Starter

2. Starter • The shoes you were saving for are now on sale for $17.56. The original price was $21.95. what percent is the discount amount of the original price?

3. Converting Units • On your Reference Sheet you have a list of Customary Conversions • It looks like this: • 8 fluid ounces = 1cup • 2 cups = 1 pint • 2 pints = 1 quart • 4 quarts = 1 gallon • 8 pints = 1 gallon • 3 teaspoons = 1 tablespoon • 16 tablespoons = 1 cup • 16 fluid oz = 1 pound • 5,280 feet = 1 mile • 12 inches = 1 foot • 3feet = 1 yard

4. What do these remind you of? • They look like scales! (ie on a map 1 in = 3miles) • Just like we set up a proportion to use scales, we will use a proportion to convert units. • The conversion is your first ratio, what your looking for is your second ratio.

5. Examples • You need 2 cups of flour for your recipe, but you only have a tablespoon to measure. How many tablespoons do you need to get 2 cups? • Using your reference sheet, what is our conversion for cups and tablespoons? • 16 tablespoons = 1 cup

6. Set up your proportion • 16 T/1 c = x T/2 c • Now you just need to cross multiply and solve! • X = 32 Tablespoons

7. Try the following problems • How many feet are in 10 yards? • How many gallons are in 12 pints? • How many pounds are in 8 ounces?

8. New Topic • Try computing • 3,596,000,000 x 42,987,400,000,000 • What do you get? • Wouldn’t it be nicer to have a shorter, easier way to work with such big numbers?

9. Scientific Notation • Scientific notation was created as a way to work with incredibly big or small numbers in a way that is easy to see and work with

10. The rules • Only one number before the decimal place • Zeros (except those used as place holders) can be eliminated • then we write x 10 • Where the 10 has an exponent equal to the number of places the decimal moved

11. Examples • Write 5,500 in scientific notation • Move decimal point so that only one number us before the decimal place • 5.500 • Eliminate extra zeros • 5.5 • Add on x 10 with an exponent equal to the number of places the decimal moved • 5.5 x 10³

12. Try a few more examples • Write the following in scientific notation • 33,050,000 • 479,000,000 • 5,002

13. Going backwards • Sometimes you will be given a number in scientific notation and you will be asked to put it in standard form. • Standard form means the number written as you would normally see it. • The process of going from scientific to standard is a very similar process

14. Try this • Write the following numbers in standard form • 2.1 x 10² = • 3.14 x 10⁵ =

15. From the CRT 1 Practice • A small virus has a diameter of about 2 x 10 ⁻⁵ millimeters. What is the diameter in standard notation? • How is this problem different? • How do you think we can solve it?

16. How to work with Negative Exponents • A positive exponent represented a very big number. • A negative exponent represents a very small number. • You will still move the decimal the number of places indicated by the exponent, you will just move in the opposite direction.

17. Practice • Write the following numbers in Scientific Notation • 0.00006 • 0.00325 • Write the following numbers in Standard form • 2.14 x 10 ⁻ ³ • 9.175 x 10 ⁻⁹

18. Starter • What part of the model is shaded?

19. Probability and Statistics Review • We will be doing more on probability and statistics after the CRT. I will do a brief review on how to approach these questions on the CRT.

20. Eight balls numbered from 1 to 8 are placed in a bowl. One ball is selected at random. What is the probability that it is NOT number 6?

21. Mary is using a spinner that has whole numbers on it. The probability of spinning an even number on this spinner is 3/8. What is the probability of spinning an odd number on this spinner?

22. A spinner is spun 100 times. The results of the spinner are listed. From the results, what can Lexie predict if she were to spin it 800 times?

23. Tree Diagrams • Sponge Bob is going on a trip and packs blue, tan, and black pants. He also packs a tank top, polo, and a t-shirt. His outfit options are shown in the tree diagram below. If he picks clothes at random, what is the probability that he wears the tan pants with the tank top?

24. The double line graph below compares rainfall, in centimeters, in Sydney and Canberra in March 1993. What is the difference in rainfall on March 3rd?

25. Starter • 8 milligrams are equal to how many grams? Hint: 1 gram = 1000 milligrams

26. Ben had a piece of heavy wire 40 inches long. He bent it into the shape of a square. Ben wants to fit a piece of glass into the square. How much glass will Ben need?

27. Ellie bought a roll of linoleum flooring 8 yards long. She is cutting it into pieces for a craft project. How many 4-foot pieces can she cut from the roll?

28. The following league records were posted. Any team winning more than 80% of their games is invited to the playoffs. Which team will go to the playoffs?

29. Which steps describe how to solve the equation 3y + 1.04 = 11 a. subtract 1.04 and then multiply by 3 b. add 1.04 and then divide by 3 c. subtract 1.04 and then divide by 3 d. divide by 3 and then subtract 1.04

30. Which of the following represents the graph of the solution of 4x ≤ 12?

31. Jerry takes 40 minutes to read 25 pages in a book. He wants to read a book containing 200 pages. Write a proportion to determine how many minutes it will take Jerry to read this book.