7-C-2 October 31, 2009

Tara Buffett

7-C-2

Page 576 4-6

4. This type of sampling, telephone sampling, would not be a random, large sampling, because some people do not have a landline phone or phone service at all.  Also some people have unlisted phone numbers.

5. Unlisted phone numbers and people without landlines or numbers that would be in the phonebook would be left out of the sample.

6. Random sampling would be best.  There should be a design so that everyone has an equal chance of being surveyed.

Page 580-581 Problems 1-6

1. The highest return rate was the envelopes labeled research study, which had a return rate of 91%.  The book said that people may have felt more of an urgency to return this type of envelope.
2. The lowest return rate was the envelopes labeled containing money, which had a return rate of 68%.  This may have been because people were more tempted to keep this type of envelope with the hope of gaining the money included.
3. The experiment envelopes may have been used as a variable that would be somewhat neutral.  People had nothing to gain except a feeling of honesty for returning the envelopes labeled research.  They didn’t even know what type of research they may have been supporting.
4. When the envelopes with potential money in them were returned, they were most likely counted as envelopes that came back unopened and envelopes that came back that had been resealed.  This would tell how many were truly honest and how many may have opened the envelope first to see what they could gain before returning it.
5. I noticed a couple of patterns.  The research study envelopes came back less than any other type of envelope.  Envelopes containing blank sheets of paper came back the most.  Among the envelopes returned with potential money in them, the poor areas returned the least, the wealthy returned the most, and the middle area returned a middle amount.

6. Perhaps this is not valid because we do not know if there were a great enough number of samples taken, and we do not know how many of each class may have peeked at the envelopes before returning them.

 

 

Module 7 Vocabulary October 31, 2009

Mean-The “mean” is the “average”, where you add up all the numbers and then divide by the number of numbers.

 

Median- The “median” is the “middle” value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first.

Mode- The “mode” is the value that occurs most often. If no number is repeated, then there is no mode for the list.

• Find the mean, median, mode, and range for the following list of values:

13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean isn’t a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.

The median is the middle value, so I’ll have to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14.  -2008 All Rights Reserved

The mode is the number that is repeated more often than any other, so 13 is the mode.

mean: 15
median: 14
mode: 13

Note: The formula for the place to find the median is “( [the number of data points] + 1) ÷ 2″, but you don’t have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer. Either way will work.

Above definitions from: http://www.purplemath.com/modules/meanmode.htm

 

Histogram-a bar graph in which the area of each bar is proportional to the frequency or relative frequency represented.

http://www.yourdictionary.com/histogram

Bar Graph- a graph in which the lengths of parallel bars are used to compare statistical frequencies, quantities, etc.

http://www.yourdictionary.com/bar-graph

binomial probability scenario October 23, 2009

A student is taking a 10 question true false (2 choices per question) test.  The student did not study for the exam and after reviewing each question realizes he does not know a single answer.

Undaunted the student decides to adopt the “guess” strategy.

What is the probability that the student will pass (make at least 60%) the exam?

Probability of success = .5 ½ or 50 percent per question

Number of independent trials = 10

Module 6 Vocabulary October 22, 2009

Probability- is the measure of how likely an event is.

Outcome- is the result of a single trial of an experiment.

Dependent  Event- Two events, A and B, are dependent if the fact that A occurs affects the probability of B occurring.

Independent Event- Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. A coin toss for heads or tails is independent.

Pascal’s Triangle- You start out with the top two rows: 1, and 1 1. Then to construct each entry in the next row, you look at the two entries above it (i.e. the one above it and to the right, and the one above it and to the left). At the beginning and the end of each row, when there’s only one number above, put a 1. You might even think of this rule (for placing the 1′s) as included in the first rule: for instance, to get the first 1 in any line, you add up the number above and to the left (since there is no number there, pretend it’s zero) and the number above and to the right (1), and get a sum of 1.

*I couldn’t get my images to show up for some reason.  Here are some links.

pascal’s triangle: http://www2.norwalk-city.k12.oh.us/wordpressmu/halgebra2/files/2009/04/pascals-triangle.gif

Dependent event: http://www.learningwave.com/lwonline/probability/prob4.gif

http://mathforum.org/dr.math/faq/faq.pascal.triangle.html

http://www.mathsisfun.com/pascals-triangle.html

October 17, 2009

Module Five Vocabulary

Faces-One of the flat surfaces making up a polyhedron. Note: The faces of a polyhedron are all polygons.

Edges-One of the line segments making up the framework of a polyhedron. The edges are where the faces intersect each other.

Vertices- A corner point of a geometric figure. For a polygon, vertices are where adjacent sides meet. For an angle, the vertex is where the two rays making up the angle meet.

Two-Dimensional- Formally, saying a plane has only two dimensions means that you can find two vectors in the plane for which neither is a multiple of the other. In addition, for any set of three vectors in the plane, one of them can be written as a linear combination of the other two.

Three- Dimensional- The property of the space in which we live and move that indicates motion can take place in three mutually perpendicular directions. This is often expressed with three-dimensional coordinates. Formally, saying a space has three dimensions means that you can find three vectors in the space for which none is a linear combination of the other two. In addition, in any set of four vectors one of them can be written as a linear combination of the other three.

all definition came from: http://www.mathwords.com

Mathematical Mosaics 5-B-2 October 16, 2009

Tara Buffett

1. 6-6-6
2. 4-8-8
3. 3-3-3-3-6
4. 4-6-12
5. A 5-6-8 mosaic is not possible since the angles of 108 + 120 + 135 = 363 and it can only be 360.
6. A 5-5- 10 mosaic could exist. The sum of the angles is 360.

108 + 108 + 144 = 360

1. In the figure, points A, B, D, and E are surrounded by 2 pentagons and a decagon.
2. The mosaic doesn’t continue because point C is not surrounded by a decagon, which leaves a gap.  Therefore, the mosaic is discontinued.
3. Judging by the example picture and number 6, I would say yes.  However, this pattern cannot continually be repeated.

Good Questions for First Grade

1. I would model creating a mosaic.  Then I would give my students pre-cut polygons and challenge them to create their own mosaics.
2. I may also let students observe a mosaic pattern.  Then I would ask them to identify the polygons, and then I would ask them to identify how many points surround each polygon.  Finally, I would ask them to create another mosaic with the same number of points surrounding the polygons.
3. Another activity that the students may do is to explore the angles around the polygons.  Students could be given a variety of possible, and they would work in groups with manipulatives to determine if the angles add up to 360.  The students would need to defend their answers.  If the suggested mosaic did not work, the students should be challenged to come up with a mosaic that would work.

Helpful Websites October 10, 2009

http://www.proteacher.com/100021.shtml

This website includes a variety of lesson plans for teachers to implement while teaching Geometry.  It provides a variety of activities as well as links to other sites that may be helpful. It contains more than Geometry plans as well.  I found it very useful

http://cte.jhu.edu/techacademy/web/2000/heal/siteslist.htm

This site contains many webquests that would allow for hands on student interaction.  Some of the links were no longer active, but many still are.  I hope you find this one useful.

http://www.ics.uci.edu/~eppstein/junkyard/teach.html

The web site contained many links to ideas for projects involving geometry.  The site suggests that the teacher use these ideas as auxiliary sources for teaching.  These are great plans to use for reteaching and reviewing.

http://mathforum.org/math_talk_landing.html

This site contains resources for teachers to communicate with other teachers about teaching math.  Teachers can ask each other questions and give advice.

Math Vocabulary Week 4 October 8, 2009

Arithmetic Sequence- Arithmetic sequence is a sequence of numbers that has a constant difference between every two consecutive terms. In other words, arithmetic sequence is a sequence of numbers in which each term except the first term is the result of adding the same number, called the common difference, to the preceding term.

Common Difference: The constant number that is added in a arithmetic sequence.

http://www.icoachmath.com/(S(bedtldvnqe2v3v45bc5aiv45))/SiteMap/DictionaryDefinition.aspx?process=sitemap/arithmeticsequence&

Geometric Sequence- Geometric sequence is a sequence in which each term after the first term a is obtained by multiplying the previous term by a constant r, called the common ratio.

1, 2, 4, 8, 16, 32, . . . is a geometric sequence.

Common Ratio: The constant number that is multiplied in a geometric sequence.

http://www.icoachmath.com/SiteMap/DictionaryDefinition.aspx?process=sitemap/geometricsequence&&AspxAutoDetectCookieSupport=1

Exponent: An exponent is a mathematical notation that implies the number of times a number is to be multiplied by itself.

Sequence of Squares October 8, 2009

Sequence of Squares:

Page 84

18. 1, 3, 6, 10, 15, 21, 28, 36, 45, 55

19.       1= 1

1+2= 3

1+2+3= 6

1+2+3+4= 10

1+2+3+4+5= 15

20. These are Triangular Numbers.

21.

1            3            6            10            15            21            28            36            45            55

4          9           16         25        36          49      64         81        100

22. The resulting numbers are the sequence of squares.

23.   I honestly had to look couple of different sites (listed below) to get a good idea of what the relationship between triangular numbers and square numbers is.  Each square number can be represented as the sum of two successive triangular numbers. Geometrically speaking, each square array can be built by adding the the next highest triangular array to it.

http://milan.milanovic.org/math/english/triangular/triangular.html

http://honolulu.hawaii.edu/distance/sci122/Programs/p6/p6.html

Works Referenced:

http://www.ijicic.org/el09-0301.pdf

http://nationalstrategies.standards.dcsf.gov.uk/downloads/pdf/ma_sf_exmp_57_59_036608.pdf

Vocabulary- Module 3 October 2, 2009

Deductive Reasoning (This is when you use logic in order to come to conclusions based on facts we believe are true.) Method of reasoning from general to particular, it is employed  in deriving general laws or principles from the observed phenomenon. With analogy and inductive reasoning, it constitutes the three basic modes of thinking. Also called deduction.

Source: http://www.businessdictionary.com/definition/deductive-reasoning.html

Inductive Reasoning (drawing conclusions from a small set of observations) Method of reasoning from particular to general; the mental process involved in creating generalizations from the observed phenomenon or principles. With analogy and deductive reasoning, it constitutes the three basic tools of thinking. Also called induction.

Source: http://www.businessdictionary.com/definition/inductive-reasoning.html

Number sense (This is knowing how to apply mathematical prinicpals.)

A person’s ability to use and understand numbers:

* knowing their relative values,
* how to use them to make judgements,
* how to use them in flexible ways when adding, subtracting, multiplying or dividing
* how to develop useful strategies when counting, measuring or estimating.

Source: http://www.mathsisfun.com/definitions/number-sense.html