Cogito
Grade 5 Math · Chapter 6 · Lesson 2
Multiplying as Scaling
Decide the size before you multiply.
10 problems · about 16 minutes · 5.NF.B.5
What this lesson teaches
The child compares a product to its factor without carrying out the multiplication.
- Multiplying resizes a number.
- Over 1 grows it, under 1 shrinks it, exactly 1 leaves it.
- You can answer "bigger or smaller?" without any working.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — A Fraction of a Fraction: 3/4 × 2/5. What is the bottom number?
Answer 20
Why 6/20, which tidies to 3/10.
Review — Line Plots and Fraction Data: 5 beakers at 2/8 litre. How many eighths in all?
Answer 10
Why 10/8 litres.
Warm Up
Straightforward practice. Get the method working first.
4 problemsWhat is 3/5 × 25?
Answer 15
Why 15.
Can you tell if a product is bigger than its factor without multiplying?
Answer Yes. Compare the other factor with 1.
Why The factor against 1 decides it every time.
Is 7/8 × 40 more or less than 40?
Answer Less.
Why 7/8 is under 1.
Is 9/8 × 40 more or less than 40?
Answer More.
Why 9/8 is over 1.
Build It Up
The same ideas with more to keep track of.
2 problemsWhat is 6/6 × 30?
Answer 30
Why 6/6 is exactly 1.
What is 2/5 × 20?
Answer 8
Why 20 ÷ 5 = 4, then 4 × 2.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsBigger or Smaller?: Is 5/4 × 12 more or less than 12?
Answer More.
Why A factor over 1 makes it bigger.
The Exact One: What is 3/4 × 20?
Answer 15
Why 15, which is indeed less than 20.