Cogito
Grade 5 Math · Chapter 1 · Lesson 2
Powers of Ten
A short way to write a long number.
10 problems · about 15 minutes · 5.NBT.A.2
What this lesson teaches
The child uses whole-number exponents to write powers of ten and explains the pattern of zeros.
- 10³ means three tens multiplied together.
- The exponent matches the number of zeros.
- A power of ten is a multiplication, not a repeated addition.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Ten Times and One Tenth: 600 ÷ 10 = ?
Answer 60
Why 60.
Review — Ten Times and One Tenth: What does moving a digit one place left do to its value?
Answer Multiplies it by 10.
Why Each place left is worth ten times more.
Warm Up
Straightforward practice. Get the method working first.
4 problemsWhat is 7 × 10² ?
Answer 700
Why 700.
What does the exponent count?
Answer How many tens are multiplied.
Why It counts multiplications, not additions.
What is 10² ?
Answer 100
Why Two zeros.
What is 10⁵ ?
Answer 100000
Why Five zeros.
Build It Up
The same ideas with more to keep track of.
2 problemsHow many zeros does 10⁴ have?
Answer 4
Why The exponent says.
Is 10³ the same as 30?
Answer No. It is 1,000.
Why Multiplied, not added.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Short Way: What is 10³ written out in full?
Answer 1000
Why 1,000.
The Big One: What is 4 × 10³?
Answer 4000
Why 4,000.