All About Exponents
A few explanation videos are imbedded but most videos are through a link because they exceeded the upload size.
- Represent repeated multiplication with exponents
Repeated multiplication means a certain number being multiplied any number of times. (See example 1) This can also apply to any negative number (see example 2). To turn a number into a power you write the base, (see example 3) which is the number being multiplied, then count the amount of times the number is being multiplied and write that as the exponent. Representing repeated multiplication with exponents saves a lot of time and space.
- Describe how powers represent repeated multiplication.
In the first learning outcome we learned how to represent repeated multiplication as an exponent, for this PLO we will learn about the opposite, how to turn powers into repeated multiplication. Just a reminder, repeated multiplication looks like (see example 1) and can be called the expanded form of a power. To turn a power such as (see example 2) into repeated multiplication you must first see what number the base is. The number that is being repeated is always the base. (See example 3) Now count the number of times the number is being multiplied by itself. This will be the exponent. (See example 4) Remember to read your power as the base (see example 5) to the power of the exponent (see example 6)
- Demonstrate the difference between the exponent and the base by building models of a given power such as 32 and 23
To do understand the difference between the exponent and base you must understand the major significance and difference even in a switch in their positions. (See example 1) To understand them better we can also break them down into expanded form as repeated multiplication. (See Example 2) We will also talk about the basic parts of a power and relate them to how they can be represented. (See example 3)
- Demonstrate the difference in two different powers in which the exponent and the base are interchanged by using repeated multiplication, such as 32 and 23.
This is very similar to what we did in PLO 3 but this time we will also look at using the answer to compare and see how different the two are even though they may contain the same numbers in different positions. We will try and find the answer as a power and while in Expanded form. (See example)
- Evaluate powers with integral bases (excluding 0) and whole number exponents
We touched on this in PLO 4 but in this PLO, we will do many different examples of evaluating and you will see why memorizing your powers comes in handy. Whole number exponents are positive numbers so in this PLO we will not be calculating with negative exponents. (See examples and audio)
6. Explain the role of parenthesis in powers by evaluating a given set of powers such as (-2)4, -24, and (-24).
In this PLO we will learn about the notorious negative sign which is a very common misconception and can lead to some very confusing mistakes. Often the negative sign is seen as a coefficient which is a vocab word we will explain (see example 1) and sometimes the negative is part of the base in which case the base itself is negative. (See example 2) In this PLO you will be sure to discover how parenthesis are crucial. We will also evaluate each one, so you can see the impact the negative plays on the answer. (See examples)
- Explain the exponent laws for multiplying and dividing powers with the same base.
In this PLO I will help you understand the Exponent Law of why dividing you subtract and when multiplying you divide and why we do that instead of actually dividing and multiplying. I will do this solving real equations, so you can apply it yourself. (Examples and audio)
- Explain the exponent laws for raising a product and quotient to an exponent.
In this exponent law of raising a product or quotient to an exponent you must understand that the power must be distributed to the quotient or power (see example 1) I will also talk about what your answer will look like and what will happen if you don’t distribute evenly. (See example 2)
- Explain the law for powers with 0.
In this PLO I will discuss how when the exponent is 0 the answer is always 1. Despite the number being negative or positive.
- Use patterns to show that a power with an exponent of 0 is 1.
This PLO is reiterating PLO 9 talking about how a power with an exponent of 0 is always 1 by using patterns. (See examples and audio)
- Explain the law for powers with negative exponents.
Starting up with negative numbers in this PLO you will understand how to use reciprocals to turn an exponent positive. I will use a range of different examples and both numbers and variables. (examples and audio)
- Use patterns to explain the negative exponent law.
For this PLO I am going to demonstrate this negative exponent law by using patterns. I will do this for both negative and positive numbers. (Examples and audio)
- I can apply the exponent laws to powers with both integral and variable bases.
This PLO is a review of the Exponent Laws making sure we can apply them to both variables and integral bases. In this I will be doing an example question with a variable base and an integral base. The laws we will talk about are Multiplying and Dividing powers with the same base PLO 7) (see example 1), Raising a product and quotient to an exponent (PLO 8) (See example 2), Powers with exponent 0(PLO 9) (See example 3), and the law of negative exponents (PLO 12) (See example 4)
- I can identify the error in a simplification of an expression of powers.
In this PLO I am going to go through some common mistakes and do questions incorrectly and then fix them and see if we can identify the error. (Examples and audio)
- Use the order of operations on expressions with powers.
Using the order of operations is what we touched on when we brought in Coefficients but in this PLO, I will make the examples slightly more complicated, remember BEDMAS! (Examples and Audio)
- Determine the sum and difference of two powers.
This PLO is very straightforward, just calculate using either what you have memorized or multiply in expanded form and then subtract to find the difference.
- Identify the error in applying the order of operations in an incorrect solution.
During this PLO I will apply BEDMAS or the order of operations incorrectly and then we will go over the errors and clarify what I should have done. (Examples and audio)
- Use powers to solve problems. (Measurement problems)
As this PLO is all about real world application, we are going to be solving a word problem about measurement with powers.
Anastasia is trying to make a garden in her backyard. Her garden is square and has a side length of 12 m, she found a contractor and he says that a garden with an area of 24 m2 would look best when she shows him her plan. Anastasia wants to pave the rest of her backyard with tiles that are square with a side length of 1m. How many full tiles does Anastasia need to buy?
- Use powers to solve problems. (Growth problems)
This PLO is also all about real world application, so we will solve the word problem about growth involving powers.
Jester’s Delight ordered 2 packages of Jolly Juice, later they were sent an email that they had won an extreme juice competition. The rules stated that they would be sent the number of juice packages they ordered times itself every hour for 12 hours as long as they told the manufacturer how much juice they would get for the following times and the total amount of packages they get. The mathematicians at Jester’s need your help, find out how much juice they receive as fast as possible for them to get it!
1 hour-
2 hours-
10 hours-
Half a day-
- Applying the order of operations on expressions with powers involving negative exponents and variable bases.
In this last PLO we will combine the exponent laws and order of operations to solve two complex equations involving negative exponents, variable bases, and integral bases. (Audio and examples).
- REVIEW
In this Lesson I will review many important lessons about exponents and I will give examples.
Core Competencies Self Reflection – Communication
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Well organized math blog with informative videos.
I loved how thoroughly the concepts and PLOs were explained. The voiceover you provided only reinforced the written examples you were given. Great Work!
I have not learned this but now I understand some things about exponents.
All the outcomes were addressed. The examples were easy to understand and what you said in the video was under the question in case you didn’t understand. There are no errors in your examples. Things that you did well were putting what you said in the video under the question because you could read while listening. I thought was very well done and there was nothing to improve.