Cogito
Grade 3 Math · Chapter 5 · Lesson 10
Fractions of Different Wholes
Half of what?
10 problems · about 13 minutes · 3.NF.A.3
What this lesson teaches
The child recognizes that comparing fractions is only meaningful when the wholes are the same.
- A fraction of a big thing is bigger than the same fraction of a small thing.
- Comparisons only work when the wholes match.
- Always ask: a fraction of what?
Warm-Up Review
From earlier lessons. Loosen up before the new work.
4 problemsReview — Fractions Greater Than One: How many fifths land on the 2?
Answer 10
Why 10/5 = 2.
Review — Equivalent Fractions: How many sixths equal 1/3?
Answer 2
Why 1/3 = 2/6.
Review — Comparing Fractions With the Same Top: Which is bigger, 3/4 or 3/6?
Answer 3/4
Why Fourths are bigger pieces than sixths.
Review — Comparing Fractions With the Same Bottom: Which is bigger, 3/4 or 1/4?
Answer 3/4
Why 3 fourths beats 1 fourth.
Warm Up
Straightforward practice. Get the method working first.
3 problemsTwo same-size pizzas. Which is more, 3/4 or 1/2?
Answer 3/4
Why 3/4 is greater than 1/2 of the same whole.
What must be true before you compare two fractions?
Answer They must be parts of the same whole.
Why Without a shared whole, the comparison has no meaning.
Is 1/2 always more than 1/3?
Answer Only if they are parts of the same whole.
Why Think about a huge cake and a tiny one.
Build It Up
The same ideas with more to keep track of.
1 problemTwo same-size bars. Which is more, 2/3 or 2/5?
Answer 2/3
Why Same whole, so compare piece sizes.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsTwo Different Cakes: Ana eats 1/2 of a small cake. Leo eats 1/4 of a huge cake. Who ate more cake?
Answer You cannot tell without the cake sizes.
Why Fractions of different wholes cannot be compared directly.
The Same Cake: Two people share one cake. One takes 1/2 and one takes 1/4. Who took more?
Answer The one who took 1/2.
Why With one shared whole, 1/2 is greater than 1/4.