Mathematics
Grade 6
15 min
Show fractions: area models
Show fractions: area models
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the numerator and denominator in a fraction represented by an area model.
Draw an area model to accurately represent a given proper fraction.
Write the fraction represented by a given shaded area model.
Use area models to represent and understand improper fractions and mixed numbers.
Compare two fractions by drawing and analyzing their respective area models.
Explain how area models demonstrate equivalent fractions.
Ever cut a pizza or share a chocolate bar with friends? 🍕🍫 How do you make sure everyone gets a fair share?
In this lesson, you'll learn how to visualize fractions using shapes called area models. This will help you understand what fractions truly represent and make them easier to work with in everyday situations.
Real-World...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole or a part of a collection.If you eat 1 slice of a pizza cut into 8 equal slices, you've eaten $\frac{1}{8}$ of the pizza.
NumeratorThe top number in a fraction, which tells you how many parts of the whole are being considered or taken.In the fraction $\frac{3}{4}$, the numerator is 3, meaning 3 parts are being considered.
DenominatorThe bottom number in a fraction, which tells you the total number of equal parts the whole has been divided into.In the fraction $\frac{3}{4}$, the denominator is 4, meaning the whole is divided into 4 equal parts.
Area ModelA visual representation of a fraction using a shape (like a rectangle or circle) divided into equal parts, where some parts are shaded to show the fraction.A rec...
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Core Formulas
Representing a Fraction with an Area Model
To represent a fraction $\frac{a}{b}$ using an area model, divide a whole shape into $b$ equal parts and shade $a$ of those parts.
This rule helps you draw a picture for any given fraction. The denominator ($b$) tells you how many total equal pieces to make, and the numerator ($a$) tells you how many of those pieces to color in.
Identifying a Fraction from an Area Model
To identify the fraction represented by an area model, count the number of shaded parts (this is the numerator) and count the total number of equal parts (this is the denominator).
This rule helps you read a fraction from a visual representation. Always ensure all parts are equal in size before counting.
Representing Improper Fractions/Mixed Numbers with Area Mod...
5 more steps in this tutorial
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Challenging
A circular pie is cut into 8 equal slices. 3 slices are eaten. What fraction of the *remaining* pie is the part that was eaten?
A.3/5
B.3/8
C.5/8
D.5/3
Challenging
An area model of a rectangle is partially covered. You can see that there are 4 shaded squares and 6 unshaded squares. All the squares are of equal size. What fraction of the rectangle is shaded?
A.4/6
B.6/10
C.4/10
D.It cannot be determined.
Challenging
Maria's garden is a square. She plants 3/5 of it with tomatoes. Leo's garden is an identical square. He plants 7/10 of it with carrots. How much more of the garden did Leo plant than Maria? Use area model logic to decide.
A.Leo planted 4/5 more.
B.Leo planted 1/10 more.
C.Maria planted 1/10 more.
D.They planted the same amount.
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