AFNORTH International Middle/ High School

MATHEMATICS 7

Course Syllabus

Mr. Prescot Farris

SY2004-2005

Parent signature _________________________________ Date ______________
COURSE TITLE: Mathematics 7

TEACHER: Mr. Prescott Farris

ROOM: A 3.2

E-MAIL: prescott_farris@eu.odedodea.edu

COURSE DESCRIPTION: The mathematics 7 course is designed to ensure that the students understand the basic concepts of mathematics. The course includes practice in the four basic operations with whole numbers, fractions, decimals, and an introduction to integers. Topics in number theory, ratios and proportion, percents, and probability and statistics are included to increase students’ ability to manipulate numbers in computational ways; and topics in measurement, geometry, perimeters, areas, volumes, and probability are included to demonstrate the application of mathematics to real life situations.

Students will review number sets then proceed to use symbols to represent numbers and abstract ideas. Step-by-step models and algorithms will be used in performing basic operations and computations. Problem solving strategies will include recognizing patterns, estimating answers, and solving multi-step problems. Students will participate in activities in numerical computation, measurement, estimation, problem solving, and in activities that involve calculator use and computers.

COURSE GOALS/ OBJECTIVES/ STANDARDS: Upon completion of the mathematics 7 course, students should be able to:

· Perform the four basic operations with whole numbers, decimals, and fractions

· Solve word problems with information displayed in tables, graphs, and charts

· Formulate word problems involving multi-step operations

· Convert fractions to decimals and percents

· Make or draw a model to scale

· Solve problems involving percents

· Solve problems in measurement to include perimeters, areas, and volumes

· Identify pairs of angles having special relationships: supplementary, complementary, vertical, and adjacent

· Identify mean, mode, median, and range to describe data

The following DODDS standards apply:

The Standards and expectancies for Pre-Algebra 7 place emphasis on solving real life problems involving, ratios, percents, proportions, probability, statistics, and rational numbers. Students formulate, write, and defend real world problems involving multi-step operations. Students collect data, organize it in tables, graphs, or charts, interpret the information presented, and validate conclusions drawn from the information. Students will be involved in investigations where they will create and solve problems using perimeter, area, volume, angle measurement, capacity, weight, and time. 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:

· Determine the rules for generating given patterns of numbers

· Translate problems into mathematical equations

· Formulate, write and defend real world problems involving multi-step operations that may or may not include extraneous or insufficient information

· Solve real life problems involving proportions, ratios, percents, probability, statistics, and rational numbers

· Present the results of extended investigative projects

· Interpret data literally and inferentially

· Utilize technology to apply (solution techniques) to real-world situations

· Work cooperatively to solve non routine problems

· Model problems concretely and verify results

· Identify and formulate equations for solving single and multiple step problems

· Examine the consequences of choosing a particular problem solving strategy

Standard - Mathematics As Communication

Students should show proficiency in being able to:

· Justify solutions in group discussions

· Explain, make conjectures about, and defend mathematical ideas

· Discuss relationships between mathematical concepts and symbols

· Use computers and calculators to store, retrieve, and communicate information.

· Articulate, symbolically represent, and defend solutions to problems

· Accept other approaches and possible solutions to given problems

· Write stories about graphs of given sets of data

· Share predictions and conjectures with small and large groups

· Discuss the reasoning used to solve problems

· Model mathematical situations with concrete objects

· Express mathematical ideas in journals

Standard - Mathematics As Reasoning

Students should show proficiency in being able to:

· Use deductive reasoning to transfer general principles to specific facts

· Use inductive and deductive reasoning to make and validate conjectures and develop generalizations from specific examples.

· Construct valid arguments for selecting a particular problem solving strategy and compare the arguments of others

· Validate reasoning in proportion problems

· demonstrate spatial reasoning by testing conjectures about shapes on an overhead projector or using concrete models

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

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

· Illustrate mathematically why a solution does not work

· Reason from counter-examples

· Find dichotomous classification systems which are used in other subject areas

· Solve 3-dimensional logic problems

Standard - Mathematical Connections

Students should show proficiency in being able to:

· Identify and write descriptions of the various uses of math in the communication media (newspapers, magazines, television, etc.)

· Collect, graph and interpret personal data collected over time and compare the data with group and/or class data

· Plot and compare time-lines of technological, musical, or scientific discoveries to other historical events

· Write stories about the necessity of numbers in life

· Create stories explaining events and their significance from given graphs

· Create graphs to describe the events in stories

· Demonstrate mathematical concepts with concrete materials and symbolically represent the concrete models

· Use scaling, similarity, ratio, and proportion in map studies

· Observe and describe patterns in the real world such as in plowed fields, haystacks, paintings, leaves on trees, spirals on pineapples, etc

· Show examples of symmetry in art, nature, and architecture

Standard - Computation And Estimation

Students should show proficiency in being able to:

· Use basic operations with integers, decimals, and fractions in problem solving

· Develop algorithms for multiplying and dividing by powers of ten

· Solve real-world problems involving ratios and proportions

· Demonstrate the importance of the order of operations

· Develop and use divisibility rules for larger numbers

· Estimate the cost of materials needed to enclose or cover certain areas

· Estimate sale prices of items when given the original prices and the percent of discount

· Use estimation in conjunction with basic operations to support solutions to problems

· Show relationships between percents and percentages

· Place squares and cubes of fractional and decimal numbers on number lines

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

Standard - Number Sense, Number Operations, And Number Relationships

Students should show proficiency in being able to:

· Compare, order, and operate with positive and negative rational numbers

· Use exponential and scientific notation to solve realistic problems

· Explain the relationship between prime factors of numbers and the permutations possible from the factors

· Demonstrate and discuss the relationship of percents, fractions, and decimals

· Research ancient number systems, including fractional systems, and compare them to our present system

· Determine whether to use fractions, decimals, or percents in known problem situations and the advantages or disadvantages of each

· Identify situations in which particular representations of numbers are appropriate

· Represent fractions, decimals, and percents in a variety of meaningful situations using concrete, pictorial, and abstract representations (area models, graphs, etc.)

· Compare numerical expressions

· Relate large numbers to familiar amounts (such as, "One billion dollars allotted to a students' community results in how much per person?")

Standard - Patterns, Relationships, And Functions

Students should show proficiency in being able to:

· Extend geometric and arithmetic sequences

· Find formulas for determining elements in sequences of numbers

· Construct sequences similar to previously studied progressions using different initial values.

· Construct beginning sequences to be completed by others

· Arrange numbers in grids, tables, or charts to illustrate given rules

· Describe patterns observed in the real world

· Organize collected information in tables, graphs, or charts

· Make predictions from mathematical models

· Make, test, and utilize generalizations about given information in problem situations

· Investigate the behavior of converging sequences such as a series of unit fractions

Standard - Probability And Statistics

Students should show proficiency in being able to:

· Collect and analyze data, make conjectures based on the analysis, and communicate information in the form of tables, plots, and graphs

· Develop an algorithm for finding the number of permutations and combinations possible in sets of at least three objects

· Use computers to determine probabilities in complex situations

· Make hypotheses, test conjectures, and refine theories on the basis of information gathered through experimentation

· Interpret statistics and make predictions in sports, weather, and other related real-world situations

· Compile frequency tables to represent data from controlled experiments and compare and contrast measures of central tendency for sets of data

· Simulate real-life probability problems using cards, dice and spinners, tally the results and make predictions about the events that follow

· Construct sample spaces to determine theoretical probabilities of real-life situations

Standard - Geometry

Student should show proficiency in being able to:

· Discuss similarities and differences of planes, lines, rays, and line segments

· Identify corresponding parts of congruent or similar figures and determine the measurements of unknown figures when the measurements of similar figures are known

· Identify pairs of angles with special relationships: supplementary, complementary, vertical, adjacent, etc

· Use compasses and straightedges to construct congruent line segments, congruent angles, and angle and segment bisectors

· Construct concrete proofs of the Pythagorean theorem

· Classify triangles according to their attributes and justify the classification

· Use computers to construct geometric figures in 2- and 3-dimensions in various positions

· Draw visual representations of geometric shapes from descriptions

· Graph and identify sets of ordered pairs on Cartesian coordinate planes

· Sketch the resulting reflections of geometric figures over given lines of symmetry

· Investigate the attributes of medians of equilateral, scalene, and obtuse triangles

Standard - Measurement

Students should show proficiency in being able to:

· Measure attributes of geometric figures using different units and express the measurements as fractions, decimals, and natural numbers

· Use instructional aids (protractors, compasses, and mirrors to construct, measure, bisect, duplicate, enlarge, or shrink angles and make or draw models to scale

· Create and solve problems using perimeter, area, volume, angle measurement, capacity, and weight

· Justify accepting a specific error of measurement in a particular problem

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.

Each quarter the students will be asked to write in their Math journals using a Math prompt. The entries will be read and score based upon the predetermined rubric concentrating mostly on the content but evaluating their understanding and use of one of the 6+1 traits. The score will add to the student’s grade as a quiz. The Problem of The Week will also be graded based on the uses of the established written format and the employment of the 6+1 writing traits.

SCOPE & SEQUENCE:

Semester 1

1^ST Quarter

Module # 1 Title: Making Choices

Content & Process Goals:

· use positive exponents: understand and use order of operations

· review the concept of percent: interpret bar and line graphs

· conduct an informal survey: make a frequency table

· choose an appropriate graph: graph ordered pairs in first quadrant of coordinate plane

· model a sequence with words, a table, a graph, or an equation: make predictions using a rule or graph

· review the concept of area: find the volume of a cube

· identify the outcomes of an experiment

· find experimental and theoretical probabilities, and compare them

· recognize patterns in a sequence: predict nth term of a sequence

2nd Quarter

Module # 2 Title: Search and Rescue

Content & Process Goals:

· compare, add, and subtract integers

· find opposites and absolute values of integers

· apply the commutative and associative properties to integer addition

· graph ordered pairs in a coordinate plane

· evaluate expressions

· use tables, graphs, and equations to model functions

· write and solve addition and subtraction equations

· measure, draws, and classify angles

· recognize and find the measures of complementary and supplementary angles

· recognize parallel and perpendicular lines in a plane

Semester 2

3rd Quarter

Module # 3 Title: A Universal Language

Content & Process Goals:

· find factors, multiples, primes, and composites

· add and subtract fractions and mixed numbers

· multiply and divide decimals by powers of ten

· write large and small numbers in scientific notation

· convert between metric units of length

· develop benchmarks for metric units of length

· write and solve multiplication and division equations

· classify triangles by side lengths: construct triangles given the side lengths

· construct circles: apply the triangle inequality

· follow a flow chart: use a tree diagram to find the probability of an event

4th Quarter

Module # 4 Title: The Art of Motion

Content & Process Goals:

· multiply and divide fractions, decimals, mixed numbers, or integers

· estimate decimal products and quotients

· apply properties to number operations

· evaluate expressions involving fractions, decimals, or integers

· write and solve equations involving two operations

· find the circumference of a circle

· rotate, translate, or dilate a figure and describe the transformation

· identify rotational symmetries, reflections, and lines of symmetry

· recognize similar and congruent figures

Portions of additional modules will be covered based on available class time.

COURSE GRADING/ASSESSMENT: Under the semester system, grades will be closed after each quarter and your final grade for the applicable semester will be determined by: 45% for first or third quarter, 45% for second or fourth quarter, and 10% for Semester exam (first or second).

QUARTER GRADES WILL BE DETERMINED BY THE FOLLOWING:

HOMEWORK/CLASS WORK 10% of your quarter grade. Homework will be assigned after each class to reinforce concepts and help students prepare for the next class.

Homework will include a Problem of the Week. Students can work with parents, peers, and/or other teachers to solve the problem. This assignment is part of the students required homework.

PROBLEM OF THE WEEK FORMAT

The following format will be used for submission of The Problem of the Week. This will allow the grading process to look at both the computational method used to solve the problem and the adherence to the 6+1 traits in explaining the solution. For further explanation of the problem solving steps refer to your textbook page 44. The solution may be done on the back of the problem of the week handout or on a separate sheet of paper stapled to the hand out. Each step should contain at least two compete sentences explaining your actions.

Step 1. Understand the problem and restate it in your own words.

Step 2. Make a plan and state your strategy for solving the problem.

Step 3. Solve the problem. In this step you should go step by step through the computations to arrive at an answer. Each step should have the proper units for your numbers as well as a short label to identify what the number represents i.e. number of student in a class, number of red marbles in the jar, length of the garden, etc.

Step 4. Look back at your work and state if it seems reasonable, accurate, and answers the problem in step 1.

The scoring rubric points will be:

5 for correct answer, correct procedure, and good command of the 6+1 traits

4 for excellent work but some error in logic or arithmetic, and average use of 6+1 traits

3 for a good try but answer is incorrect and/or procedure faulty, and need work on 6+1 traits

2 for attempting the problem, and written steps did not conform to 6+1 traits

1 for writing out what one knows

0 for no work turned in

Problems will be passed out at the beginning of each week and can be turned in any time prior to the passing out of the next problem. At the end of each quarter, the problem of the week scores will be averaged and added to the student’s grade as a quiz.

NOTEBOOK 20% of your quarter grade

Your notebook must contain all class notes, handouts, homework, class work, group activities, and glossary of terms. The first page should be this syllabus.

TESTS/QUIZZES/ PROJECTS: 70% of your quarter grade

Tests will be announced and follow a unit of study. Tests may include questions from earlier work. Preparation for each test will include module reviews, question and answer drills, and after school help sessions. Projects are completed at home and are another way to assess your understanding of a topic. The Lion’s Roar will be graded daily and averaged as one test/quiz grade at the end of each quarter. The Problem of the Week will be graded weekly and averaged as one test/quiz grade at the end of each quarter. Journal entries will be graded and added as a test/quiz grade.

TEXTBOOK: MATH Thematic, Book 2

Rick Billstien/Jim Williamson

McDougal Littell

CLASSROOM EXPECTATIONS/ CONSEQUENCES: In order to have a safe productive year certain rules must be followed. These rules are implemented so we as a class can dispense with needless interruptions and enjoy a normal learning environment. Students are already familiar with proper behavior and the rules outlined in the student handbook so this will only review those rules, which might not be enforce school wide.

1. Students will be in your seat at the start of class ready to work. Pencil sharpening, paper borrowing, restroom visits, visitation with peers, and walks to lockers will all be done before the start of class.

2. Everyone is expected to treat fellow students and the teacher with respect. Name-calling, profanity, and/or physical aggression are not acceptable. Stop and think before you react and save yourself a lot of stress.

3. Do not bring gum, food, or drink to class. Hats, scarves, bandanas, and/or sweatshirt hoods are not to be worn in the classroom at any time. Do not sit on the desks, or tables. Throwing of anything in class is not tolerated and will be dealt with appropriately.

4. Take notes, ask questions, listen to the questions and answers of other students and seek help when necessary. Please let the teacher know when you are experiencing difficulty. We need to work together.

5. For safety respect equipment and materials that are available for class work. Students must obey the instructor’s directions. Students should focus on their work and return all equipment to their proper places before leaving the room. Always get your instructor’s permission before attempting any activity beyond the assigned work or explorations. Always read the procedure carefully. When in doubt, ask. Before leaving, always clean up your area.

SUPPLIES: REQUIRED: Pencil, paper, three-ring notebook, ruler, compass, protractor, textbook, and calculator. RECOMMENDED: TI-82 or TI-83 Graphing calculator.

HOMEWORK POLICY: Homework must have the following in the upper right hand corner for a grade: Name, Date, Block Number, Page Number and Problem Numbers (when applicable), work shown clearly, answers checked and corrected if necessary. Remember if you do not follow these rules, you will NOT receive credit. HOMEWORK IS DUE THE NEXT CLASS PERIOD. Late homework will not be accepted. One of the functions of homework is to prepare the student for the next class. If the assignment is not complete, the student will not be prepared and therefore will not benefit from the lesson.

MAKE-UP WORK POLICY: Students that are sick or otherwise excused from school will be allowed to make-up work as prescribed in the student handbook. Tests and quizzes that are below passing maybe made-up to a 60% by redoing the problems marked wrong on a separate sheet of paper and turning-in the whole package.

NOTEBOOK ASSESSMENT SHEET:

MATHEMATICS

NOTEBOOK ASSESSMENT SHEET

Notebook will not be graded if the Grade Seven (7) Mathematics Syllabus is not in the front of the notebook and signed by one parent. The notebook will have a homework, class notes sections organized by due date, a notes section organized by date presented, a glossary of terms (vocabulary) organized by topic, a test/quiz section, and Math journal section. A Table of Contents will be included.

Homework Section ________

Points determined by % of HW corrected 15 points

And present in the notebook. Problem of

The Week goes here also.

Class Notes Section ________

Points determined by completeness of 15 points

the notes, neatness, and accuracy.

Lion’s Roar, handouts, class work activities, etc.

belong in this section.

Glossary of Terms Section ________

Points determined by completeness, 10 points

neatness and accuracy.

Tests and Quizzes Section ________

Points determined by completeness. 20 points

Journal ________

Each student will maintain a section of the notebook 20 points

for a Math journal. This section will contain entries

made in class and at home.

In a Three Ring Binder ________

All papers are in the binder neatly. 20 points

CLASSROOM PROCEDURES:

1. Students are free to choose their classroom seat. At the discretion of the teacher, students’ seats will be changed to maintain a disruption free, learning environment.

2. Students will raise their hands to obtain permission to speak. Shouting out or speaking with out permission will not be tolerated. Three such occurrences in a class period will result in the student being asked to spend the rest of the period in the office. This type of rude behavior will not be allowed to disrupt other students or the classroom environment.

3. Each class will start with a five-problem set on the overhead called THE Lion’s ROAR. This activity will be done without the aid of a calculator or notes.

4. A work will be handed-in via the block paper trays located in the front of the room.

5. The class will be given a signal (ringing of a desk bell) when talking is to stop and listening is to begin.

6. The teacher will be dismissed each class when everyone is seated, the desks are aligned, and the floor is free of litter.

7. NO STUDENT WILL LEAVE THE CLASSROOM WITHOUT PERMISSION!