AFNORTH INTERNATIONAL MIDDLE/HIGH SCHOOL

Math 8

Course Syllabus

Mr. Zuber

SY 2004-2005

COURSE TITLE: MATH 8

TEACHER: Lloyd H. Zuber

E-MAIL: lloyd_zuber@eu.odedea.edu

COURSE DESCRIPTION:

The grade 8 math curriculum encourages students to investigate mathematical concepts through exploratory, activity-based learning. The grade 8 math course is designed to present topics in computation, including operations with whole numbers, decimals and fractions, integers, rational numbers, and real numbers. Number theory facts are employed to solve problems with fractions, ratios, and percents. Students will be introduced to solving one- and two-step equations and inequalities: measuring angles, perimeters, volumes and area using metric and customary units: graphing to include the coordinate plane: and estimating conclusions through the use of probability and statistics. The use of hands-on individual and cooperative activities and concrete models makes each concept more understandable and memorable. Instructional activities will involve students in a step-by-step process in performing computations mentally, with paper and pencil, and with calculators or computers; in using proper instruments for geometric constructions and measurement; and in applying mathematical concepts to everyday situations. Problem-solving strategies will teach students to read, analyze, plan, solve and check multi-step problems.

COURSE STANDARDS:

The Standards and expectancies for Pre-Algebra 8 place emphasis on core concepts of algebraic and geometric reasoning. Students will also be involved in investigations, and demonstrate understanding in the areas of data analysis, the mathematics of chance, fractal geometry and chaos theory, and functions. A strong emphasis on mathematical concepts and understanding also supports the development of problem solving. While learning mathematics, students will be actively engaged, using tools and appropriate technologies such as calculators and computers. Students should be encouraged to explain summarize, analyze, design and evaluate mathematical ideas in writing and discussion for the following set of standards.

Standard - Mathematics As Problem Solving

Students should show proficiency in being able to:

· Solve multi-step problems using mathematical operations with real numbers

· Use proportional reasoning to solve real-life problems involving probability, geometric attributes, and statistics

· Select appropriate problem-solving strategies such as guess and check, solve a simpler problem, find patterns, work backwards, model, or use technology to solve problems

· Evaluate alternative problem solving techniques to choose effective approaches to particular situations.

· Solve realistic problems having consumer and career applications

· Formulate problems to be solved based on the student's own interests

· Formulate questions from given sets of graphical, written, or oral information

· Compare and contrast different solutions to the same problem

· use divergent thinking to develop and defend possible solutions to open-ended questions

· Work cooperatively to solve non-routine problems

Standard - Mathematics As Communication

Students should show proficiency in being able to:

· Function effectively as a contributor during group activities

· Express, discuss, and justify problem solving strategies and processes in oral and written form

· Use calculators or appropriate technology to store, retrieve, and communicate information

· Write and discuss ideas to interpret and formulate solutions, including making predictions and conjectures

· Explain the mathematical concepts attached to the symbols used in middle school mathematics

· Use mathematical vocabulary purposefully in communicating concepts and interpret information described in graphs or charts

· Formulate written problems that reflect situations encountered in real life

· Model mathematical situations with concrete objects including transformations

Standard - Mathematics As Reasoning

Students should show proficiency in being able to:

· Develop and apply appropriate deductive or inductive reasoning strategies to solve problems

· Draw appropriate diagrams to aid in the solution of problems in 3-dimensional space

· Draw representations of 3-dimensional objects rotated a certain number of degrees in a given direction if shown the pictorial representation of the 3-dimensional object

· Write logical arguments to mathematically illustrate why solutions do not work

· Reason from counter-examples

· Develop dichotomous classification systems which can be used in other subject areas

· Solve logic problems in 3-dimensions

· Test mathematical conjectures

· Collect data, represent it graphically, interpret the information presented, and validate the conclusions

· Generate sets of specific instances, organize those instances, and identify patterns within the sets

Standard - Mathematical Connections

Students should show proficiency by being able to:

· Categorize and graph mathematics used in newspapers or periodicals such as stock market activity over a specified time

· Collect, organize, graph, and interpret class data obtained from other subject areas

· Use various resources to collect, plot, and display information from our own and other countries such as death rate and gross national product

· Write poems or journal entries about the relationship between mathematics and everyday life

· Recognize the relationships between timelines and number lines by plotting events from students' personal lives on timelines

· Use road atlases and calculators to determine distances between cities and compute costs of travel

· Find and record patterns and symmetry in nature such as honeycombs, snowflakes, leaves, spider webs, etc and identify numerical patterns in musical compositions

· Gather information on past local, regional or national weather and make predictions about future weather conditions

· Calculate the cost of utilities after finding the cost of kilowatt hours of electricity, cubic meters of natural gas, liters of gasoline, and minutes of long distance telephone calls

· Connect the concepts of simplifying arithmetic fractions and simplifying algebraic fractions

Standard - Computation And Estimation

Students should show proficiency in being able to:

· Solve problems involving the use of the four basic operations with rational numbers

· Solve equations and proportions

· Demonstrate the relationship between percents and percentages

· Solve problems which require the use of scientific notation

· Solve problems which involve the percent increase or decrease

· Estimate the solutions of problems involving real numbers

· Plot x and y values for rules involving addition and subtraction of fractions

· Explain orally or in writing what happens when two fractions are multiplied

· Construct pie charts from data sets

· Generate equivalent expressions of portions of whole numbers in a variety of formats [i.e. 1/5 of 25, 20% of 100, (57)(.10)] and explain why they are equivalent

· NOTE: It is understood that all students will have access to calculators at all times.

Standard - Number Sense, Number Operations, And Number Relationships

Students should show proficiency in being able to:

· Use multiple representations of numbers in problem writing

· Find examples of scientific research in which whole numbers and decimals are expressed in exponential form and using scientific notation.

· Illustrate and use the properties of addition and multiplication to simplify expressions

· Demonstrate the hierarchy of the real number system with set notation

· Explain the attributes of prime and composite numbers

· Demonstrate the results of arithmetic operations on positive and negative integers and write rules to govern the operations

· Compare and order irrational numbers on number lines

· Represent irrational numbers geometrically, such as square roots of non-perfect squares

· Use the relationship among ratio, percent, and proportion to solve real-world problems

· Express whole numbers in bases other than 10

· Make generalizations about the size of fractions as their denominators and/or numerators move toward specific limits

Standard - Patterns, Relationships, And Functions

Students should show proficiency in being able to:

· Describe the advantages and disadvantages of using tables of data, graphs, and expressions to describe functions

· Use observed patterns in gathered data to generalize to other situations

· Distinguish between constants and variables in commonly used formulas

· Compose rules in statement form and translate the written statements to symbolic form

· Construct graphs from tables of values

· Determine the relationship between parts of geometric figures by analyzing proportional data gathered from repeated measurements

· Generalize the process of predicting the maximum area determined by given perimeters.

· Describe how changing the value of an independent variable affects the dependent variable in linear relationships

· Combine concrete objects to form all possible combinations from sets containing at least 3 objects

Standard - Probability And Statistics

Students should show proficiency in being able to:

· Interpret and analyze displayed data and make appropriate inferences and predictions

· Choose appropriate scales to construct graphs, charts, or diagrams for data

· Collect, organize, and present numerical data in a variety of forms (stem and leaf plots, box and whiskers, scatterplots, etc.)

· Find the measures of central tendency of sets of data and describe the statistics

· Use tables of outcomes from sample spaces to predict the probability of future outcomes and construct area models to determine expected values of probability problems

· Determine the probability of a pair of independent or dependent events

· Predict the theoretical probability of an event occurring after analyzing collected trial data

· Compare collected trial data and computer simulated results to theoretical probabilities

· Use computer spreadsheet software to investigate how changes in one or more quantities affects the measures of central tendency

Standard - Geometry

Student should show proficiency in being able to:

· Use the Pythagorean relationship to determine the unknown side in right triangles

· Identify and analyze fundamental transformations of translations, reflection, and rotations

· Complete constructions using a compass, straightedge, or reflective device

· Identify and classify the symmetries of geometric figures

· Use computer programs, such as Logo or a geometric manipulator, to test conjectures

· Identify objects in the classroom and in the environment which are proportioned according to the golden ratio

· Recognize and construct regular and semi-regular tessellations and write conjectures about regular polygons which will or will not tessellate a plane either in isolation or combination

· Use Pick's Theorem in connection with geoboards to determine formulas for areas of irregular figures

· Determine the slopes of lines graphed on coordinate planes

· Use concrete objects to validate theorems

· Solve problems involving constant and varying rates in relationship to time

Standard - Measurement

Students should show proficiency in being able to:

· Make and display scale drawings of objects and determine surface areas and volumes of solids

· Demonstrate the proper use of a variety of measuring instruments such as rulers, protractors, compasses, thermometers, scales, balances, etc

· Discuss the amount of error acceptable in a particular measurement

· Determine the inherent error in measuring instruments by comparing a variety of measurements made with a given instrument (i.e., speedometers)

· Write stories which contain metric and English measurements in problem situations

· Formulate problems involving constant and varying rates in relationship to time

· Solve elapsed time problems

· Use concrete materials to demonstrate the effect of holding one variable constant while changing the value of another variable such as building polyhedra with varying volumes and constant surface areas

Standard -Algebra

Students should show proficiency in being able to:

· Evaluate given expressions requiring the use of accepted order of operation rules

· Graph linear functions on coordinate planes

· Find the slope of lines

· Develop formal methods for solving linear equations and inequalities after experimenting with informal methods

· Solve given problems algebraically using proportions, formulas, and functions

· Use concrete, numerical, and graphic models to describe algebraic models for relationships (i. e., perimeter equals twice the length plus twice the width)

· Use graphing utilities to generate relationships between two expressions from real world contexts

· Draw transformations on coordinate systems from given descriptions and vice-versa

· Solve linear equations when given replacement sets for one variable

· Make predictions of decay from exponential sequences

AFNORTH International Middle/High School’s CSP (Continuous School Progress) goal is:

“All students will improve their written communication skills across the curriculum.” The 6 + 1 trait is the model selected to improve school-wide writing in all subject areas. The 6+1 Trait writing framework is a powerful way to learn and use a common language to refer to characteristics of writing as well as establish a common vision of what “strong” writing looks like. Teachers and students will use the 6+1 Trait model to identify areas of strength and weakness as they continue to strive towards continued writing improvement. Success of all students requires that the 6 + 1 Trait become a consistent and integral component of each course taught at AFNORTH International Middle/High School.

• All tests (4-5 per quarter) will contain at least one problem in which the student will be required to write a paragraph detailing how they would solve and check that problem. These problems will be scored based on a rubric involving both content and their understanding and use of one of the 6+1 Traits
• Students will receive in class training and practice in writing the above paragraphs.
• Students will be able to receive full credit on one wrong problem per test by completing the following written extra credit sheet.

Name________________________________ Date______________

Rewrite

Problem #_____________

a) Complete Explanation of what I did wrong on this problem:

_________________________________________________________________

B) Detailed explanation of the correct solution: Be sure to explain your reasoning and what you know about the underlying concepts.

c) Correct solution to the problem, with all of my work shown.

SCOPE AND SEQUENCE:

Lesson 1: Diagnostic Test

Lesson 2: Problem solving and rates; Displaying data

Lesson 3: Scatter plots

Lesson 4: Perimeter, circumference, area, volume

Lesson 5: Write and solve equations: Simplify expressions

Lesson 6: Area and perimeter

Lesson 7: Samples and percents

Lesson 8: Proportions and percents

Lesson 9: Percent of change

Lesson 10: Exploring probability; Theoretical probability

Lesson 1: Adding Integers

Lesson 2: Multiplying and dividing integers

Lesson 3: Adding positive and negative fractions

Lesson 4: Subtracting positive and negative fractions

Lesson 5: Graphing inequalities

1^st

1^st quarter notebook

2^nd quarter Notebook

Module1: Amazing feats facts and fiction

Module 2: At the Mall

SEMESTER MODULE LESSONS

COURSE GRADING AND ASSESSMENT:

Each Semester is split into two quarters. During the quarter, a student will take four or five tests worth 100 points each. Assignments can be expected daily. These will be checked by a 10-point homework quiz based on the assignment. It is required that work be shown on all assignments. All assignments should have a heading in the upper right hand corner consisting of:

Name

Page numbers and Exercise Numbers

Section Number.

Other Quizzes will be given at various times. These will be worth 5 to 20 points.

Grading Scale:

A+ 97 – 100%

A 93 - 96

A- 90 -92

B+ 87 - 89

B 83 - 86

B- 80 - 82

C+ 77 - 79

C 73 – 76

C- 70 - 72

D+ 67 - 69

D 63 - 66

D- 60 - 62

F Below 60%

A notebook is required, and will be picked up each quarter. This notebook should contain all assignments, class notes, and handouts. It is worth 100 points.

The Semester grade consists of the two quarter grades plus a Semester Exam. The Semester Exam equals one half of a quarter grade making it worth 20 percent of the grade.

COURSE EXPECTATIONS/CONSEQUENCES:

It is expected that all students will come to class with a willingness to learn. Classroom time is to be used for learning. Behavior should never interfere with learning. Students are expected to bring all necessary supplies with them. No gum chewing is allowed. No Walkmans or other listening devices are allowed. No sunglasses are allowed. Students need to use the restrooms in between class periods. If a student must use the restroom during class, they will be expected to remain after class for a period of 3 minutes.

TEXTBOOKS:

Middle Grade Maththematics, Book 3, McDougal Little

SUPPLIES:

Notebook – 3 ring binder preferred Loose-leaf paper

Graph paper pen or pencils

Ruler – Metric and English calculator*

*A set of graphing calculators will be available for classroom use.

HOMEWORK POLICY:

Assignments are essential. Very few students can pass Math 8 without faithfully completing the assignments. Assignments are expected to be turned in on time. An extension of one day will be granted if a student is having difficulty with an assignment. Otherwise, late assignments will receive one point.

MAKE-UP WORK POLICY:

Assignments not turned in because the student was absent when it was assigned are not considered late. This applies only to excused absences. A student will routinely have an extension of as many days as he was absent. It is expected that tests missed due to excused absences will be made up within one week of the absence.

EXTRA HELP:

Please feel free to come see me during seminar period if you feel that you need extra help. I am also available after school by appointment.