Understanding SAT Math Score Percentiles
Learn how to determine your score percentile on the math section of the SAT by using a normal distribution curve to find where your score falls relative to other students. Discover the concept of percentiles and how they reflect your position in relation to the mean and standard deviations of the scores. Avoid common mistakes in interpreting percentiles and gain insights into graphing distributions of SAT math scores.
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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?
In this lesson, you will learn how to find percentiles by using a normal curve to represent the distribution of univariate data.
Lets Review Let s Review Remember that normal distributions are symmetric, bell-shaped curves with no significant gaps or outliers that approximately follow the empirical rule:
Lets Review Let s Review 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.
Lets Review 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. Collection 7 0 2 4 6 8 10 12 14 16 18 x
Lets 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 68th percentile. Percentiles represent the total percent that score at or below your score.
Core Lesson Let s Review 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?
Core Lesson Let s Review Well, statisticians often approximate normal distributions of data to a smooth curve that displays the shape of the data without all the lumpiness.
Core Lesson Let s Review We know the normal curve for the distribution of SAT math scores in your state would look something like this:
Core Lesson Let s Review Distribution Plot Normal, Mean=520, StDev=110 0.004 0.003 Density 0.002 0.001 0.000 190 300 410 520 X 630 740 850
Core Lesson Let s Review 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:
Core Lesson Let s Review
Core Lesson Let s Review 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.
Core Lesson Let s Review 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%
Core Lesson Let s Review 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 84th percentile of all test takers in your state.
Core Lesson Let s Review 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 total area left of a variable of interest. between the
In this lesson you have learned how to find percentiles by using a normal curve to represent the distribution of univariate data.
Guided Practice Let s Review Now, how would you determine the percentile of a student who scores a 410 on the SAT math section in your state?
Guided Practice Let s Review Since a score of 410 would be one standard deviation to the left mean, you would need to subtract the area from 50%, so the area of interest is 50%-1/2(68%)=16%. to the left of the subtract
Guided Practice Let s Review So a student who scores a 410 on the SAT math section is in the 16th percentile of all test takers in the state.
Guided Practice Let s Review Finally, determine the percentile of a student who scores a 740 on the SAT math section in your state.
Guided Practice Let s Review 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 97.5th percentile of all test takers.
Extension Activities Let s Review 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?
Extension Activities Let s Review 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.
Extension Activities Let s Review 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 on the exam? higher than a 95
Quick Quiz Let s Review 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.
Quick Quiz A score of 24 on the ACT in 2009 would place a student in what percentile? Let s Review About what percent of the 2009 ACT test-takers scored at or below a 6?
Lesson Slides Rubric Use this rubric to ensure your lesson plan is great!
Math Rubric Criteria for Success Things to avoid 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 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 objective follows the form (you will learn X by doing Y) Is concise and follows the form provided in the examples 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. 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 Storyline or Arc of the Lesson Hook Slide 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 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) Objective Slide 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 Let s Review
Points out a common mistake that students make Concisely explains the thought process that leads to that mistake 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 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 Is at the same difficulty level modeled in the lesson Is connected to the initial hook question Isn t actually a mistake students make (too simple) Is confusing or vague Common 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 Modeling a Way of Looking at It Creates abrupt feeling between the lesson and the reviewing (subtext: we re done with this lesson, let s quickly bring it to a close. ) Objective Review Seem unrelated to the hook question Is at a different difficulty level than that modeled in the lesson Guided Practice
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 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) 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 Extension Activity Suggestions 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 Aesthetics
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Lets Review Let s Review Let s Review Core Lesson A Common Mistake Guided Practice Let s Review Extension Activities Let s Review Quick Assessment Let s Review
