# Kim Delaney NYPD Blue Prince Harry

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```					    STATISTICS & PROBABILITY
IN ELEMENTARY & MIDDLE SCHOOL.

by

RICK A. CAZZATO
Hinsdale South High School

http://www.hinsdale86.org/staff/rcazzato/

rcazzato@hinsdale86.org

(630) 468-4448
Randomization & Bias
Random Rectangle Activity & “Numbers” worksheet

Reference: http://www.pbs.org/newshour/extra/teachers/lessonplans/math/recall_math_handout.pdf

One Variable Statistics
The mean and median.

Resources:    Seeing Math: http://seeingmath.concord.org/sms_interactives.html
Illuminations: http://illuminations.nctm.org/

Two Variable Statistics
Ice Cream problem & Age problem.

Probability
Flipping a coin versus Spinning a Coin

Tack Toss

What is the Probability of a Kiss? (It’s Not What You Think)
http://www.amstat.org/publications/jse/v10n3/haller.html

Cup toss:
http://www.nsa.gov/teachers/es/prob44.pdf#search='statistics%2C%20probability%20of%20a%2
0cup%20landing%20on%20its%20side'

Counting Problems
Clown Activity Sheet
http://illuminations.nctm.org/LessonDetail.aspx?ID=L614
http://illuminations.nctm.org/lessons/combinations/Combinations-AS-Clowns.pdf

Shorts and Shirts Activity Sheet
http://illuminations.nctm.org/ActivityDetail.aspx?ID=3 (Applet)
http://illuminations.nctm.org/LessonDetail.aspx?ID=U75
http://illuminations.nctm.org/LessonDetail.aspx?ID=L180
http://illuminations.nctm.org/lessons/combinations/Combinations-AS-ShortsandShirts.pdf

Ice Cream Cones
http://illuminations.nctm.org/LessonDetail.aspx?ID=L181
http://illuminations.nctm.org/lessons/combinations/Combinations-AS-IceCreamCones.pdfProblem
1    1
2    2
3    3
4    4
5    5
6    6
7    7
8    8
9    9
10   10
11   11
12   12
13   13
14   14
15   15
16   16
17   17
18   18
19   19
20   20
21   21
22   22
23   23
24   24
25   25
26   26
27   27
28   28
29   29
30   30
31   31
32   32
33   33
34   34
35   35
36   36
37   37
38   38
39   39
40   40
41   41
42   42
43   43
44   44
45   45
46   46
47   47
48   48
49   49
50   50
Rank each of the flavor of ice cream from your favorite (1) to your least favorite (10).

Partners
Flavor            My rank        rank
Butter Pecan
Chocolate
Chocolate Chip
Coconut
Mint Chocolate
Chip
Orange Sherbert
Peppermint
Strawberry
Vanilla

10

8

6

4

2

0
0                                         5                                   10
Name                 Estimate        Actual
Fats Domino
Kate Moss (model)
Cheryl Crow
Lance Armstrong
Russel Crow
Jerry Seinfeld
Ellen DeGeneres
Jennifer Aniston
Wayne Gretzky
Henry Winkler
Misssy Elliiot
Christian Slater
Al Roker
Dweezil Zappa (Singer)
Kim Delaney (NYPD Blue)
Prince Harry

100

90

80

70

60

50

40

30

20

10

0
0     10      20      30     40       50        60   70   80   90   100
arm
Name               span    height   gender
Mr. C             188.5    181       m
Amy               167.3   169.5       f
Kim               166.2   168.3       f
Arsen              179.5   177.5      m
Muff               180     177       m
Maggie             164.7   166.6       f

Class Data

190

185

180
Armspan

175

170

165

160
160           165         170         175     180   185   190
Height
Tack Toss

100

90

80

70

60

50

40

30

20

10

0
0   1   2   3   4   5   6   7   8   9   10
Problem Solving
Instructional programs from prekindergarten through grade 12 should enable all students to—

   build new mathematical knowledge through problem solving;
   solve problems that arise in mathematics and in other contexts;
   apply and adapt a variety of appropriate strategies to solve problems;
   monitor and reflect on the process of mathematical problem solving.

Reasoning and Proof

Instructional programs from prekindergarten through grade 12 should enable all students to—

   recognize reasoning and proof as fundamental aspects of mathematics;
   make and investigate mathematical conjectures;
   develop and evaluate mathematical arguments and proofs;
   select and use various types of reasoning and methods of proof.

Communication

Instructional programs from prekindergarten through grade 12 should enable all students to—

   organize and consolidate their mathematical thinking through communication;
   communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
   analyze and evaluate the mathematical thinking and strategies of others;
   use the language of mathematics to express mathematical ideas precisely.

Connections

Instructional programs from prekindergarten through grade 12 should enable all students to—

   recognize and use connections among mathematical ideas;
   understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
   recognize and apply mathematics in contexts outside of mathematics.

Representation

Instructional programs from prekindergarten through grade 12 should enable all students to—

   create and use representations to organize, record, and communicate mathematical ideas;
   select, apply, and translate among mathematical representations to solve problems;
   use representations to model and interpret physical, social, and mathematical phenomena.
Data Analysis and Probability Standard for Grades Pre-K–2

Expectations
Instructional programs from              In prekindergarten through grade 2 all students should—
should enable all students to—

Formulate questions that can be          • pose questions and gather data about themselves and their
addressed with data and collect,             surroundings;
organize, and display relevant data to   • sort and classify objects according to their attributes and organize
•   represent data using concrete objects, pictures, and graphs.

Select and use appropriate statistical   • describe parts of the data and the set of data as a whole to determine
methods to analyze data                      what the data show.

Develop and evaluate inferences and
predictions that are based on data
• discuss events related to students' experiences as likely or unlikely.

Understand and apply basic
concepts of probability

Data Analysis and Probability Standard for Grades 3–5

Expectations
Instructional programs from              In grades 3–5 all students should—
should enable all students to—

addressed with data and collect,             collection methods affect the nature of the data set;
organize, and display relevant data to   •   collect data using observations, surveys, and experiments;
answer them                              •   represent data using tables and graphs such as line plots, bar graphs,
and line graphs;
•   recognize the differences in representing categorical and numerical
data.

Select and use appropriate statistical   • describe the shape and important features of a set of data and
methods to analyze data                      compare related data sets, with an emphasis on how the data are
distributed;
•   use measures of center, focusing on the median, and understand
what each does and does not indicate about the data set;
•   compare different representations of the same data and evaluate how
well each representation shows important aspects of the data.

Develop and evaluate inferences and      • propose and justify conclusions and predictions that are based on
predictions that are based on data           data and design studies to further investigate the conclusions or
predictions.

Understand and apply basic               • describe events as likely or unlikely and discuss the degree of
concepts of probability                      likelihood using such words as certain, equally likely, and impossible;
• predict the probability of outcomes of simple experiments and test the
predictions;
• understand that the measure of the likelihood of an event can be
represented by a number from 0 to 1.

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