Record Fraction Comparisons with >, =, and < Symbols

Students compare two fractions using multiple strategies (common denominators, benchmarks, number lines) and record the result using the correct inequality or equality symbol. They justify their comparisons with reasoning.

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Grade 4 · Comparing Fractions · question 1 of 3

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20 rungs. A star at the top.

Vic helped at the zoo and gave the parrots of a bag of seeds. The monkeys got of the same bag. Choose the symbol sentence that is true.

How it is taught

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Fractions with the same bottom can be compared by the tops.

The larger top means the larger share of the same whole.

Read it: Hold each fraction against a half

Which is more, 2/3 or 3/8? 2 is more than half of 3, and 3 is less than half of 8, so 2/3 is the greater fraction.

Pick a benchmark both fractions are near: 1/2 or 1 whole.
Decide if each fraction is more or less than the benchmark.
The one above the benchmark is greater. Write the sign with its open side toward it.

A fraction is more than 1/2 when its top number is more than half of its bottom number.

If one fraction is above the benchmark and the other below, the benchmark sits between them.

Then no common denominator is needed to tell which is greater.

Compare each fraction with 1/2 or 1. The benchmark decides which is greater.

Calling 3/8 greater because 8 is a bigger number than 3.

Eighths are smaller pieces than thirds. 3/8 is less than 1/2 and 2/3 is more, so 2/3 is greater.

5/12 ___ 4/6 — <. 4/6 is more than 1/2 and 5/12 is less, so 5/12 < 4/6.

Compare 3/4 and 2/3

Today we'll compare two fractions and record what we see using the greater-than, less-than, or equal symbol.

Here are our two fractions: three-fourths and two-thirds. Which one is bigger?

Let's draw a bar for each fraction so we can see them.

We shade three of the four parts, and two of the three parts.

The pieces are different sizes, so let's rewrite both fractions with the same-size pieces. Twelfths work for both four and three.

Multiply the top and bottom of three-fourths by three. That gives us nine-twelfths.

Multiply the top and bottom of two-thirds by four. That gives us eight-twelfths.

Now the bottoms match, so we just compare the tops. Nine is greater than eight.

Grade 4 · Use common denominators, then record with the right symbol

We record this as three-fourths is greater than two-thirds, using the greater-than symbol.

Tip: the symbol always opens toward the bigger number — like an alligator's mouth chomping the bigger snack.

Three-fourths is greater than two-thirds. Now you can record any comparison with greater-than, less-than, or equals.

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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