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Mathematics · Grade 5

Place Value and Powers of Ten

Learners discover that each place is worth ten times the place to its right, use exponents to write powers of ten, and explain why digits shift when a number is multiplied or divided by 10, 100 or 1,000. They then read, write, compare and round decimals to thousandths, and carry the same reasoning into metric measurement.

  • 4 lessons
  • About 85 minutes
  • Place value and powers of ten check: 10 questions
  • Ways to answer: fill in the blanks, choose an answer, type a fraction, match pairs, type a number and place on a number line
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What learners will discover

  • Explain that a digit in one place is worth 10 times what it would be worth one place to its right and 1/10 of what it would be worth one place to its left.
  • Write powers of ten with whole-number exponents and multiply or divide whole numbers and decimals by powers of ten, explaining the shift of the digits.
  • Read, write and compare decimals to thousandths using place value, number names and expanded form.
  • Round decimals to any place and use place-value reasoning in a new situation such as metric measurement.

Lessons

  1. Ten times as much, one tenth as much 9 steps5 practiceabout 20 min
  2. Powers of ten and shifting digits 9 steps6 practiceabout 22 min
  3. Decimals to thousandths: read, write, compare 8 steps5 practiceabout 22 min
  4. Rounding and a new context: metric measures 8 steps5 practiceabout 21 min
  5. Place value and powers of ten check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Array OrchardPlant trees in rows, pack fruit into crates and split big fields to multiply.
  • Fraction BridgesSaw planks into equal parts, paint fractions, build bridges that match and lay planks end to end to add.

More 5th grade math

Guide for grown-ups