Week 5 of 10

Fraction Pizza Shop

Students run a pizza shop to learn that a fraction names equal parts of a whole - the denominator tells how many equal parts the whole is cut into, and the numerator tells how many are used - and compare and find equivalent fractions with pizza and fraction-bar models.

Estimated time: 45-60 minutes
Grade range: Grades 2-5
Skill focus: Fractions as equal parts, Numerator and denominator, Comparing simple fractions, Equivalent fractions
Theme: The Fraction Pizza Shop: every slice tells a story

The story

Business is booming at the Fraction Pizza Shop. A customer orders 'half a pizza,' the next wants 'three fourths,' and a third asks for 'two sixths.' The catch: every pizza must be cut into equal slices, or the orders won't be fair. As today's pizza chef, you'll learn to read every order like a fraction - and to spot when two different orders are secretly the same amount.

What you'll learn

Explain that the denominator tells how many equal parts a whole is split into and the numerator tells how many of those parts are used.
Compare two fractions with the same denominator, and use a model to compare fractions like 1/2 and 1/3.
Show with pizza or fraction-bar models that fractions such as 1/2 and 2/4 are equivalent.

Key ideas

Fractions only work when the parts are equal.
The denominator is the number of equal parts; the numerator is how many you take.
Different fractions can name the same amount (equivalent fractions).

Words to know

Fraction: A number that names equal parts of a whole.
Numerator: The top number; how many equal parts you have.
Denominator: The bottom number; how many equal parts the whole is split into.
Whole: The complete thing before it is cut into parts.
Equivalent fractions: Different fractions that name the same amount, like 1/2 and 2/4.
Equal parts: Parts that are exactly the same size.

The lesson

A fraction describes equal parts of a whole. The bottom number, the denominator, tells how many equal parts the whole is cut into. The top number, the numerator, tells how many of those parts you are talking about. In 3/4, the pizza is cut into 4 equal slices and you have 3 of them.

Equal parts matter. If you cut a pizza into four pieces but one is huge and three are tiny, you cannot call a small piece '1/4.' A fourth means one of four equal slices. This is the rule that makes fractions fair.

When two fractions have the same denominator, the one with the bigger numerator is bigger - 3/4 is more than 1/4 because you have more of the same-sized slices. When denominators differ, a model helps: cut one pizza into halves and another into thirds, and you can see 1/2 is bigger than 1/3, because splitting into fewer parts makes each part larger.

Some fractions look different but name the same amount. Cut a pizza in half, then cut each half again: now you have four pieces, and two of them (2/4) cover exactly the same amount as the original one half (1/2). Fractions that name the same amount are called equivalent.

Worked examples

In the fraction 5/8, what does each number mean?

8 = equal parts in the whole; 5 = parts being used

The denominator 8 says the whole is cut into 8 equal slices. The numerator 5 says we are talking about 5 of those slices.

Which is bigger, 2/3 or 1/3?

2/3

Same denominator (thirds), so compare the numerators: 2 slices of the same size are more than 1 slice.

Is 1/2 equivalent to 2/4?

Yes

Cutting each half of a pizza into two makes four equal pieces; two of them (2/4) cover the same amount as one half (1/2), so they are equivalent.

Try it: interactive practice

This is the week's practice game. Work through it right here - try each step yourself, then check your thinking.

Activity

Fill the Pizza Order

Setting the denominator (slices) and then the numerator (shaded slices) separately makes the two jobs of a fraction concrete and hard to mix up.

Task 1 of 7

Shade the bar to show 1/2. Click a part to shade or unshade it.

Shaded: 0 of 2 equal parts

Hands-on challenge

Paper Pizza Fractions

What you need

Paper circles
Scissors
Crayons or markers

Steps

1
Cut three paper circles ('pizzas') the same size.
2
Fold and cut one into halves, one into fourths, and one into eighths, keeping the slices equal.
3
Build orders by combining slices, then find two different ways to make one half (for example, 2/4 and 4/8).

You've got it when: You can lay slices on top of each other to prove two fractions are equivalent and explain why the parts must be equal.

Checkpoint

Quick checks before you move on. Try each one first, then reveal the answer.

1
In 4/6, which number is the denominator and what does it tell you?
Show answer
6 is the denominator; it tells you the whole is cut into 6 equal parts.
2
Which is larger, 3/5 or 2/5?
Show answer
3/5, because with equal fifths, three parts are more than two.
3
Name a fraction equivalent to 1/2.
Show answer
2/4 (also 3/6 or 4/8) - all name the same amount.

Think about it

Why must the pieces of a pizza be equal before we can call one piece '1/4'? What goes wrong if they aren't equal?

Challenge problem

Maria ate 2/4 of a pizza and Sam ate 1/2 of an identical pizza. Who ate more, or did they eat the same amount? Prove it.

Show hint

Try drawing both pizzas with equal slices, or find a fraction equivalent to one of the amounts so both have the same denominator.

Show answer

They ate the same amount. 2/4 is equivalent to 1/2, so both ate half the pizza.

Extension · go further

Design a pizza-shop menu with three deals written as fractions, then find an equivalent fraction for each deal so customers see they're getting a fair amount.

Finished the lesson, activity, and challenge? Mark this week complete to track your progress through the 10-week course.