Cogito
Grade 5 Math · Chapter 4 · Lesson 3
When Multiplying Makes Things Smaller
A rule that has finally run out.
10 problems · about 16 minutes · 5.NBT.B.7, 5.NF.B.5
What this lesson teaches
The child explains why multiplying by a number less than 1 gives a smaller answer.
- Multiplying does not always make things bigger.
- A factor over 1 grows it, under 1 shrinks it.
- A factor of exactly 1 changes nothing.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Multiplying a Decimal by a Whole Number: 9 × 0.3, in tenths?
Answer 27
Why 27 tenths, which is 2.7.
Review — Multiplying by Powers of Ten: 0.08 × 100 = ?
Answer 8
Why 8.
Warm Up
Straightforward practice. Get the method working first.
4 problemsWhat is 0.25 × 40?
Answer 10
Why 10.
What decides whether multiplying grows or shrinks a number?
Answer Whether the factor is more or less than 1.
Why More than 1 grows it, less than 1 shrinks it.
Will 0.3 × 40 be bigger or smaller than 40?
Answer Smaller.
Why 0.3 is less than 1.
Will 1.5 × 40 be bigger or smaller than 40?
Answer Bigger.
Why 1.5 is more than 1.
Build It Up
The same ideas with more to keep track of.
2 problemsWhat is 0.5 × 30?
Answer 15
Why Half of 30.
What is 1 × 30?
Answer 30
Why Multiplying by 1 changes nothing.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsHalf of It: What is 0.5 × 12?
Answer 6
Why 6, which is smaller than 12.
A Quarter of It: What is 0.25 × 20?
Answer 5
Why 5, much smaller than 20.