Cogito
Grade 3 Math · Chapter 5 · Lesson 7
Comparing Fractions With the Same Top
Same number of pieces, so the piece size decides.
10 problems · about 13 minutes · 3.NF.A.3
What this lesson teaches
The child compares two fractions with the same numerator by reasoning about piece size.
- Same top number means the same number of pieces.
- Then the bigger denominator loses, because its pieces are smaller.
- A bigger bottom number never means a bigger fraction.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Comparing Fractions With the Same Bottom: Which is bigger, 3/4 or 1/4?
Answer 3/4
Why 3 fourths beats 1 fourth.
Review — Fractions Equal to One: 6/6 equals which whole number?
Answer 1
Why 6/6 = 1.
Review — Fractions on the Number Line: A line cut into 5 parts. How many parts along is 2/5?
Answer 2
Why 2/5 is two parts along from 0.
Warm Up
Straightforward practice. Get the method working first.
3 problemsWhich is bigger, 3/4 or 3/6?
Answer 3/4
Why Fourths are bigger pieces than sixths.
Does a bigger bottom number mean a bigger fraction?
Answer No. It means smaller pieces.
Why A bigger denominator cuts the whole into more, smaller pieces.
Which is bigger, 4/5 or 4/8?
Answer 4/5
Why Fifths are bigger pieces.
Build It Up
The same ideas with more to keep track of.
1 problemWhich is bigger, 1/2 or 1/6?
Answer 1/2
Why Halves are much bigger pieces.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsWhich is bigger, 5/6 or 5/8?
Answer 5/6
Why Sixths are bigger than eighths.
Two Cakes: Would you rather have 3/4 of a cake or 3/8 of the same cake?
Answer 3/4.
Why Fourths are bigger than eighths, so 3/4 is more.
The Ribbon: Which is longer, 2/5 of a metre or 2/8 of a metre?
Answer 2/5.
Why 2/5 is longer.