Integrated Math I Syllabus
2006 - 2007
Instructor: Wm. George, Room 5
Email bgeorge@msad56.org Website http://sdhsmath.blogspot.com
(Blue 1, Blue 2, and Blue 3) (White 4 - Ms. King)
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 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 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. During this year, you will continue to sharpen these 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
Students will understand and demonstrate a sense of what numbers mean and how they are used. Students will be able to describe the structure of number systems and when to use it.
Numbers are used to describe and interpret phenomena. Building a sense of number relationships is essential for developing the ability to deal with any set of numbers. Number sense involves understanding the meaning of numbers, relationships among numbers, relative number magnitudes, and the effects of operations on numbers. Skilled estimation is also an important component of number sense.
Students will understand and demonstrate computation skills. Students will be able to approximate solutions, determine the reasonableness of answers, and justify the results.
Understanding the fundamental operations of addition, subtraction, multiplication, and division is central to knowing mathematics. Proficiency in computational skills is essential to problem-solving and other mathematical activities. Estimating, evaluating reasonableness of answers, and obtaining accuracy in calculations are included in this proficiency. Understanding relationships in operations allows students greater facility with mental computation. Computational skill promotes efficient and confident learners.
Students will understand and apply concepts of data analysis.
Students will be able to:
• Determine and evaluate the effect of variables on the results of data collection.
• Predict and draw conclusions from charts, tables, and graphs that summarize data from practical situations.
• Demonstrate an understanding of concepts of measures of central tendency, variation, and correlation and how they relate to data analysis.
We are faced with massive quantities of information which must be selected, sorted, and analyzed to reach conclusions. Sound decision making requires the ability to collect data effectively, organize data, discover patterns, summarize trends, make inferences, draw conclusions, and make predictions.
Students will understand and apply concepts of probability. Students will be able to make predictions by applying probability theory and apply probability distributions to solve problems.
Probability is the study of uncertainty. Informed consumers of information understand the basic principles of probability. People need to understand the uncertainties and limitations involved when drawing conclusions from data.
Students will understand and apply concepts from geometry. Students will be able to draw and manipulate geometric figures and be able to describe relationships between them.
Geometry is the study of the spatial world and its symmetries. The ideas of geometry are used to describe, interpret, represent, and change the spatial world in which we live. The understanding and development of spatial and visual skills strengthens problem-solving abilities.
Students will understand and demonstrate measurement skills.
Students will be able to:
• Use measurement tools and units.
• Derive and use formulas for area, surface area, and volume of many types of figures.
Measurement is valuable as an integrating skill throughout the curriculum and in everyday life. The use of estimation is vital in determining the reasonableness of measurement. Measurement attributes (e.g., length, volume, minutes), units, and tools enhance the ability to describe and understand the world.
Students will understand that mathematics is the science of patterns, relationships, and functions.
Students will be able to:
• Create a graph to represent real-life situation and draw inferences from it.
• Translate and solve a real-life problem using symbolic language.
• Model phenomena using a variety of functions (linear, quadratic, exponential, trigonometric, etc.)
• Identify a variety of situations explained by the same types of function.
Relationships are central to mathematical understanding. A study of patterns often reveals regularity, indicating the presence of a mathematical relationship. Studying relationships allows students to make generalizations and predictions about phenomena and occurrences.
Students will understand and apply algebraic concepts.
Students will be able to:
• Use tables, graphs, and spreadsheets to interpret expressions, equations, and inequalities.
• Investigate concepts of variation by using equations, graphs, and data collection.
• Formulate and solve equations and inequalities.
• Analyze and explain situations using symbolic representations.
Algebra and analytic thinking are fundamental tools for working in and thinking about mathematics. These tools provide ways to generalize and predict problem solutions when not all information is known. Taught within the context of mathematical and practical applications, the concept of functions is a unifying theme for algebraic concepts.
Students will understand and apply concepts in discrete mathematics. Students will be able to use networks and matrices to find solutions to problems.
Discrete mathematics studies discrete processes (e.g., all possible bus routes in a school district). This study includes the exploration of diagrams, networks, and flowcharts that students construct to model situations or use for planning, scheduling, and decision making. Three main concerns of discrete mathematics are: existence (Is there a solution?), counting (How many solutions are there?), and efficiency (What is the best solution?).
Students will understand and apply concepts of mathematical reasoning. Students will be able to analyze situations where more than one logical conclusion can be drawn from data presented.
Reasoning is fundamental to the knowing and doing of mathematics. To give more students access to mathematics as a powerful way of making sense of the world, it is essential that an emphasis on reasoning pervade all mathematics. Students need a great deal of time and many experiences to develop their ability to construct valid arguments in problem settings and to evaluate the arguments of others.
Students will reflect upon and clarify their understanding of mathematical ideas and relationships. 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.
Communication plays a key role in helping make important connections among physical, pictorial, graphic, symbolic, verbal, and mental representations of mathematical ideas. Providing individual and collaborative opportunities for discussions about issues, people, and the cultural implications of mathematics reinforce student understanding of the connection between mathematics and our society.
Course Content
Units Mathematics:
Unit 1 Patterns in Data Statistics
Unit 2 Patterns of Change Algebra & Functions
Unit 3 Linear Models Algebra & Functions
Unit 4 Graph Models Discrete Mathematics
Unit 5 Patterns in Space & Visualization Geometry & Trigonometry
Unit 6 Exponential Models Algebra & Functions
Unit 7 Simulation Models Statistics & Probability
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, or after school in Academy.
Exceeds the Standard 4 or 4.5
Meets the Standard 3 or 3.5
Partially Meets the Standard 2 or 2.5
Not Engaged N/E
Please sign and return this portion:
I have read and understood the course syllabus for Integrated Math I.
Student Signature: _______________________________________ Date: ___________
Parent/Guardian Signature:_________________________________ Date: ___________
Questions, Comments, Concerns:
