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Justify Fraction Comparisons with Models and Reasoning

Students will use visual models (area models, number lines, fraction bars) and written or verbal reasoning to explain and justify comparisons between two fractions with the same numerator or same denominator. Students will also recognize that comparisons are valid only when both fractions refer to the same whole.

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Justify Fraction Comparisons with Models and Reasoning

Grade 3 · Comparing Fractions · question 1 of 3

0 of 12

12 rungs. A star at the top.

Which of these makes 3/4 > blank true: 1/4, 3/4, 7/4 or 8/4?

How it is taught

0:00 of 3:30

Same-size wholes let you compare fractions fairly.

More same-size pieces means a greater fraction.

Read it: Bigger pieces, more chocolate

Maya has 3/4 of a bar. Leo has 3/8 of the same bar. 3 pieces each — but look at how big those pieces are.

  1. See Maya's 3 shaded pieces: her bar is cut into 4.
  2. See Leo's 3 shaded pieces: his bar is cut into 8.
  3. Compare the piece size: fourths are bigger, so 3/4 is more.

Counting 3 against 3 looks even, but Leo's eighths are smaller parts of the same bar.

A whole cut into 4 has bigger parts than a whole cut into 8.

3 big fourths cover more of the bar than 3 small eighths.

Same top number, same whole: the bar cut into fewer parts has bigger parts, so 3/4 is more than 3/8.

Seeing 8 on the bottom and saying 3/8 is more, because 8 is bigger than 4.

8 on the bottom means the whole is cut into smaller parts, so 3 of them are less than 3/4.

Which is more, 2/4 or 2/6? — 2/4. A whole cut into 4 has bigger parts than a whole cut into 6, so 2/4 is more than 2/6.

Compare 2/3 and 2/5

Let's compare two fractions: two-thirds and two-fifths. Which one is bigger?

First, an important rule — both fractions must be about the same-size whole. Same pizza, same bar.

Here's a bar split into three equal pieces. We shade two of them — that's two-thirds.

Here's the same-size bar split into five equal pieces. We shade two — that's two-fifths.

Look at the pieces themselves. Thirds are bigger because we split the bar fewer times.

Two big pieces cover more bar than two small pieces.

Which is bigger: 23 or 25?Same-size whole!Comparisons only work on equal wholes.2325More bar covered ↑Same numerator → smaller denominator winsfewer splits = bigger pieces23 > 25ANSWER23 > 25bigger pieces win
Grade 3 · Same numerator, different denominators

When the numerators match, the fraction with the smaller denominator wins — its pieces are bigger.

So we write two-thirds is greater than two-fifths.

Two-thirds is greater than two-fifths. Same number of pieces, but bigger pieces win!

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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