Final review.

Here are a few websites to look at:

http://www.cut-the-knot.org/pythagoras/index.shtml — Proving the Pythagorean Theorem

http://www.regentsprep.org/regents/math/geometry/games/geometrygames.htm — Geometry game

Final review.

Here are a few websites to look at:

http://www.cut-the-knot.org/pythagoras/index.shtml — Proving the Pythagorean Theorem

http://www.regentsprep.org/regents/math/geometry/games/geometrygames.htm — Geometry game

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**Activities:**

- Finish boxplot activity from last time.
- Do a bar graph activity (handout will be given)
- Talk about mean, median, and average.
- Do an activity about averages. When is each used? When is one preferable over the other?
- If there is time, here are some practice problems: 3, 4, 5, 10, 12, 14, 17 from 30.4.

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**Class work: **

**Relevant Common Core Standards:**

6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

6.SP.5.Summarize numerical data sets in relation to their context, such as by:

- Reporting the number of observations.
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. *For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.*

7.SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. *For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.*

**Activities:**

- Answer homework questions.
- Finish graphing from last time. Look at Excel and Illuminations. We will discuss histograms a little more, and note that in middle school and high school mathematics, it is too complicated to have bins of different widths, and we will therefore assume that all bins have the same width. We will review the difference between bar graphs and histograms.
- We looked at Gapminder. Have fun exploring the website on your own!
- Learn how to make box plots. Here is a document that explains how to create a boxplot by hand.
- Do an activity with box plots. Handout will be given in class. We will finish on Wednesday.

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Here are the topics that you should expect on the final. For the most part, you should expect problems to be less conceptual and more problem-solving oriented.

- Properties of polygons (which one have congruent diagonals, which ones have perpendicular diagonals, etc.)
- The meaning of area and perimeter; formulas for the area and perimeter of polygons (triangles, quadrilaterals, and polygons that can be broken up into triangles) and circles.
- Similarity: properties of similar figures and finding missing lengths and angles given pairs of similar figures.
- Pythagorean theorem: using the theorem in different contexts, and being able to outline a proof of the theorem.
- Surface area and volume of prisms, pyramids, and cylinders; volume of cones; knowing how to apply the formulas in problems.
- Probability: problems similar to ones we did in class and on homework, not like the ones that were on the quiz. In particular, look at Sections 28.1-28.3.
- Statistical graphs: analyze and create pie charts, bar graphs, histograms, line graphs, and boxplots, and know when each is applicable.
- Mean, median, mode: computing each, knowing the difference between the three, knowing situations in which each of the three is appropriate, knowing how each changes when data changes.

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**Class work: **sampling, creating statistical graphs

**Relevant Common Core Standards:**

2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems^{1} using information presented in a bar graph.

3.MD.3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. *For example, draw a bar graph in which each square in the bar graph might represent 5 pets.*

4.MD.4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. *For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.*

5.MD.2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. *For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.*

6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. *For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.*

6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. *For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.*

**Activities:**

- Finish lecture notes from last time.
- Talk about making bar graphs, circle graphs, histograms, and line plots in Excel and by hand. I showed you an example of an activity from Giaudrone Middle School, then walked you through making some graphs in Excel, and then gave you an activity to work on to create your own statistical graphs. This didn’t work out too well, partly because I have never used Office 2008 on a Mac. We will go over graphs again on Monday, hopefully with more success.

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**Class work: **Probability quiz, statistics practice if there is time.

**Sections covered: ****none**

**Activities:**

- Work on probability quiz
- If you finish early, work on the statistical graph problems I will give out in class. These will be due on Monday.

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**Class work: **finish probability, discuss statistical graphs

**Sections covered: **Parts of 29.1-30.2

**Activities:**

- Revisit the problem from last time (problem 9 in Section 28.4).
- Discuss group homework assignment.
- Talk about statistical graphs. We will use PowerPoint slides. We will probably not finish this today, but on Friday.
- Here is a document from the Columbia University statistics department about lying with statistics.

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