OML Search



Videos to help Grade 6 students learn what are exponents and how to use exponents

New York State Common Core Math Module 4, Grade 6, Lesson 5

Related Topics:
Lesson Plans and Worksheets for Grade 6

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 6

Common Core For Grade 6

Lesson 5 Student Outcomes

Students discover that 3x = x + x + x is not the same thing as x3 which is x • x • x.

Students understand that a base number can be represented with a positive whole number, positive fraction, or positive decimal and that for any number b, we define bm to be m factors of b where b is the base and m is called the exponent or power of b.

Opening Exercise

As you evaluate these expressions, pay attention to how you arrive at your answers.

4 + 4 + 4 + 4 + 4 + 4 + 4 +4 + 4 + 4
9 + 9 + 9 + 9 + 9
10 + 10 + 10 + 10 + 10

Multiplication is a faster way to add numbers when the addends are the same.

When we add five groups of 10, we use an abbreviation and a different notation, called multiplication.
10 + 10 + 10 + 10 + 10 = 10 × 5 = 50.

If multiplication is a more efficient way to represent addition problems involving the repeated addition of the same addend, do you think there might be a more efficient way to represent the repeated multiplication of the same factor, as in 10 x 10 x 10 x 10 x 10.

When we add 5 groups of 10, we write 5 × 10, but when we multiply 5 copies of 10, we write 105. So, multiplication by 5 in the context of addition corresponds exactly to the exponent in the context of multiplication.

The repeated factor is called the base and the exponent is also called the power.

There is a special name for numbers raised to the second power. When a number is raised to the second power, it is called squared.

There is also a special name for numbers raised to the third power. When a number is raised to the third power, it is called cubed.

Write equivalent expressions:
5 × 5 × 5 × 5 × 5
2 × 2 × 2 × 2

2. What is the difference between 3g and g3?

The base number can be written in decimal or fraction form.


1. Fill in the missing expressions for each row. For whole number and decimal bases, use a calculator to find the standard form of the number. For fraction bases, leave your answer as a fraction.

2. Write “five cubed” in all three forms: exponential form, written as a series of products, standard form.

3. Write “fourteen and seven tenths squared” in all three forms.

4. One student thought two to the third power was equal to six. What mistake do you think they made and how would you help them fix their mistake?

Lesson Summary

Exponential Notation for Whole Number Exponents: Let be a non-zero whole number. For any number b, the expression bm is the product of m factors of b.

The number b is called the base, and m is called the exponent or power of b.

When m is 1, “the product of one factor of ” just means b, i.e. b1 = b. Raising any non-zero number to the power of 0 is defined to be 1, i.e., b0 = 1 for all b ≠ 0.


Lesson 5 Examples and Exercises

Examples 1 - 5
Go back to Examples 1–4 and use a calculator to evaluate the expressions.

Example 6

Example 7
2.1 × 2.1

Example 8
0.75 × 0.75 × 0.75

The base number can also be a fraction. Convert the decimals to fractions in Examples 7 and 8 and evaluate. Leave your answer as a fraction.

Example 9
1/2 × 1/2 × 1/2

Example 10

Exercises 1 - 4

Lesson 5 Exit Ticket

1. What is the difference between 6z and z6?

2. Write 10 3as a multiplication expression having repeated factors.

3. Write 8 × 8 × 8 × 8 using exponents.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site

follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines