Same Math › Grades 3–4 › Equivalent fractions with models
How do kids learn equivalent fractions?
Equivalent fractions are different names for the same amount, like 2/3 and 4/6. Kids learn them first by cutting a model into smaller pieces, then learn why multiplying the top and bottom by the same number works.
- 2/3 of the top strip is shaded.
- Cut each third in half and you get sixths.
- Same length shaded: 2/3 = 4/6
Why schools teach it
The rule comes after the picture
Third graders find simple equivalent fractions with models like strips and number lines (3.NF.A.3). In 4th grade they explain why multiplying top and bottom by the same number works: you make more pieces, but each piece is smaller by the same amount (4.NF.A.1).
Equivalent fractions are the step behind comparing and adding fractions with different denominators, so a solid picture now saves trouble later.
At the kitchen table
What to say, and what to skip
Say this
If we cut every piece in half, how many pieces are there now?
Did the shaded part get bigger or smaller?
Neither. That's the key idea.What did you do to the bottom number? Did you do the same to the top?
Can you find another fraction equal to 1/2?
2/4, 3/6, 4/8, 5/10. Kids enjoy finding the pattern.
Skip this
Just multiply the top and bottom by 2.
Fine as a 4th-grade shortcut, but 3rd graders need to see why first.- Adding the same number to top and bottom.2/3 is not equal to 3/4. Multiply, don't add.
- Calling them equal because they look similar.Ask them to prove it with a model.
See it in action
Finding a fraction equal to 3/4 with eighths
Shade 3/4 of a strip
Cut each fourth into 2 equal pieces
4 pieces become 8Count the shaded eighths
3/4 = 6/8
Both numbers doubled, because every piece was split in two.
Free practice sheet
Make an equivalent fractions sheet
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Parents also ask
Why does multiplying top and bottom work?
Multiplying the bottom by 2 makes twice as many pieces. Multiplying the top by 2 takes twice as many of them. The amount stays the same.
Can you divide instead?
Yes. 6/8 = 3/4 by dividing both by 2. That's simplifying, usually taught in 4th and 5th grade.
What's the difference between equal and equivalent?
In this case, nothing. Equivalent fractions are equal in value; they just use different numbers.
Why use models when the rule is faster?
The model explains the rule, so kids don't mix it up with adding.