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Understand Fraction Equivalence Using Models

Students will use area models (fraction bars, circles, rectangles) and number lines to understand that two fractions are equivalent if they represent the same size or the same point. For example, students will see that 1/2 and 2/4 cover the same amount of a shape and land on the same point on a number line.

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Understand Fraction Equivalence Using Models

Grade 3 · Equivalent Fractions · question 1 of 3

0 of 12

12 rungs. A star at the top.

A rectangle in 4 parts with 2 shaded is the same as 2.

How it is taught

0:00 of 3:27

Equivalent fractions name the same amount.

A model shows that different cuts can match.

Read it: Same chocolate, new name

Maya has 1 piece of chocolate, half a bar. Leo cuts his half into 2 and says he got more. The bar shows 1/2 = 2/4.

  1. Maya has 1 piece out of 2: 1/2.
  2. Leo cut his half into 2, so 2 pieces out of 4: 2/4.
  3. Slide Leo's 2 pieces together. They match Maya's 1.

Cutting into more pieces changes the count, not how much chocolate there is.

1/2 and 2/4 name the same amount — more pieces, each smaller.

A whole cut into 4 has parts half the size of a whole cut into 2, so 2 of them make the same half.

Cut each piece the same way: more pieces, same chocolate, a new name.

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

Fourths are smaller than halves. 2 of them make the same half.

4/8 = ___/6 — 3. 4/8 and 3/6 both fill half of the bar, so 4/8 = 3/6.

1/2 = 2/4

Today we'll find out when two fractions are actually equal — even if they look different.

Here's a bar split into two equal pieces. We shade one piece. That's one-half.

Now here's the same-size bar split into four equal pieces. We shade two of them. That's two-fourths.

Look — the shaded parts cover the exact same amount of bar.

When are two fractions equal?1224Same amount shaded!01142434122412 = 24EQUIVALENT12 = 24same point
Grade 3 · Same amount, different names

Let's check on a number line from zero to one.

One-half lands right in the middle.

Two-fourths lands on the very same point.

Same size, same point — so one-half and two-fourths are equivalent fractions!

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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