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Slope

Calculating slope from a graph. Slope. Click mouse to play movie. The Magnum Cedar Point, OH. Superman 6 Flags Magic Mountain. Ghost Rider Knott’s Berry Farm. Xcelerator Knott’s Berry Farm. These are completely vertical!. Son of Beast King’s Island, OH.

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Slope

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  1. Calculating slope from a graph Slope Click mouse to play movie Becky Afghani, LBUSD Math Curriculum Office, 2003

  2. The Magnum Cedar Point, OH Superman 6 Flags Magic Mountain Ghost Rider Knott’s Berry Farm Xcelerator Knott’s Berry Farm These are completely vertical! Son of Beast King’s Island, OH How steep is the steepest roller coaster?

  3. Objective Given a graph of a line, you will calculate the slope of the line. How steep is it? Becky Afghani, LBUSD Math Curriculum Office, 2003

  4. Why are we learning this? • You will use slope to graph a line without having to use a T-table • Knowing slope is a 7th grade standard: • AF 3.3: Graph linear functions, noting that the vertical change per unit of horizontal change is always the same and know that the ratio (“rise over run”) is called the slope of a graph. • There are 2 items on the CAHSEE relating to slope. Becky Afghani, LBUSD Math Curriculum Office, 2003

  5. Imagine a roller coaster moving from LEFT to RIGHT Becky Afghani, LBUSD Math Curriculum Office, 2003

  6. There are four different kinds of slope the coaster could encounter... Becky Afghani, LBUSD Math Curriculum Office, 2003

  7. Positive Slope Uphill Becky Afghani, LBUSD Math Curriculum Office, 2003

  8. Negative Slope Downhill Becky Afghani, LBUSD Math Curriculum Office, 2003

  9. And 2 Special Cases… The impossibly scary coaster The zero-fun coaster What kind of slope are they? Becky Afghani, LBUSD Math Curriculum Office, 2003

  10. Zero Slope Horizontal Aw! That’s zero fun! Becky Afghani, LBUSD Math Curriculum Office, 2003

  11. Undefined Slope That’s a really scary coaster, so the slope is… Vertical Becky Afghani, LBUSD Math Curriculum Office, 2003

  12. A B What are the 4 types of slope? • Determine who will be shoulder-partner A and shoulder-partner B • A says the name of a type of slope • B describes what it looks like • Name and describe all four types of slope One type of slope is… That one is… Becky Afghani, LBUSD Math Curriculum Office, 2003

  13. For the following slides,call out whether the slope is positive,negative, zero, or undefined. Wait for the count of 3 before you say your answer! Becky Afghani, LBUSD Math Curriculum Office, 2003

  14. 1 2 3 negative Becky Afghani, LBUSD Math Curriculum Office, 2003

  15. 1 2 3 positive Becky Afghani, LBUSD Math Curriculum Office, 2003

  16. 1 2 3 zero Becky Afghani, LBUSD Math Curriculum Office, 2003

  17. 1 2 3 undefined Becky Afghani, LBUSD Math Curriculum Office, 2003

  18. How can you describe the steepness of a roller coaster? • Slopeis a number which describes the steepness of a line. • We use the variable m to stand for slope. Dude, why’d you use the letter m? I named it after my Mom Becky Afghani, LBUSD Math Curriculum Office, 2003

  19. A B What is slope? • Determine who will be shoulder-partner A and shoulder-partner B • A describes what slope is • B tells what letter is used for slope Slope is… We use the letter… Becky Afghani, LBUSD Math Curriculum Office, 2003

  20. What do big slopes and small slopes look like? When the slope is positive… m = 1 is a 45 degree angle m > 1 is a steep line 0 < m < 1 is a shallow line Negatives are the same but downhill… Show me! Becky Afghani, LBUSD Math Curriculum Office, 2003

  21. Slope is positive one m = 1 45 Becky Afghani, LBUSD Math Curriculum Office, 2003

  22. Slope is greater than positive one m = 3 Steep climb for a coaster Becky Afghani, LBUSD Math Curriculum Office, 2003

  23. Slope is between zero and one m = 1/4 Shallow climb for a coaster Becky Afghani, LBUSD Math Curriculum Office, 2003

  24. Slope is negative one m = -1 45 Same as positive one, just downhill Becky Afghani, LBUSD Math Curriculum Office, 2003

  25. Slope is less than negative one Steep drop for a coaster m = -3 These are “big” negative numbers Becky Afghani, LBUSD Math Curriculum Office, 2003

  26. These are “small” negative numbers m = -1/4 Shallow drop for a coaster Slope is between negative one and zero Becky Afghani, LBUSD Math Curriculum Office, 2003

  27. Let’s see if you can remember… You will see a graph and some choices. Use what you know about steep and shallow lines to pick the only possible slope. Becky Afghani, LBUSD Math Curriculum Office, 2003

  28. Do you remember? m = 1 m = 8 m = -1 Becky Afghani, LBUSD Math Curriculum Office, 2003

  29. Do you remember? m = 1 m = 4 m = 1/4 Becky Afghani, LBUSD Math Curriculum Office, 2003

  30. Do you remember? m = 1 m = 3 m = 1/3 Becky Afghani, LBUSD Math Curriculum Office, 2003

  31. Do you remember? m = -1 m = 1 m = -4 Becky Afghani, LBUSD Math Curriculum Office, 2003

  32. Do you remember? m = -1 m = -3 m = -1/3 Becky Afghani, LBUSD Math Curriculum Office, 2003

  33. Do you remember? m = -1 m < -4 m = -1/4 Becky Afghani, LBUSD Math Curriculum Office, 2003

  34. Now, let’s practice… • You will be given a slope. • Make the line with your arms. • Think… Positive or Negative • Then… Steep, Shallow or 45-degree Becky Afghani, LBUSD Math Curriculum Office, 2003

  35. Stand up and show me with your arms – wait for my signal m = 1 Becky Afghani, LBUSD Math Curriculum Office, 2003

  36. Stand up and show me with your arms – wait for my signal m = -1 Becky Afghani, LBUSD Math Curriculum Office, 2003

  37. Stand up and show me with your arms – wait for my signal m = 3 Becky Afghani, LBUSD Math Curriculum Office, 2003

  38. Stand up and show me with your arms – wait for my signal m < -3 Becky Afghani, LBUSD Math Curriculum Office, 2003

  39. Stand up and show me with your arms – wait for my signal m = 1/4 Becky Afghani, LBUSD Math Curriculum Office, 2003

  40. Stand up and show me with your arms – wait for my signal m = -1/4 Becky Afghani, LBUSD Math Curriculum Office, 2003

  41. How do you calculate the slope of a line? • Pick two points on the line • Calculate “rise over run” • Determine the sign There are 3 steps: Becky Afghani, LBUSD Math Curriculum Office, 2003

  42. Not OK Not OK Not OK OK OK OK OK OK OK OK OK Step 1 Start with 2 points on gridline intersections (2, 3) (1, 1) (0, -1) (-1, -3)

  43. Step 2 Run = 1 Rise = 2 How do you calculate the slope of a line? Vertical change m Slope = divided by Horizontal change Rise m OR... Slope = divided by Run Becky Afghani, LBUSD Math Curriculum Office, 2003

  44. Step 3 Show me! What sign is it? Look to see if the slope is increasing Positive Or decreasing Negative Becky Afghani, LBUSD Math Curriculum Office, 2003

  45. Step 2: Rise Slope = divided by Run 2 1 Rise divided by Run Model # 1: Watch me do the three steps Step 1: Choose 2 points Run = 1 positive Rise = 2 Step 3: Determine the sign m = 2 +

  46. Step 2: Rise Slope = divided by Run 1 3 Rise divided by Run Model # 2: Watch me do the three steps Step 1: Choose 2 points Run = 3 Rise = 1 negative Step 3: Determine the sign m = 1/3 -

  47. Rise Over Run Choose Two points Determine Sign With your partner… • Put these three steps in the correct order. • I will choose a student at random to share out. Becky Afghani, LBUSD Math Curriculum Office, 2003

  48. Rise divided by Think Pair Share Run Rise = 3 Run = 2 Practice # 1: Find the slope of this line + Step 1: Choose Two points Step 2: Rise Over Run Step 3: Determine Sign

  49. Rise divided by Think Pair Share Run Run = 3 Rise = 1 Practice # 2: Find the slope of this line negative Step 1: Choose Two points Step 2: Rise Over Run Step 3: Determine Sign

  50. Think Pair Share Rise = 2 Run = 5 Practice # 3: Find the slope of this line + Step 1: Choose Two points Step 2: Rise Over Run Step 3: Determine Sign

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