Grade 3 (age 8-9)

Introduction to Fractions

A fraction is a number showing how many parts of a whole you have when it is divided into equal pieces. Cut a pizza into 4 equal slices, eat 1, and that is one-fourth, written as ¼. The denominator on the bottom is how many pieces the whole is split into and the numerator on top is how many you have, so a bigger denominator makes each piece smaller. Drag the sliders for the slices and the colored slices to explore fraction sizes with the pizza and bars.

What is a Fraction?

🍕 Think with Pizza!

①Cut pizza into 4 slices

②Eat 1 slice?

③1 of 4 slices = "one-fourth"

④Write it as ¼!

Fractions with Pizza

Total Slices (Denominator)4

Colored Slices (Numerator)1

💡 Numerator and Denominator

①Denominator = bottom = how many parts the whole is split into

②Numerator = top = how many you have

③Bigger denominator = smaller each piece!

Compare with Bars

📏 Size of Fractions

①Same denominator: bigger numerator = bigger fraction

②Same numerator: bigger denominator = smaller fraction

③Numerator = denominator → whole = 1!

Summary

Fraction Structure

numeratordenominator

Top = numerator (how many), bottom = denominator (total parts)

Unit Fraction

12, 13, 14 ...

Fractions with numerator 1 are unit fractions

Fraction = 1

denominatordenominator = 1

Numerator = denominator → 1 (whole)

🎯 Key Points

①Fraction = part of an equally divided whole

②Denominator is bottom, numerator is top

③Same denominator: bigger numerator = bigger

④Bigger denominator = smaller each piece

⑤Numerator = denominator → 1 (whole)

Examples and Unit Test

Example 1

A pizza is cut into 4 equal slices and 1 is colored. Write the colored part as a fraction.

The total slices, 4, is the denominator; the colored slices, 1, is the numerator.

Numerator 1, denominator 4, so it is one-fourth.

▸ 14 (one-fourth)

The denominator is the total parts; the numerator is the colored (held) parts.

Example 2

Which is greater, three-fifths or two-fifths?

The denominators are both 5, so compare only the numerators.

Numerator 3 is bigger than numerator 2, so three-fifths is greater.

▸ 35 (three-fifths)

With the same denominator, a bigger numerator means a bigger fraction.

Unit Test

What does six-sixths equal?

①0

②16

③1

④6

▸ ③ 1

The numerator and denominator are both 6.

Numerator = denominator means the whole, which is 1.

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Division

Plane Figures