Fourth Grade · Math · week 28

Equivalent fractions with models

Generate equivalent fractions using area models and the multiply-top-and-bottom-by-the-same-number rule.

Equivalent fractions name the exact same amount using different-size pieces. If you cut every piece of a fraction model into the same number of smaller pieces, both the shaded count and the total count multiply by that same number, so the fraction value never changes.

That cutting picture is exactly what the rule "multiply the numerator and denominator by the same number" means. Always multiply both parts together, never add.

📋 For the teacher
Teach it (10–15 min):
  • Physically fold paper strips or draw bars split into equal parts, then re-split every part the same way.
  • Show that cutting the picture is the same move as multiplying the top and bottom by the same number, just drawn out.
  • Always multiply, never add, to a fraction top and bottom to keep the value the same.
  • Have them find two different equivalent fractions for the same starting fraction to prove there is more than one right answer.
Talk about it:
  • Why does multiplying top and bottom by the same number keep a fraction value the same?
  • How is cutting a fraction bar the same as the multiplication rule?
  • Can you find two different equivalent fractions for 1/2?

Mastery looks like: They generate equivalent fractions using an area model and the multiply-top-and-bottom rule, and check whether two fractions are equivalent.

Common stumbles: Adding the same number to the top and bottom instead of multiplying; multiplying only the numerator or only the denominator.

See it visually

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

FractionsSlice bars and circles into equal parts and compare them.try →MultiplicationEqual groups and arrays make products finally click.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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