1. How do you determine your score percentile on the math section of the SAT? I just got my score report for the SAT. If I made a 630 on the Math section, what percent of students did I score as well or better than?

2. In this lesson, you will learn how to find percentiles by using a normal curve to represent the distribution of univariate data.

3. Let’s Review Remember that normal distributions are symmetric, bell-shaped curves with no significant gaps or outliers that approximately follow the empirical rule:

4. The empirical rule states that for a normal distribution: about 68% of the data lie within one standard deviation of the mean about 95% of the data lie within two standard deviations of the mean about 99.7% of the data lie within three standard deviations of the mean.

5. Let’s Review The distribution on the following dotplot is approximately normal. It is symmetric about the mean, bell-shaped and approximately follows the empirical rule.

6. Let’s Review A Common Mistake If your SAT math score is one standard deviation to the right of the mean, it does not mean that your score is at the 68 th percentile. Percentiles represent the total percent that score at or below your score.

7. Let’s Review Core Lesson Suppose that the distribution of math SAT scores in your state is approximately normal with a mean of 520 and a standard deviation of 110. How can we graph the distribution without knowing every individual score?

8. Let’s Review Core Lesson Well, statisticians often approximate normal distributions of data to a smooth curve that displays the shape of the data without all the lumpiness.

9. Let’s Review Core Lesson We know the normal curve for the distribution of SAT math scores in your state would look something like this:

10. Let’s Review Core Lesson

11. Let’s Review Core Lesson Now we can use this normal curve to determine the percent of SAT math scores that are at or below your score of 630. Since 630 is one standard deviation to the right of the mean, the area of interest would look like this:

12. Let’s Review Core Lesson

13. Let’s Review Core Lesson We know 50% of your state’s SAT math scores are at or below 520. We determine that a score of 630 is one standard deviation above the mean, so we must add this additional area in order to determine your score percentile.

14. Let’s Review Core Lesson We also know 68% of the data on a normal curve is between one standard deviation left and right of the mean, so we just need to add half of that area to 50% in order to have our area of interest: 50% + 1/2(68%)=84%

15. Let’s Review Core Lesson By using the normal curve for this distribution of data, we have now been able to determine that your score on the math SAT is in the 84 th percentile of all test takers in your state.

16. Let’s Review Core Lesson We now see that although 68 percent of the data was between one standard deviation of the mean, that is not equivalent to the percent of data that is located to the left. Percentiles represent the total area left of a variable of interest.

17. In this lesson you have learned how to find percentiles by using a normal curve to represent the distribution of univariate data.

18. Let’s Review Guided Practice Now, how would you determine the percentile of a student who scores a 410 on the SAT math section in your state?

19. Let’s Review Guided Practice Since a score of 410 would be one standard deviation to the left of the mean, you would need to subtract the area from 50%, so the area of interest is 50%-1/2(68%)=16%.

20. Let’s Review Guided Practice So a student who scores a 410 on the SAT math section is in the 16 th percentile of all test takers in the state.

21. Let’s Review Guided Practice Finally, determine the percentile of a student who scores a 740 on the SAT math section in your state.

22. Let’s Review Guided Practice A score of 740 would be located two standard deviations above the mean: 50%+1/2(95%)=97.5%. A score of 740 on the SAT math section in your state is in the 97.5 th percentile of all test takers.

23. Let’s Review Extension Activities The distribution of exam scores in the math department of a large university is approximately normal with a mean of 81 and a standard deviation of 7. Sketch and label a normal curve to represent this distribution. Next, shade the region under the curve that represents the percent of exam scores at or below 67. What percent of the data would be in this shaded region?

24. Let’s Review Extension Activities The distribution of heights of adult American men is approximately normal with a mean of 69.2 inches and a standard deviation of 3.1 inches. Determine the height percentile for a male who is 75.4 inches tall.

25. Let’s Review Extension Activities The distribution of exam scores in the math department of a large university is approximately normal with a mean of 81 and a standard deviation of 7. What percent of students score higher than a 95 on the exam?

26. Let’s Review Quick Quiz Use the information provided here to answer the questions on the next slide: In 2009, the mean ACT score was 18 and the standard deviation was 6. The distribution of ACT scores is approximately normal.

27. Let’s Review Quick Quiz A score of 24 on the ACT in 2009 would place a student in what percentile? About what percent of the 2009 ACT test-takers scored at or below a 6?

28. Lesson Slides Rubric Use this rubric to ensure your lesson plan is great!

29. Math Rubric Criteria for SuccessThings to avoid Storyline or Arc of the Lesson  There is a clear arc to the lesson. One slide leads naturally to the next so that there is a flow and a building of meaning  All the components of the lesson are there but they seem disconnected, as if the author wrote each without thinking about how they fit into the whole. Hook Slide  The teacher poses a simple question that illicits the response, “yeah, I do wonder how that works…”  The question is short  A relevant example is included when it is short and further pulls the learner in  The question mirrors what the student will learn, then need to do later in the guided practice  The question seems formulaic, inauthentic, or overly “school- ish” (message: you have to learn this because you’re in school rather than, this is genuinely interesting)  The hook is overly-complicated and potentially confusing  The question does not parallel the guided practice questions Objective Slide  The objective follows the form (you will learn X by doing Y)  Is concise and follows the form provided in the examples  Does not follow the form  Is overly vague in describing either the X or the Y  Is too long  Is written for teachers but not students Let’s Review  Reminds the student of how this lesson fits with other lessons (the lesson, however, should still be able to stand on its own)  Reminds the student of important vocabulary  Is as concise as possible  Uses visuals whenever possible  Is either too detailed or not detailed enough in connecting the lesson to other lessons  Leaves out important touch points  Makes the lesson overly dependent on the other lessons (student will be confused or feel like they’ve made a mistake, if they watch this lesson alone)

30. Common Mistake  Points out a common mistake that students make  Concisely explains the thought process that leads to that mistake  Isn’t actually a mistake students make (too simple)  Is confusing or vague Modeling a Way of Looking at It  Clearly models a way to look at the standard  Uses visuals as often as possible to show how the way of looking works  Is in “think aloud” format. The teacher is opening up his/her thought process to the student  Takes advantage of every opportunity to explain why the math works the way it works  Engages the learner by asking questions along the way to build suspense  Uses an an example to show the way in action  Explains how this way of looking at it shows why the common mistake (see above) is a mistake  Focuses on the algorhythm (or trick) instead of on showing a way of looking at the math  Fails to use visuals to show a way  Fails to explain his/her thinking along the way. The teacher effortlessly runs through the steps as if it’s all obvious and easy  Does not ask any questions along the way to pull the learner in  Misses opportunities to explain the why behind the math  Fails to explain why this way of looking at the math addresses the common mistake Objective Review  Reviews the objective in a way which conveys, “we’ve come full cicle and now you see this objective with new eyes.”  Serves as a “let’s pull this all together” moment that helps organize the lesson in the learner’s mind  Creates abrupt feeling between the lesson and the reviewing (subtext: “we’re done with this lesson, let’s quickly bring it to a close.”) Guided Practice  Is at the same difficulty level modeled in the lesson  Is connected to the initial hook question  Seem unrelated to the hook question  Is at a different difficulty level than that modeled in the lesson

31. Extension Activity Suggestions  Includes a suggestion for a struggling student who needs more opportunities for practice  Includes a suggestion for students who seem to get it but need more practice  Includes a suggestion for students who get it and are ready to be challenged further  Suggestions should clearly build from the approach in the core lesson  Does not include differentiation  Does not thoughtfully connect or flow from the lesson  Does not clearly build from the approach in the core lesson  Does not give a range of activities Aesthetics  The slides use the correct colors (blue, green, red) in the correct sequence.  The slides use the correct fonts  The slides use handwriting and the handwriting appears as written in the right places  The slides only use the headers/titles provided  The slides use the provided visuals or include visuals created by the author or LearnZillion  The slides use animation, highlighting, and circling to scaffold the learning, keeping the eye focused on what the teacher is introducing/explaining  The slides clean and uncluttered. The visuals and text do not exceed the maximum amount (see tutorial for example of maximum)  The slides use other colors or vary the order of the colors  The slides add new headers/titles that aren’t part of the template  The slides use clip art  The slides are cluttered  Animation is distracting and feels more like sizzle than part of the steak

32. Graphic and Image Templates Copy and Paste items from these slides to make your presentation look great!

33. You can copy and paste these items into any slide Green text box that appears letter by letter Green text box that fades in Blue text box that appears letter by letter Blue text box that fades in Red text box that appears letter by letter Red text box that fades in

34. You can copy and paste these items into any slide — make sure you copy both the bubble and the text! Do I feel strongly about it? Do I have a lot to say? Do I feel strongly about it? Do I have a lot to say? Do I have a lot to say?

35. You can copy and paste these items into any slide. You can resize them as needed! Use black text when you write in me please! Also, keep my text left-justified rather than centered! Use black text when you write in me please! Also, keep my text left-justified rather than centered! Use black text when you write in me please! Also, keep the text left-justified rather than centered! Use black text when you write in me please! Also, keep the text left-justified rather than centered!

36. All arrows can be recolored by changing the “shape fill.” You can also resize them or rotate them!

37. [Write first step here…] 1 2 [Write second step here…] 3 [Write third step here…] You can use these when discussing main ideas or steps in a process…

38. You can resize any of these boxes and use them to highlight text or ideas.

39. Let’s Review A Common Mistake Let’s Review Guided Practice Let’s Review Quick Assessment Let’s Review Extension Activities Core Lesson