Fifth Grade · Math · week 1

Place value: x10 and div10 patterns

Multiply and divide whole numbers and decimals by 10, 100, and 1000 by shifting digits, and explain the pattern using place value.

When you multiply a number by 10, every digit moves one place to the left in the place-value chart -- it becomes ten times bigger. Multiply by 100, and every digit moves two places left. The digits never change; only where they sit changes.

Dividing by 10 does the opposite: every digit moves one place to the right, becoming one tenth as big. This works for whole numbers AND decimals -- watch the decimal point shift instead of the digits, and you get the same result.

📋 For the teacher
Teach it (10–15 min):
  • Draw a place-value chart on paper and physically slide digit cards left or right so the shift is visible, not just a rule.
  • Say the pattern out loud every time: times 10, digits march left one place; divide by 10, digits march right one place.
  • Warn against the "just add a zero" shortcut on decimals -- 5.2 x 10 is 52, not "5.20 with a zero stuck on," so the shortcut only ever really works cleanly on whole numbers.
  • Connect to money: 10 dimes make a dollar, which is the same x10 grouping idea living in the place-value chart.
Talk about it:
  • What happens to every digit when you multiply by 10?
  • Why does the "add a zero" trick fail on a decimal like 5.2?
  • How are multiplying by 10 and dividing by 10 opposite moves?

Mastery looks like: They can multiply or divide any whole number or decimal by 10, 100, or 1000 by shifting digits, and explain the shift using place value.

Common stumbles: Using the "add a zero" shortcut on decimals; shifting digits the wrong direction for division; losing track of the decimal point during the shift.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

Place ValueWatch ones, tens, hundreds, and thousands build big numbers.try →MultiplicationEqual groups and arrays make products finally click.try →DivisionShare fairly and build equal groups.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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