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Understand Equivalent Fractions with Visual Models

Students use fraction bars, area models, and number lines to see why two fractions that look different can represent the same amount. They identify equivalent pairs and explain the relationship using visual evidence.

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Understand Equivalent Fractions with Visual Models

Grade 4 · Equivalent Fractions · question 1 of 3

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20 rungs. A star at the top.

AB

How many of strip B's parts make the shaded part of strip A?

Both strips are the same size.

How it is taught

0:00 of 4:55

Equivalent fractions name the same amount.

More pieces, more of them taken.

Read it: Same amount, different name

Two friends share a chocolate bar. Leo breaks his half into two pieces and says he has more, because two is more than one. Look at the chocolate, not the pieces.

  1. Maya has one piece out of two: 1/2.
  2. Leo cut his half into two, so he has two pieces out of four: 2/4.
  3. Slide Leo's two pieces together. They are exactly the size of Maya's one.

Cutting a piece into more pieces changes how many pieces there are. It does not change how much chocolate there is.

A fraction is a name for an amount. The same amount can carry more than one name — 1/2, 2/4, 3/6, 4/8 all name Maya's half.

When the top and the bottom are both multiplied by the same number, the name changes and the amount stays.

Multiply the top and the bottom by the same number: the fraction has a new name and the same value.

Reading 2/4 as more than 1/2 because 2 is more than 1.

The bottom number says how small the pieces are. Fourths are smaller than halves, so two of them are only worth one half.

A bar shows 3/4 shaded. What fraction in eighths covers the same amount? — 6/8. Multiply the top and bottom of 3/4 by 2: 3 × 2 = 6 and 4 × 2 = 8.

1/2 = 2/4 = 4/8

Some fractions look different but mean the same amount. Let's see how that works!

Here is a chocolate bar split into two equal pieces, with one piece shaded.

One out of two parts is shaded — that's one half.

Now let's cut the same size bar into four equal pieces instead.

We shade the same amount of chocolate as before — two pieces.

Two out of four parts are shaded — that's two fourths.

Look closely — the shaded part ends at exactly the same spot!

Let's slice it even smaller, into eight equal pieces.

We shade the same amount again — that takes four pieces.

Four out of eight parts shaded — four eighths.

All three cover the same chocolate, so the fractions are equal.

One half, two fourths, and four eighths are equivalent fractions — different names for the same amount!

Same amount, different names?1224Same shaded length!4812 = 24 = 48EQUIVALENT12 = 24= 48same amount
Grade 4 · Same amount, different names

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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