In class Wed 9/30

Today we worked in class on the review handout for Unit 1 Lessons 2 and 3, Measures of Center and Measures of Variability, for the assessment which will be on Friday.

Homework Mon 9/28

Today we measured and compared variability in data sets, by making several box and whisker plots on the same scale using car rating data. We found the five number summary, minimum, quartile 1, median, quartile 3, and maximum and used graphing calculators to create multiple box and whisker plots to compare their variability. We used the handout provided in class to examine how mean and standard deviation can be used to describe and compare data sets. Homework is pg 121 on the handout, #6. We use the CPMP tools:
http://www.wmich.edu/cpmp/CPMP-Tools/ to see how a distribution can have the mean determined using the balance point and how to estimate the standard deviation.

In class Thurs 9/24

Today we began by creating a box and whisker plot (boxplot) and looked at the following vocabulary:

Percentile = A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.

Quartile = A quartile is any of the three values which divide the sorted data set into four equal parts, so that each part represents 1/4th of the whole data set

Determine the 5-Number Summary

* Minimum = lowest data value
* Quartile 1, (Q1) = (25th Percentile) = lower quartile = cuts off lowest 25% of data
* Median, (Q2) = (50th Percentile) = middle value
* Quartile 3, (Q3) = (75th Percentile) = upper quartile = cuts off highest 25% of data, or lowest 75%
* Maximum = highest data value

the Interquartile Range (IQR) is the difference between the third and first quartiles

the Range is the difference of the maximum and the minimum

We described the shape of the distribution of data from boxplots.
We determined when data is an outlier by collecting hand spans, compared it to a pro basketball players handspan, by using the rule for the fences:
Q1 - (1.5 x IQR)
Q3 + (1.5 x IQR)

Finally we determined the average deviations (distances) from the mean in each class to compare class variability.

Homework Tues 9/22

Todays homework is pg. 49-50, #2,3,4,5,7 and 8. You must use the growth chart we used in class to answer questions. Get a copy at:

For Girls, aged 2-20:
http://www.cdc.gov/nchs/data/nhanes/growthcharts/set2clinical/cj41l072.pdf

For Boys, aged 2-20:
http://www.cdc.gov/nchs/data/nhanes/growthcharts/set2clinical/cj41l071.pdf

Be familiar with percentiles, the value of a variable below which a certain percent of observations fall. So the 45th percentile is the value (or score) equal to or below which 45 percent of the observations may be found and 55 percent are found above it.

There will be the assessment on Unit 1, Lesson 2, measures of center coming up. Be able to create and interpret the stem and leaf plots(including back-to-back stem and leaf plots), number line plots, and histograms. Mean, Median, and Mode should be able to be found and interpreted. Understand sensitivity/resistance to changes in outliers for mean and median.

Homework Fri 9/18

Today we examined measures of central tendancy: "What is a typical number". As a class, we discussed Resistance To Outliers, pg 36, #6. After finding the mean of 13 and median of 4 for a set of numbers {1,2,3,4,5,6, 70} containing an outlier, then modifying the set of data to one with no outlier {1,2,3,4,5,6,7}, but a symmetric distribution, we found that the mean and median were both 4.

This led to the discovery that:

* the Mean is a measure of center that is sensitive to changes in outliers
* the Median a measure of center that is not very sensitive (resistant) to changes in outliers

We used the graphing calculator to sort lists (ascending or descending order) and to find the mean and median.

For homework, find four data sets using only six single digit numbers from the set {1,2,3,4,5,6,7,8,9} so that:

a) Mean = Median (mode different)
b) Mean > Median
c) Mean < Median
d) Mean = Median = Mode

Bonus for those whose mean and median have the largest difference between them.

We also registered for http://www.aleks.com

In Class and homework Wed 9/16

Today we did the first assessment, Unit 1, Lesson 1. Be able to describe and compare data distributions using the mathematical vocabulary we have used so far, and be able to create stem and leaf plots, number line plots and histograms.

In class we worked on pg. 30-31, #2. Read the passage then answer questions about the two graphs and one table that describe the data.

We also began creating and analyzing back-to-back stem and leaf plots to compare the amount of cholesterol between hamburgers and chickenburgers from data on pg. 32 and from pg. 33, #1.

Then we examined measures of central tendancy: "What is a typical number".

For classwork, we produced histograms with the TI-84 calculators, which allowed us to quickly describe and compare various data sets of car ratings from pg. 21, #2 (using data from pg.15)
Homework was from pg.24, #1, pg. 28, #3 and 4. (For an extra challenge, pg. 30, #2) will be done on Wednesday 9/17.

Skewed Left (data stretches to the left)
[also called negative skew]


Skewed Right (data stretches to the right)
[also called positive skew]

Symmetric distribution or nearly symmetric (both halves have same size and shape, through a line of symmetry)

This graph is approximately symmetric with some small variation from left to right halves.


Web sites to examine:
http://graphs.gapminder.org/world/
http://www.math.yorku.ca/SCS/Gallery/

In Class and homework Thurs 9/10

Todays homework is pg. 16, #2 in class and pgs. 17-18, #4, 5, & 6; and pg. 18-19, the "On Your Own" (OYO) questions. Work for class included organizing and interpreting distributions of data using number line plots and histograms. Be able to create these by hand as well as use them to answer questions about the data.
Be able to describe the distribution of a data set on a stem and leaf plot, a number line plot (dotplot) or a histogram using the concept of SYMMETRY. A Symmetric distribution would have both halves of the data set displayed have same size and shape, through a line of symmetry.
There will be the first assessment over Unit 1, Lesson 1, Describe/Compare/Explain using stem and leaf plots coming up.

Homework Tues 9/8

Today homework is from pgs. 12 and 13, # 8 to 11 and the On Your Own (OYO) #a and b.
There will be the first assessment upcoming next week over the Unit 1, lesson 1.
In class we were able to DESCRIBE, COMPARE, and EXPLAIN about data sets.
Be able to descibe data using appropriate vocabulary. Describe "what do you see?". If a feature is not present, you must say that it not present.

Vocabulary to DESCRIBE data (partial list):

* Maximum [highest value]
* Minimum [lowest value]
* Peaks [category(ies) of data that have distinctly most values, mode]
* Clusters [Grouping(s) of data]
* Gaps [Missing data value(s) in a distribution]
* Outliers [Data point(s) that is(are) distinctly separate from the rest of the data]

To COMPARE sets of data look for similarities and differences. Use "describe" words to address your similarities and differences.

When you EXPLAIN your reasoning, use clear, logical, and complete sentences with appropriate mathematical vocabulary to justify your conclusions. Be sure to answer the question as completely as you can.

In Class Thurs 9/3

Today after randomizing groups, we distributed the Integrated Math I Syllabus, parents letter, and Unit 1 rubrics. Be sure to return your completed syllabus acknowledgment form next class.

We distributed textbooks. Be sure to get your book covered!
We did a questionaire on getting to know you to be passed in next class.

We began an activity from the textbook, pg. 4-6, by collecting data including: height, armspan, thumb and wrist circumference, foot size and stride. After recording the class information, we discussed ways to describe the data. We will, next class, define and use appropriate vocabulary to describe, explain, and compare the data and make inferences from it.

Integrated Math I Syllabus 2009-2010

Integrated Math I Syllabus
2009 - 2010
Instructor: Wm. George, Room 16
Email bgeorge@msad56.org Class Website http://sdhsmath.blogspot.com
Core Plus project website: http://www.wmich.edu/cpmp
(White 2, White 3, White 4)
Text: Contemporary Mathematics in Context (Core-Plus)

Overview

This course is the first year of a four-year integrated mathematics program developed by the CORE PLUS MATHEMATICS PROJECT. Processes of problem solving, reasoning, communication, and connections are an integral part of each lesson. Investigations into real life situations use the mathematical topics of Algebra & Functions, Geometry & Trigonometry, Statistics & Probability, and Discrete Mathematics.
Learning is done collaboratively in small teams with assistance from the teacher. Students are assessed in a number of ways, including daily work, homework, projects, and tests and quizzes. During this year, you will encounter a fair amount of mathematical ideas.  You will learn new concepts and skills not merely by having someone tell you the facts and what to do but rather by you participating in activities and discussions. You will be using a graphing calculator every day and will become proficient with it by the end of the year. You will rely on the thinking of fellow classmates and expected to share your thoughts and ideas with them.
As your teacher, I will direct and moderate discussions and set up the activities.  You will maintain your own notebook (toolkit) that will summarize concepts, facts, skills, and methods that you will be learning.  The majority of class time will be spent with you working in collaborative groups.  The reason for this is that business and industry leaders are calling for workers who can think and reason about quantitative situations, who can communicate effectively, and who can work together on teams to solve problems.
During this year, you will continue to sharpen your mathematical skills.  Of course your effort is very important.  You must be willing to try hard, listen to others’ ideas, be willing to help, and ask for help.   I hope you set high goals for yourself and keep in mind that I will be here to do everything I can to help you reach those goals.

Math Content Standards

Number
Number Sense: Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations, with different types of numbers, use the structure and properties of numbers with operations to solve problems. Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers. It is expected that students use numbers flexibly, using forms of numbers that best match a situation.

Computation: Students compute efficiently and accurately as they perform mathematical computations. Estimation should always be used when computing with numbers or solving problems.


Data
Data Analysis and Statistics: Students make measurements and collect, display, evaluate, analyze, and compute with data to describe or model phenomena and to make decisions based on data.

Probability: Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement.

Geometry
Measurement: Students will understand and demonstrate measurement and observation skills to describe objects based on their sizes and shapes. Students use estimation to check the reasonableness of results when making or calculating measures.

Geometry: Students describe objects based on their sizes and shapes, model or construct two- and three- dimensional objects, solve problems involving geometric properties, compute areas and volumes based on object properties and dimensions, and perform transformations on geometric figures.

Algebra
Patterns, Relations, Functions: Students use symbols to represent or model quantities, patterns, and relationships and use symbolic manipulation to evaluate expressions and solve equations.

Algebra Concepts: Students solve problems using symbols, tables, graphs, and verbal rules choosing the most effective representation and converting among representations.

Communication and Reasoning
Communication: Students will be able to approximate solutions, verify the answers, and justify the results. Students will reflect upon and clarify their understanding of mathematical ideas and relationships.

Reasoning: Students will understand and apply concepts of mathematical reasoning. Students will be able to restate, create, and use definitions in mathematics to express understanding, classify figures, and determine the truth of a proposition or argument.





Course Content

Units
Mathematics:
Unit 1 Patterns of Change - Data Analysis and Statistics
Unit 2 Patterns in Data - Data Analysis and Statistics
Unit 3 Linear Functions - Algebra & Functions
Unit 4 Graph Models - Discrete Mathematics
Unit 5 Exponential Functions - Algebra & Functions
Unit 6 Patterns in Shape - Geometry & Trigonometry
Unit 7 Quadratic Functions - Algebra & Functions
Unit 8 Patterns in Chance - Data Analysis and Statistics


Grading Policy

The following scale will be used to access all work. Students will be expected to meet the standard on all assessed work. Students having difficulty meeting the standards will receive extra assistance during the school day in Lab, after school in weekly study sessions, or after school in Academy.






Integrated Math I Syllabus 2009-2010



Please sign both sections and return this page to me:



I have read and understood the course syllabus for Integrated Math I.


۞ Student Signature: _______________________________________ Date: ___________


۞ Parent/Guardian Signature:_________________________________ Date: ___________


Phone Number and/or Email for Contact: ___________________________________


Questions, Comments, Concerns:










I understand that if I am not meeting Integrated Math I Standards, I am required to attend study sessions after school from 2:10 p.m. to 2:55 p.m.. If I am not meeting Standards at Academy times, I am required to attend all necessary Academy sessions.


۞ Student Signature: _______________________________________ Date: ___________


۞ Parent/Guardian Signature:_________________________________ Date: ___________

First day of class for 9th graders, Tues 9/1

Welcome to the new 2009-2010 school year

Today is the first day of classes for 9th grade students, welcome to S.D.H.S.! There will be a mini schedule of classes from 11:10am to 1:48pm. 10th, 11th, and 12th graders will arrive on Wednesday, Sept. 2nd.

Integrated Math I students are reminded to get a notebook (1.5 inch, three ring binder type preferred) for your Math Toolkit, and an assignment book for your use.