers; decimal approximations.

Teach (10 min)

  • √30: 5² = 25 and 6² = 36, and 30 is between them. So √30 is between 5 and 6.
  • 30 is 5 above 25 and 6 below 36, so √30 is a little closer to 5.
  • 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/roots.estimate?lesson=8-roots-estimate-1&at=8

Exit ticket (5 min)

  • Three questions on a slip:
  • 1. √38 is between which two whole numbers?
  • 2. Which whole number is √55 closest to?
  • 3. Which whole number is √47 closest to?

Question set

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

  1. √38 is between which two whole numbers?
  2. Which whole number is √55 closest to?
  3. Which whole number is √47 closest to?
  4. √32 is between which two whole numbers?
  5. √45 is between which two whole numbers?
  6. √8 is between which two whole numbers?
  7. Which whole number is √43 closest to?
  8. Which whole number is √6 closest to?
  9. Which whole number is √45 closest to?
  10. √42 is between which two whole numbers?
Answers
  1. 6 and 7
  2. 7
  3. 7
  4. 5 and 6
  5. 6 and 7
  6. 2 and 3
  7. 7
  8. 2
  9. 7
  10. 6 and 7

Printable sheet

Name: ____________________   Date: ____________

Irrational numbers (8th grade)

  1. Which whole number is √58 closest to?
  2. Which whole number is √42 closest to?
  3. √47 is between which two whole numbers?
  4. Which whole number is √45 closest to?
  5. √42 is between which two whole numbers?
  6. Which whole number is √50 closest to?
  7. √42 is between which two whole numbers?
  8. ∛117 is between which two whole numbers?
  9. Which whole number is √3 closest to?
  10. Estimate √3 to the nearest tenth. (Hint: try squaring numbers with one decimal place.)
  11. Estimate √42 to the nearest tenth. (Hint: try squaring numbers with one decimal place.)
  12. Estimate √30 to the nearest tenth. (Hint: try squaring numbers with one decimal place.)
Key
  1. 8
  2. 6
  3. 6 and 7
  4. 7
  5. 6 and 7
  6. 7
  7. 6 and 7
  8. 4 and 5
  9. 2
  10. 1.7
  11. 6.5
  12. 5.5

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.