Naming and Introducing Exponents
Exponents are a form of math shorthand. They tell us how many times to multiply the base by itself. You may also hear exponents referred to as powers or indices depending on the reference source you are using. You may also see an exponent indicated by the use of upward carrot symbol (^). The number located before (left of) that symbol is the base number and the number located after (right of) that symbol is the exponent. As an example 83 may be written as 8^3. These worksheets and lessons introduce the concept of an exponent to students.
Aligned Standard: 5.NBT.A.2
- Step-by-Step Lesson- We work on converting back and forth between exponential form and expanded form.
- Guided Lesson - We work on both conversion formats twice each.
- Guided Lesson Explanation - We aimed to make this very visual and vivid for kids.
- Practice Worksheet - Condense the expanded form by using exponents.
- Introducing Exponents Worksheet - This covers everything for this skill.
- Answer Keys - These are for all the unlocked materials above.
Introduction to Exponents Sheets
Complete the table for: Power, Base, Exponent, Expanded form, Value.
- Homework 2 - Complete the blanks in the table below.
- Homework 3 - Label the Power, Base, and the Exponent.
Naming the Exponents Worksheets
Name the following exponents using either numbers or words to complete the table.
- Practice 1 - Name the following exponents using either numbers or words to complete the table.
- Practice 2 - Put the value in your own words.
- Practice 3 - Write the missing number or words to name the exponents.
- Practice 4 - Convert the values between the number names and words.
Start with expanded form and make yourself an exponent.
- Practice 2 - Write the following expanded form problems as exponents.
- Practice 3 - Have another go at it!
An exponent indicates how many times a number is to be multiplied by itself. If you look to the right, you will see the exponent 43 and how it is equal to 4 x 4 x4. The larger number to the left is called the base number that is the value you will be multiplying. The little number in the upper right corner of the base number is the exponent and that indicates how many times the base number will be multiplied by itself.
What is the Difference Between the Expanded Form to Exponential Form?
There are two different methods that we can use to write numbers. You can either use the expanded form to write a number, or you can simplify the number by writing it in exponential form. The values are the same, just the way in which they are viewed is different. This is kind of a mathematically slag. For instance, our culture refers to money with many different terms such as: bucks, bread, cabbage, cash, coin, moolah, bones, clams. It all is intended to me the same thing; it just is presented differently.
Expanded form is a technique where you write a number by breaking it according to their place values. It is a form where we clearly write down a number where the value of each digit is clearly visible. If you have to write the number 1,238 in its expanded form, you divide it into its place values.
The number comprises of one 1000, two 100s, three 10s, and eight 1s.
The expanded form can be written as 1000 + 200 + 30 + 8
The second method that we can use to write a number in is the exponential form that we also refer to as the scientific notation. It is a simple way to write numbers that are too big or too small. Moreover, if a number is being multiplied repeatedly, we can write it in the exponential form. Exponential form is a shortcut for repeating multiplication. When it comes to scientific notation, we are repeatedly multiplying a 10. Taking that same value, we explored before (1,238) if we were to write it in scientific notation it would be written as 1.238 x 103.