1. Lesson 1.1 Expressions and Variables September 15, 2008 Expressions and Variables 1.1 LESSON Goal: Students will be able to evaluate and write variable expressions Agenda: 1.Check hmwk with partner 2.Review 1.1 3.Begin lesson 1.2

2. Review: How are numerical and variable expressions similar? NumericalVariable

3. Vocabulary numerical expression variable variable expression evaluate verbal model Expressions and Variables 1.1 LESSON

4. Expressions and Variables 1.1 LESSON Page 8 Number 51 (independent work) Zach belongs to an online DVD rental service. His yearly rental budget is $200 (wow!). Each rental costs $4.00. 1.Copy and complete the table. DVDs 1 2 3 4 Cost ($) 4 8 ? Amount left 196 192 ? 2. Write a variable expression for the cost of r rentals. 3. Write variable expression for the amount of his budget left after r rentals.

5. DVDs 1 2 3 4 Cost ($) 4 8 12 16 Amount left 196 192 188 184 Writing: How many DVDs will Zach be able to rent before the $200 is spent? Explain how you found your answer. Sample Answer: Zach could rent 50 DVDs. There is a pattern with the number of DVDs rented and the cost—each number of DVDs rented is multiplied by 4. Therefore, 50 * 4 = 200, which allows Zach to spend the entire $200 without going over his budget. Remember to show all work when completing problems

6. Lesson 1.2 Powers and Exponents September 15, 2008 Powers and Exponents 1.2 LESSON Goal: Students will be able to use powers to describe repeated multiplication. CB Standards We are Working Towards: 2.1 understand and apply concepts related to #s, # systems, and # relationships; 2.2 Understand and apply concepts related to computation; 2.8 Use algebraic methods to describe patterns Assessment: Teacher Observation; Checkpoints

7. Powers and Exponents 1.2 LESSON Math Message Heather sends an email to Morgan, Brianna, Nathan, and Brennan. Each then sends the email to 4 more friends. Each of those friends sends it to 4 friends. How many people have received that email? What are a few ways you might go about solving this problem. Table Talk

8. Vocabulary : Match the vocab wd to the best definition 1.power 2.base 3.exponent 5 3 1.It is the result of a repeated multiplication of the same factor 2.Top number of the power 3.Bottom number of the power

9. Powers and Exponents 1.2 LESSON How to read powers PowerIn WordsValue 5 1 5 5 to the first power (0.5) 2 0.5 to the second power; 0.5 squared (0.5)(0.5) = 0.25 5 3 5 4 5 to the third power; 5 cubed 5 to the fourth power 5*5*5= 125 5*5*5*5= 625

10. Powers and Exponents 1.2 LESSON Example 1: Write the product using an exponent a. 2*2*2*2 = 2 4 b. (0.2)(0.2)(0.2)=______ c. n * n * n * n * n = ______

11. Powers and Exponents 1.2 LESSON Checkpoint-use dry erase board to solve Directions: Write the produce using an exponent. 1. (4.3)(4.3) =_____ 2. x * x * x * x =_____

12. Powers and Exponents 1.2 LESSON Example 2: Evaluating Powers with Variables Evaluate the expression x when x = 0.5 4

13. Checkpoint Evaluate the expression when x = 3 mmmm 2 4 = =

14. Powers and Exponents 1.2 LESSON Example 3: Using Powers in Formulas What formulas require the use of powers? Area in square units; Volume in cubic units

15. Powers and Exponents 1.2 LESSON Example 3: Using Powers in Formulas Brandon is going to use cube-shaped block of ice to make an ice sculpture for a competition. Find the volume of the ice. 20 in. V = s 3 Step 1: Write the formula = (20) Step 2: substitute 20 for s = (20)(20)(20) Step 3: evaluate the power 3 Answer: The volume of the block of ice is 8,000 cubic inches. = 8,000 Step 4: multiply

16. Checkpoint Find the area of a square with the given side length 9 meters A = 81 meters squared

17. Powers and Exponents 1.2 LESSON Math Message Heather sends an email to Morgan, Brianna, Nathan, and Brennan. Each then sends the email to 4 more friends. Each of those friends sends it to 4 friends, and so on.

18. Powers and Exponents 1.2 LESSON How did you use powers in this problem to describe repeated multiplication? Heather sends an email to Morgan, Brianna, Nathan, and Brennan. Each then sends the email to 4 more friends. Each of those friends sends it to 4 friends, and so on. How would this chart look if we continued the pattern? Stage Emails Sent as Power Value of Power 144 2416 3_______ 4_______ 1 2 9 4 262,144 emails 9

19. Page 12 # 2

20. Page 12 #s 6, 8, 11 I will be the reporter Need a volunteer to be the recorder at the front board

21. Math Matters Partner Work Page 12 #s 14-28 evens Label notebook with page # Read all directions Show all work Be neat When finished you may play 24 We will check as whole group in approximately 12 minutes

22. Closing Written Response Page 13 # 34 Use complete sentences Will review as whole class

23. Homework Page 8 #39 (check in back of book) Page 9 #s 57-60 all and #67 Label each piece of hmwk with page number Show all work in notebook Be neat

24. Lesson 1.2 Powers and Exponents September 16, 2008 Powers and Exponents 1.2 LESSON Goal: Students will be able to use powers to describe repeated multiplication. Check hmwk with partner (star/circle items you’d like to review) Page 8 #39 (check in back of book) Page 9 #s 57-60 all and #67 CB Standards We are Working Towards: 2.1 understand and apply concepts related to #s, # systems, and # relationships; 2.2 Understand and apply concepts related to computation; 2.8 Use algebraic methods to describe patterns Assessment: Teacher Observation; Checkpoints

25. Whole Class Revisit Lesson 1.2 Page 12 # 4 and # 12 I need a recorder, please. Powers and Exponents

26. p. 13 #36 Properly label your notebook Be neat Show all work You may work with a partner Play 24 when finished; we will review as whole group in approximately 5 minutes

27. 1.2 Practice A #s 3, 6, 12, 16, 18, 25, 26 With a partner, create a problem similar to #31 –Be neat and creative –Solve showing all of your work Powers and Exponents Play 24 when finished Will share problems in approximately 18 minutes

28. Visit http://fvollman.wikispaces.comhttp://fvollman.wikispaces.com Helpful websites Portaportal for Math Textbook Section 1.2 online worksheet http://snipurl.com/3qlw2

29. Homework Practice Wksh 1.2 3-29 odds only Label notebook with Practice wksh 1.2 Show all work in notebook Be neat Quiz on lessons 1.1-1.3 on Friday, September 19 Powers and Exponents Label notebook for hmwk each night; example for tonight your notebook should look like: Practice Wksh 1.2 #s 3-29 odds9/16/08 3.

30. Lesson 1.3 September 17, 2008 Order of Operations 1.3 LESSON Goal: Students will be able to use order of operations to evaluate numerical and variable expressions. Check hmwk with partner(star items you’d like to review) Practice Wksh 1.2 #5-29 odds CB Standards We are Working Towards: 2.1 understand and apply concepts related to #s, # systems, and # relationships; 2.2 Understand and apply concepts related to computation; 2.8 Use algebraic methods to describe patterns Assessment: Teacher Observation; Checkpoints

31. How does the order of operations pertain to this plant??!! The Boojum Plant It is a strange plant that is found in Baja, California. It was founded by Godfrey Sykes in 1922. He named it after a mythical creature in the poem “The Hunting of the Snark”. This creature was found in desolate, far away places. The name suits it quite well! http://farm3.static.flickr.com/2318/2145881083_d46bb61fd8.jpg?v=0 http://www.bajainsi der.com/baja- life/plants-animals- baja/insider_booju m.htm

32. Order of Operations 1.3 LESSON Order of operations: 1.Evaluate expressions inside grouping symbols 2. Evaluate powers 3.Multiply and divide from left to right 4. Add and subtract from left to right PEMDAS Please Excuse My Dear Aunt Sally set of rules for evaluating expressions involving more than one operation

33. Order of Operations 1.3 LESSON Table Talk: Why might order of operations be important when finding the total number of flowers in the flag? About 2,000 plants in each of the 50 stars of this flower flag. There about 64,100 plants in each of the 7 short stripes 106,700 plants in each of the 6 long stripes The blue region contains about 198,900 plants

34. Order of Operations 1.3 LESSON There are about 2,000 plants in each of the 50 stars of this flower flag. There about 64,100 plants in each of the 7 short stripes and 106,700 plants in each of the 6 long stripes. The blue region contains about 198,900 plants. Write a numerical expression to find the total number of plants. 50 * 2000 + 7 * 64,100 + 6 * 106,700 + 198,900 100,000 + 448,700 + 640,200 + 198,900 Approximately 1,387,800 were used in this flower flag

35. Order of Operations 1.3 LESSON Order of operations: 1.Evaluate expressions inside grouping symbols 2. Evaluate powers 3.Multiply and divide from left to right 4. Add and subtract from left to right PEMDAS Please Excuse My Dear Aunt Sally set of rules for evaluating expressions involving more than one operation

36. Order of Operations 1.3 LESSON Using Grouping Symbols Directions: Evaluate the expression a) 8(17 – 2.3) = = 8 (14.7) = 117.6 Show all of your work 14.7 * 8

37. Order of Operations 1.3 LESSON Using Grouping Symbols Directions: Evaluate the expression 14 + 6 12-7 = (14 + 16) (12-5) Rewrite the fraction as division 20 5 = 4 Evaluate within parentheses Divide

38. Order of Operations 1.3 LESSON What other type of grouping symbol might you see this year? Directions: Evaluate the expression = 5 * [ 36 – ( 22)] 14 36 -22 c) 5 * [ 36 – ( 13 + 9 )] = = 5 * 14 14 5 70 Work from inner symbol to the outer symbol

39. Order of Operations 1.3 LESSON Checkpoint 1.10 ( 1.5 + 0.6) 2.72 [(11 – 7) * 2] 21 9

40. Order of Operations 1.3 LESSON Page 18 1. Give three examples of grouping symbols. Numbers 4, 6, 7, 8 We will use the board and the overhead. All eyes on board; you will be told when to write Students will be able to use order of operations to evaluate expressions.

41. Page 19 Number 28 The Boojum Plant http://farm3.static.flickr.com/2318/2145881083_d46bb61fd8.jpg?v=0 A boojum is a very slow- growing cactus. One fifty- year-old boojum is 1.5 meters tall, and has been growing about 0.03 meter each year. Assume the same pattern keeps going. There are 3.28084 feet in a meter. 2. How tall will the boojum be 50 years from now? 1. Write an expression for the height in meters of the boojum y years from now.

42. Variable Expression: 1.5 + 0.03y 1.5 + 0.03(50) 1.5 + 1.5 = 3 The boojum would grow 3 meters. Remember your goal: You will be able to use the order of operations to evaluate numerical and variable expressions.

43. With your Math Matters Partner you will visit http://fvollman.wikispaces.com “helpful websites” Login as a guest—fvollman Think through activities under Math-Order of Operations

44. Order of Operations 1.3 LESSON Students will be able to use order of operations to evaluate expressions. The table shows the numbers of sets of twins, triplets, quadruplets, and quintuplets registered at a twin convention. Write and evaluate an expression for the total number of people who registered at the convention. Type Sets Twins 2697 Triplets 29 Quadruplets 2 Quintuplets 1

45. Wksh 1.3A #s 12-28 evens only Show all work neatly in notebook Label notebook for hmwk each night; example for tonight your notebook should look like: 1.3 Practice A #s 12-28 even9/17/08 12.