014. Powers and Index Notation
Learning Intentions
- To know the meaning of the terms: powers, index form, basic numeral, base number and index number
- To understand what
means when and are whole numbers - write a product in index form if there are repeated factors
- Evaluate numeric expressions involving powers Use multiplication
Pre-requisite Summary
- Understanding multiplication as repeated addition
- Knowledge of multiplication facts
- Understanding repeated multiplication (e.g.
) - Ability to multiply whole numbers
- Understanding mathematical notation and brackets
Worked Examples
Worked Example 1
Identify the terms in:
a)
b)
Worked Example 2
Write in expanded form:
a)
b)
c)
Worked Example 3
Write in index form:
a)
b)
c)
Worked Example 4
Evaluate using multiplication:
a)
b)
c)
Worked Example 5
Evaluate expressions involving powers:
a)
b)
c)
Problems
Problem 1
Identify the terms:
a)
b)
Problem 2
Write in expanded form:
a)
b)
c)
Problem 3
Write in index form:
a)
b)
c)
Problem 4
Evaluate:
a)
b)
c)
Problem 5
Evaluate expressions:
a)
b)
c)
Exercises
Understanding and Fluency
Exercise 1.
Identify base and index:
a)
b)
c)
Exercise 2.
Write in expanded form:
a)
b)
c)
Exercise 3.
Write in index form:
a)
b)
c)
Exercise 4.
Evaluate powers:
a)
b)
c)
Exercise 5.
Evaluate expressions:
a)
b)
c)
Exercise 6.
Mixed practice:
a)
b)
c)
Reasoning
Exercise 7.
Explain what
Exercise 8.
A student says
Exercise 9.
Compare
Exercise 10.
Why is
Problem-solving
Exercise 11.
A cube has side length
Exercise 12.
A square has side length
Exercise 13.
Find the value of
Exercise 14.
A number is written as
Exercise 15.
Evaluate
Potential Misunderstandings
- Students may think
means - Students may confuse base and index
- Students may stop multiplying too early when expanding powers
- Students may incorrectly write repeated multiplication in index form
- Students may evaluate multiplication before powers incorrectly
- Students may think
instead of