Mathematics
Grade 3
15 min
Compare fractions using models
Compare fractions using models
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1
Introduction & Learning Objectives
Learning Objectives
Use area models (rectangles and circles) to compare fractions with the same numerator.
Use area models to compare fractions with the same denominator.
Use a number line to visually compare the size of two fractions.
Correctly use the symbols >, <, and = to write comparison statements based on visual models.
Explain why one fraction is greater than, less than, or equal to another by referring to a visual model.
Create their own visual fraction models to represent and compare fractions.
Would you rather have 1/2 of a pizza or 1/4 of a pizza? 🍕 Let's use pictures to find out which slice is bigger!
In this lesson, we will learn how to use pictures, like rectangles and number lines, to see which fraction is bigger. This is a very useful skill for...
2
Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that shows a part of a whole. The whole must be divided into equal parts.The fraction 1/4 means we have 1 part out of 4 equal parts.
NumeratorThe top number in a fraction. It tells us how many equal parts we are talking about.In the fraction 3/5, the numerator is 3. It means we have 3 parts.
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. It means the whole is cut into 5 equal parts.
Area ModelA picture, like a circle or a rectangle, that is divided into equal parts to show a fraction.A rectangle cut into 3 equal parts with 1 part shaded is an area model for 1/3.
Number Line ModelA line with numbers marked on it. We can show fractions on a number line be...
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Core Formulas
Comparing Fractions with the Same Denominator
If $\frac{a}{c}$ and $\frac{b}{c}$ have the same denominator, the fraction with the larger numerator is greater. If $a > b$, then $\frac{a}{c} > \frac{b}{c}$.
When the total number of pieces (denominator) is the same, you just need to see who has more pieces (numerator). A model will show that more shaded pieces of the same size make a bigger fraction.
Comparing Fractions with the Same Numerator
If $\frac{a}{b}$ and $\frac{a}{c}$ have the same numerator, the fraction with the smaller denominator is greater. If $b < c$, then $\frac{a}{b} > \frac{a}{c}$.
When you have the same number of pieces (numerator), think about the size of each piece. A smaller denominator means the whole was cut into fewer, bigger pieces. A mode...
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Challenging
A student's model attempts to show 1/2. The rectangle is divided into two parts, but one part is much larger than the other. The student uses this model to claim that 1/2 is less than 1/4. What is the main reason their model of 1/2 is incorrect?
A.The whole rectangle is too big.
B.The parts are not equal.
C.The shading is on the wrong side.
D.fraction of 1/2 must be shown with a circle.
Challenging
Four students model the fraction of a project they have completed. Amy's number line shows she is at 3/5. Ben's circle graph shows he has completed 4/8. Chloe's fraction strip shows she has done 5/10. David's rectangular model shows he has finished 2/3. Based on the models, who has completed the MOST of their project?
A.Amy
B.Ben
C.Chloe
D.David
Challenging
Model X shows a rectangle with 4/6 shaded. Model Y shows an identical rectangle with 4/8 shaded. Which statement correctly compares the fractions and gives the correct reason?
A.4/6 < 4/8 because a whole cut into 6 pieces has smaller pieces.
B.4/6 > 4/8 because sixths are larger pieces than eighths.
C.4/6 = 4/8 because the numerators are both 4.
D.4/6 < 4/8 because the unshaded part in Model X is smaller.
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