Mathematics
Grade 3
15 min
Compare fractions using models
Compare fractions using models
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the numerator and denominator of a fraction.
Represent fractions using area models (like rectangles and circles).
Represent fractions on a number line.
Compare two fractions with the same denominator by comparing their numerators.
Compare two fractions with the same numerator by comparing their denominators.
Use the symbols >, <, and = to correctly write a comparison of two fractions.
Would you rather have 1/2 of a pizza or 1/8 of a pizza? 🍕 Let's use models to figure out which piece is bigger!
In this lesson, we will learn how to compare fractions by looking at pictures called models. This helps us see which fraction is bigger, smaller, or if they are the same size. Understanding this is a key step to becoming a fractions superstar!...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that shows a part of a whole or a part of a group.1/4 is a fraction. It means 1 part out of 4 equal parts.
NumeratorThe top number in a fraction. It tells us how many equal parts we have.In the fraction 3/5, the numerator is 3.
DenominatorThe bottom number in a fraction. It tells us how many equal parts the whole is divided into.In the fraction 3/5, the denominator is 5.
Area ModelA picture, like a rectangle or a circle, that is divided into equal parts to show a fraction.A rectangle cut into 4 equal strips with 1 strip shaded shows the fraction 1/4.
Number LineA line with numbers on it that can be used to show the position and size of a fraction.A line from 0 to 1 can be split into 3 equal sections to show where 1/3 and 2/3 are.
Comparison SymbolsSy...
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Core Formulas
Greater Than
\frac{a}{b} > \frac{c}{d}
Use this symbol when the first fraction is larger than the second fraction. The symbol opens towards the bigger fraction, like an alligator's mouth eating the bigger meal.
Less Than
\frac{a}{b} < \frac{c}{d}
Use this symbol when the first fraction is smaller than the second fraction. The symbol points to the smaller fraction.
Equal To
\frac{a}{b} = \frac{c}{d}
Use this symbol when both fractions represent the same amount or value.
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Challenging
Two identical pies are modeled. Pie A is cut into 6 slices and 3 slices are eaten. Pie B is cut into 8 slices. How many slices of Pie B must be eaten to equal the amount eaten from Pie A?
A.3 slices
B.4 slices
C.5 slices
D.6 slices
Challenging
Look at the two fraction bar models. The top bar (Fraction X) shows a fraction greater than 1/2. The bottom bar (Fraction Y) shows a fraction with a denominator of 6. The model shows that Fraction X is greater than Fraction Y. Which pair could be Fraction X and Fraction Y?
A.X = 2/3, Y = 5/6
B.X = 3/4, Y = 4/6
C.X = 1/3, Y = 2/6
D.X = 5/8, Y = 2/6
Challenging
A student is shown three models that demonstrate 1/2 > 1/3, 1/3 > 1/4, and 1/4 > 1/5. Based on the pattern shown in these models, what is a true statement about fractions that have a 1 in the numerator?
A.As the denominator gets bigger, the fraction gets bigger.
B.The size of the denominator does not change the size of the fraction.
C.Fractions with a 1 in the numerator are always small.
D.As the denominator gets bigger, the fraction gets smaller.
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