Cogito
Grade 5 Math · Chapter 2 · Lesson 3
A Fraction Is a Division
The leftover has a name after all.
10 problems · about 16 minutes · 5.NF.B.3
What this lesson teaches
The child interprets a fraction as division and writes a quotient as a fraction.
- a ÷ b can be written a/b.
- The leftover is shared out too, instead of being left over.
- Dividing a smaller number by a bigger one gives an answer under 1.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Dividing by Two Digits: 552 ÷ 24 = ?
Answer 23
Why 20 + 3 = 23.
Review — Multiplying Large Numbers: 124 × 12 = ?
Answer 1488
Why 1,488.
Warm Up
Straightforward practice. Get the method working first.
4 problems5 ÷ 8 as a fraction. What is the top number?
Answer 5
Why 5/8.
Must the number being divided be the bigger one?
Answer No. The answer is just less than 1.
Why That old rule stops being true this year.
2 ÷ 5 as a fraction. What is the top number?
Answer 2
Why The amount shared.
2 ÷ 5 as a fraction. What is the bottom number?
Answer 5
Why How many share it.
Build It Up
The same ideas with more to keep track of.
2 problems11 ÷ 3. How many whole ones?
Answer 3
Why 3 × 3 = 9.
Can you divide 4 by 6?
Answer Yes. The answer is 4/6.
Why The answer is less than 1.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Ribbon: 7 metres of ribbon shared among 8 people. What is the top number of the fraction each gets?
Answer 7
Why Each gets 7/8 of a metre.
The Cakes: 9 cakes shared among 4. How many whole cakes does each get?
Answer 2 whole cakes
Why 2 whole cakes, plus a quarter.