MJ2

1. MJ2 Ch 1.2 – Powers & Exponents

2. Bellwork • Define and give an example of the following terms: • Factor • Base • Exponent

3. Objective • Students will use power and exponents

4. Before we begin… • Please take out your notebook and get ready to work… • As you know…your main goal this year is to pass this class and go to 8th grade… • One of the tools that you will use to help you achieve that goal is taking effective notes… • The notes are to be used for studying for quizzes, tests, and the semester exams as well as completing your homework…

5. Taking Notes… • Open your notebooks to the first page • On the first page…fold over the paper starting from the upper right hand corner and bringing it to the center of the book…this should create a triangle…Fold and crease the paper…this is a book mark…Label the bookmark as Chapter 1 • On the next page in the upper right hand corner write today’s date. • Drop down a line and on the left hand side of the page write and underline the chapter section…today it will be Chapter 1.2 – Powers & Exponents • Drop down a line and write and underline the word OBJ: (OBJ stands for objective)…You will have a different objective each day and the objective represents what we will work on that day…

6. Taking Notes • As we go through the lesson you are expected to take notes… • Some tips on taking notes… • Generally speaking you should abbreviate as much as possible…however, you must understand what your abbreviation is…A strategy you can use is the 1st time write the word out and put the abbreviation in parenthesis…Example: Exponents (Exp)…thereafter, use the abbreviation…

7. Taking Notes • Underlining and highlighting is an effective way to draw your eye to important concepts when studying… • Also, using indentations and white space and arrows…helps keep your notes organized… • Finally, on a daily basis you will be required to summarize the key concepts that we covered in the lesson…You should use your own words to summarize your understanding… • A couple of more things…Each day you should start a new notes page…keep the pages in chronological (date) order…You can also use what we discussed about notes in your other classes… • This is all about you becoming responsible for your learning and taking care of your business…which is to go to the next grade level…

8. Using Your Notes… • First and foremost…you don’t study what you already know…to do so is ineffective… • When studying…review at the daily summary you did…If you know the material, skip it and go on to the next section… • If you don’t know it…review your notes…then go to the chapter section and pick some problems and try working them out….pick the odd problems and check your answers in the back of the book…If you get it…then move on.. • If you still don’t get it …look at the examples in the text…pick apart what they did, then choose some more examples to work out… • If you still don’t get it…you should be talking to either a family member, friend or me…

9. How to use lesson slides • In each lesson, each slide will have a category at the top. You can use this to identify topics that we will talk about…When taking notes you should write the title, underline or highlight it…then skip a space and indent to take the slide notes… • I try to make the body of the slides as brief and concise as possible…I also provide examples of what we are discussing…sometimes its appropriate to draw an arrow from the text to the spot in the example to demonstrate the concept… Body

10. Lets Begin… • At this point you should have your date in the upper right hand corner… • You should have chapter 1.2 – Powers and Exponents in the upper left hand corner • You should have your objective on your notes page… • Now lets take some notes…

11. Factors • When you multiply two or more numbers together to get a product each of those numbers multiplied are called factors • Example: 2 x 5 = 10 3 x 3 x 3 = 27 Today we will explore how to write special factors using exponents Products Factors

12. Common Factors • When the same factor is used to multiply, you can use an exponent to simplify writing the same factor. Example: • Instead of writing 5 x 5 x 5 x 5 x 5. • This expression can be simplified by using an exponent to get 55. • 55 is called an exponential expression is read as five to the fifth power

13. Special Terms • A number with no exponents is said to be raised to the 1st power. Example – 5 = 51 and is read as five • A number to the 2nd power is called squared Example – 32 is read as three squared • A number to the 3rd power is called cubed Example – 43 is read as four cubed

14. Your Turn • In the notes section of your notebook write the exponential expression in number and words for the following: • 5 x 5 x 5 • 8 x 8 • 6 x 6 x 6 x 6 x 6 x 6 x 6

15. Parts of an Exponential Expression 124 Exponent Base In an exponential expression the exponent tells the base how many times to multiply itself. In the example above the exponent (4) tells the base (12) how many times to multiply itself. When you multiply you get the following: 12 x 12 x 12 x 12 = 20,736

16. CAUTION! • When working with exponents students often multiply the base times the exponent to get the answer. This is incorrect! • Example: 85 Incorrect 8 x 5 = 40 Correct 8 x 8 x 8 x 8 x 8 = 32,768 As you can see there is a big difference between the two answers!

17. Expectations • After learning about powers and exponents you will be expected to do the following: 1. Write powers as products 2. Write powers in standard form 3. Write numbers in Exponential form

18. Write powers as products • To write powers as products just multiply the base the number of times the exponents tells you to • Example 75 = 7 x 7 x 7 x 7 x 7 92 = 9 x 9 84 = 8 x 8 x 8 x 8

19. Your Turn • In the notes section of your notebook write the powers as products • 103 • 252 • 26

20. Write Powers in Standard Form • You can evaluate, or find the value of a power by multiplying the factors. Numbers written without powers are called standard form • Example: 25 = 2 x 2 x 2 x 2 x 2 = 32 43 = 4 x 4 x 4 = 64 Standard Form

21. Your Turn • In the notes section of your notebook write the following in standard form • 102 • 1003 • 54

22. Write Numbers in Exponential Form • Numbers written with an exponent are written in exponential form. • Example 3 x 3 x 3 x 3 x 3 = 35 In this example 3 is the base and its multiplied 5 times to get the exponential form of 35

23. Your Turn • In the notes section of your notebook write the following in exponential form • 5 x 5 x 5 x 5 • 10 x 10 x 10 • 6 x 6

24. Summary • On a daily basis you will be expected to summarize, in your notebook, key concepts that we covered in the lesson. • Use your own words to describe the concepts • This information will be used to help you study for exams. • At the bottom of today’s notes write a heading and underline it like this: Summary • Indent and use bullet points to summarize key concepts – I will do the first summary for you…

25. Example Summary Summary: • Today we learned how to write the same factor as an exponents. • Example 3 x 3 x 3 x 3 = 34 • The 3 represents the base and the 4 represents the exponent • The exponent tells the base how many times to multiply itself. • Never multiply the base times the exponent • 3 x 4 • Standard form is a number with no exponent • Exponential form is a number with an exponent. X

26. Assignment • Workbook p. 7