How do you determine your score percentile on the math section of the SAT? - PowerPoint Presentation

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Slide1

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?Slide2

In this

lesson,

you

will learn how to find percentiles

by using a normal curve to represent the distribution of

univariate

data.Slide3

Remember that normal distributions are symmetric, bell-shaped curves with no significant gaps or outliers that approximately follow the

empirical

rule:Slide4

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.Slide5

The distribution on the following

dotplot

is approximately normal. It is symmetric about the mean, bell-shaped and approximately follows the

empirical

rule.Slide6

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.Slide7

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? Slide8

Well, statisticians often approximate normal distributions of data to a smooth curve that displays the shape of the data without all the lumpiness. Slide9

We know the normal curve for the distribution of SAT math scores in your state would look something like this:Slide10
Slide11

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:Slide12
Slide13

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.Slide14

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%Slide15

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.Slide16

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.Slide17

In this lesson you

have learned how to find percentiles

by using a normal curve to represent the distribution of

univariate

data.Slide18

Now, how would you determine the percentile of a student who scores a 410 on the SAT math section in your state?Slide19

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%.Slide20

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.Slide21

Finally, determine the percentile of a student who scores a 740 on the SAT math section in your state.Slide22

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.Slide23

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?Slide24

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.Slide25

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?Slide26

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.Slide27

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?Slide28

Lesson Slides Rubric

Use this rubric to ensure your lesson plan is great!Slide29

Math Rubric

Criteria for Success

Things 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)Slide30

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 lessonSlide31

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 steakSlide32

Graphic and Image Templates

Copy and Paste items from these slides to make your presentation look great!Slide33

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 inSlide34

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?Slide35

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 the text left-justified rather than centered!Slide36

All arrows can

be

recolored by

changing the “shape fill.” You can also resize them or rotate them!Slide37

[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…Slide38

You can resize any of these

boxes and use them to highlight text

or ideas

.Slide39

Let’s Review

Let’s Review

Let’s Review

A Common Mistake

Let’s Review

Guided Practice

Let’s Review

Quick Assessment

Let’s Review

Extension Activities

Core Lesson