Cogito
Grade 4 Math · Chapter 5 · Lesson 2
Equivalent Fractions
Same amount, cut a different way.
10 problems · about 15 minutes · 4.NF.A.1
What this lesson teaches
The child explains why a/b equals (n × a)/(n × b) using a visual model.
- Equivalent fractions are the same amount written differently.
- Cutting every piece the same way changes both numbers together.
- The amount on the line never moves.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — A Fraction Counts Units: How many sixths are in 5/6?
Answer 5
Why 5/6 is 5 copies of 1/6.
Review — Number Patterns: Start at 7, add 4. What is the 5th term?
Answer 23
Why Four steps of 4 from 7 gives 23.
Warm Up
Straightforward practice. Get the method working first.
4 problems2/3 = ?/9. What is the top number?
Answer 6
Why 2/3 = 6/9.
Why do both numbers change together?
Answer Every piece is cut the same way.
Why Cutting every piece the same way changes both numbers by the same factor.
1/2 = ?/10. What is the top number?
Answer 5
Why 2 × 5 = 10.
2/5 = ?/10. What is the top number?
Answer 4
Why Both numbers double.
Build It Up
The same ideas with more to keep track of.
2 problems3/4 = 9/?. What is the bottom number?
Answer 12
Why 3 × 3 = 9, so 4 × 3.
Does cutting a cake into more slices give more cake?
Answer No. Only smaller slices.
Why The amount does not change.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Same Amount: 3/4 written in eighths has what top number?
Answer 6
Why 3/4 = 6/8.
The Cake: 1/3 written in twelfths has what top number?
Answer 4
Why 1/3 = 4/12.