Mathematics
Grade 3
15 min
Add fractions with like denominators using number lines
Add fractions with like denominators using number lines
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1
Introduction & Learning Objectives
Learning Objectives
Identify the whole and the fractional parts on a number line derived from a two-dimensional shape.
Represent a fraction with a like denominator as a 'jump' on a number line.
Use a number line to model the addition of two fractions with the same denominator.
Write an equation that represents the addition of fractions shown on a number line.
Explain how partitioning a rectangle into equal parts relates to the tick marks on a number line between 0 and 1.
Solve simple word problems involving adding fractions by drawing and using a number line.
Imagine you have a long rectangular garden divided into 8 equal rows. If you plant carrots in 3/8 of the garden and lettuce in 2/8, how can we show this on a line to see how much you've planted? 🥕
In th...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that shows a part of a whole. A fraction is made of two parts: a numerator and a denominator.1/4 of a square is one part out of four 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.
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, meaning the whole is split into 5 equal parts.
Like DenominatorsWhen two or more fractions have the same bottom number (denominator).2/8 and 5/8 have like denominators because they are both 8.
Number LineA straight line with numbers placed at equal intervals. We can use it to show fractions between whole numbers like 0 and 1.A line...
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Core Formulas
Adding Fractions Rule
\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}
When the denominators (bottom numbers) are the same, you just add the numerators (top numbers). The denominator stays the same because the size of the pieces doesn't change.
Number Line Starting Point
Start at 0
When modeling fraction addition on a number line, your first 'jump' always begins at the 0 mark.
Jumps on the Number Line
Numerator = Number of Spaces to Jump
The numerator of each fraction tells you how many spaces to jump forward from your current position on the number line.
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Challenging
A number line from 0 to 1 represents the perimeter of a square. A spider starts at 0, crawls 2/8 of the way, and then crawls another 3/8. On which side of the square does the spider stop? (Assume the corners are at 0, 2/8, 4/8, and 6/8).
A.The first side (from 0 to 2/8)
B.The second side (from 2/8 to 4/8)
C.The third side (from 4/8 to 6/8)
D.The fourth side (from 6/8 to 8/8)
Challenging
A path covers the perimeter of two identical hexagons. The path is shown on a number line from 0 to 2. A bee flies 4/6 of the way around the first hexagon, then 3/6 of the way around the second hexagon. Which number line correctly shows the bee's final position?
A.number line showing a jump from 0 to 4/6, then a jump of 3/6 to 7/6 (or 1 and 1/6).
B.number line showing a jump from 0 to 1, then a jump of 1/6 to 1 and 1/6.
C.number line showing a single jump from 0 to 7/6.
D.number line showing a jump from 0 to 4/6, then a jump of 3/6 to 1.
Challenging
A rectangular rug is 10 feet long, marked in tenths on a number line. A toy car starts at 2/10. It moves forward a fraction with a denominator of 10. It stops on the rug somewhere *after* the 6/10 mark but *before* the 9/10 mark. Which addition could be shown on the number line?
A.2/10 + 3/10 = 5/10
B.2/10 + 4/10 = 6/10
C.2/10 + 7/10 = 9/10
D.2/10 + 5/10 = 7/10
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