Cogito
Grade 4 Math · Chapter 5 · Lesson 5
Why 1/2 + 1/3 Is Not 2/5
You cannot count two different things together.
10 problems · about 15 minutes · 4.NF.B.3
What this lesson teaches
The child explains why unlike denominators cannot be added directly.
- Adding the bottom numbers gives a wrong answer.
- Different units cannot be counted together.
- Rewrite both in one unit first, then count.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Adding Fractions with the Same Unit: 3/10 + 4/10. What is the top number of the answer?
Answer 7
Why 7/10.
Review — Comparing Unlike Fractions: 2/3 written in twelfths has what top number?
Answer 8
Why 2/3 = 8/12.
Review — Equivalent Fractions: 2/3 = ?/9. What is the top number?
Answer 6
Why 2/3 = 6/9.
Warm Up
Straightforward practice. Get the method working first.
3 problems1/4 + 1/2, in quarters. What is the top number?
Answer 3
Why 1/4 + 2/4 = 3/4.
How can you tell 2/5 is a wrong answer to 1/2 + 1/3?
Answer It is smaller than the half you started with.
Why Adding made it smaller, which is impossible.
1/2 + 1/3, in sixths. What is the top number?
Answer 5
Why 3/6 + 2/6.
Build It Up
The same ideas with more to keep track of.
1 problem1/3 + 1/6, in sixths. What is the top number?
Answer 3
Why 2/6 + 1/6.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsCan you add halves and thirds by counting them together?
Answer No. They are different units.
Why Apples and elephants.
The Size Test: Is 1/2 + 1/4 bigger or smaller than 1/2?
Answer Bigger.
Why Adding always makes a sum bigger than either part.
In Quarters: 1/2 + 1/4, written in quarters. What is the top number?
Answer 3
Why 2/4 + 1/4 = 3/4.