2. Multimedia Grant Presentation Susan Weimer, Jan Kurtz and Jenny Loach May 2000 BEGIN

3. SOL Patterns, Functions, and Algebra 5.20 The student will select an open sentence to represent a given mathematical relationship. n Purpose: To further investigate how math problems are expressed by open sentences. n Audience: Small groups or individuals that already grasp the concept of variables.

4. Contents What is an open sentence ? What is a variable ? How are math problems represented by open sentences? Follow-up activities (Skip to activities)

5. What is a variable ? n To solve problems, mathematicians often use letters to represent the numbers they wish to find. The letters are called “unknowns” or “variables”. X is the most common variable, but other letters or symbols also work. 5 + 2 = X

6. The variables in these open sentences are written in blue. 6 - X = 2 J + 9 = 13 5 x 3 = V

7. What is an Open Sentence ? An open sentence is an equation containing a variable. 25 = n + 18

8. Open sentences can also express math problems. You have 5 cookies. You ate 3. How many do you have left? 5 - 3 = x

9. Let’s take a closer look: You had 5 cookies. You just ate 3. How many are left? THINK: You started with 5 and took away 3 (when you ate them). This is shown 5-3. The unknown ( x ) is how many left. The open sentence for this problem would be 5 - 3 = x

10. How are math problems expressed by open sentences ? It’s as easy as 1, 2, 3! Three steps, that is...

11. STEP 1) Decide what the variable stands for. STEP 2) Decide which mathematical sign is needed. Look for clue words! STEP 3) Test your answer by putting a number in place of the variable.

13. PROBLEM: I just bought a new pair of pants. They were on sale for $10.00 off the regular price, so I paid $10.00 less than the regular price. Which expression shows how much I paid? ANSWER CHOICES: A) $10.00 - P B) $10.00 + P C) P - $10.00 D) $10.00/P $10 off

14. What does the variable P stand for? How much was saved? How much was spent? The regular price of the pants? STEP 1) Decide what the variable stands for.

15. Remember, you already know that you saved $10.00. A variable stands for an unknown. Try again. $10 off

16. Before we can figure out how much you saved, we need to know the regular price of the pants. PRICE ?

17. Before we can figure out how much you spent, we need to know the regular price of the pants. PRICE ?

18. P stands for the regular price of the pants.

19. Decide which mathematical sign you need. Hint: Look for clue words! PROBLEM: I just bought a new pair of pants. They were on sale for $10.00 off the regular price, so I paid $10.00 less than the regular price. Which expression shows how much I paid? The word “less” tells us to: + (add)- (subtract) x (multiply) / (divide) STEP 2) Decide which mathematical sign is needed. Look for clue words!

20. The key words for addition problems are: “total”, “in all”, “altogether”, “more than”

21. The key words for division are: “each”, “per”, “separate”, “split”

22. The key words for multiplication problems are: “total”, “in all”, “altogether”, “how many”

23. The word “less” suggests subtraction. Go to step 3

24. Try putting a number in place of the variable. This will help you check your final answer. Let’s use $30 for P. P - $10 =$30 - $10 = $20 $10 - P =$10 - $30 = ???? How can we take $30 away when we only have ten? Are you ready to choose your answer? Click here! STEP 3) Test your answer by putting a number in for the variable.

25. PROBLEM: I just bought a new pair of pants. They were on sale for $10.00 off the regular price, so I paid $10.00 less than the regular price. Which expression shows how much I paid? ANSWER CHOICES: A) $10.00 - P B) $10.00 + P C) P - $10.00 D) $10.00/P $10off

26. Let’s try another one!

28. PROBLEM: I have $230 more than Nick. Which expression shows how much money I have? M/230 M-230 230M M+230 Go to step one

29. M stands for how much money Nick has. M stands for how much money I have. M stands for how much money Nick and I spent. STEP 1) Decide what the variable stands for.

30. M stands for the amount of money Nick has. Now go to step 2

31. Remember, before we can find out how much money I have we need to know how much money Nick has.

32. How much money was spent doesn’t have anything to do with the problem.

33. PROBLEM: I have $230 more than Nick. Which expression shows how much money I have? What does “more than” tell us to do? The words “more than” tells us to: + (add)- (subtract) x (multiply) / (divide) STEP 2) Decide which mathematical sign is needed. Look for clue words!

34. Subtraction words are “less than”, “how many more than”, “difference.”

35. The words “more than” tell us that I have more than Nick, so we need to ADD on to what Nick has. Now go to step 3

36. PROBLEM: I have $230 more than Nick. Which expression shows how much money I have? Let’s pretend that Nick has $170. So M = 170 STEP 3) Test your answer by putting a number in for the variable.

37. M+230 $170 + $230 = $400 I have $400! That’s $230 more than Nick. Now you’re ready to try some on your own!

38. You and your best friend are splitting a pizza with 6 slices. Which open sentence shows how many pieces each of you would get? 6 - 2 = Z 6 + 2 = Z 6 x 2 = Z 6 / 2 = Z

39. If 6 - 2 = Z, then Z = 4 Now, THINK! Is it possible that each of you could get 4 slices from 1 6-slice pizza? No. Return to the question.

40. If 6 + 2 = Z, then Z = 8 Now, THINK! Is it possible that each of you could get 8 slices from 1 6-slice pizza? No. Return to the question.

41. If 6 X 2 = Z, then Z = 12 Now, THINK! Is it possible that each of you could get 12 slices from 1 6-slice pizza? No. Return to the question.

42. If 6 / 2 = Z, then Z = 3 Now, THINK! Is it possible that each of you could get 3 slices from 1 6-slice pizza? YES!!! CONGRATULATIONS.!!!!

43. CLASSROOM FOLLOW-UP ACTIVITIES More activities online Worksheet 1 Worksheet 2 Worksheet 3 Worksheet 4 Problems based on children’s books (check your work)

44. Worksheet #1 Answers 1.829 calories 2.1,313 gallons 3.1,461 seats 4.1388 miles

45. Worksheet #2 Answers 1.4,812 2.5,394 feet 3.10,330 miles 4.$32,900

46. Worksheet #3 Answers 1.2,148 days 2.44.5 minutes Yes 3.160 bedrooms 4.$672 5.$56

47. Worksheet #4 Answers 1.83 points 2.40.8 students 3.58 degrees 4.926 days

48. CREDITS http://www.barrysclipart.com http ://cgl.microsoft.com/ clipgallerylive http://www.mathstories.com http://www2.hawaii.edu / suremath