CIC Mathematics Curriculum Documentation

INTEGRATED MATH I

COURSE OVERVIEW

Through a carefully sequenced study of elementary algebra, geometry, statistics and probability, students acquire a foundation in the major components of high school mathematics. They become aware of the fundamental rules that govern the operations and systems of numbers they are using. They work with patterns and abstractions, recognizing how they apply to a variety of situations in pure mathematics and other disciplines. Connections between different strands of mathematics are emphasized as well as active student involvement, individually and in groups, through explorations, investigations and projects.

For Grade 8

This course is designed for eighth grade students who have demonstrated competence in arithmetic operations and critical thinking and are ready to move toward more abstract and theoretical mathematics.

Students who complete this course with a high level of achievement will be eligible to take Honors Int. Math II as their next course in this sequence. Other students will take the regular level of Int. Math II.

For Grade 9

This is the first of a three year sequence of high school mathematics following Math 8. Upon successful completion, students will take Int. Math II as their next course.

CONTENT SUMMARY

Unit I

Communicating with diagrams. Investigating patterns. Patterns with powers. Writing and evaluating expressions. Modeling the distributive property. Working together on congruent polygons. Exploring quadrilaterals and symmetry.

Unit II

Numbers and estimates. Using negative numbers. Exploring scientific notation. Estimating measures: length and area. Exploring angles relationships. Expressions for measures. Solving equations: balancing and undoing. Square roots and cube roots.

Unit III

Using matrices and graphs. Mean, median and mode. Inequalities and intervals. Histograms and stem-and-leaf plots. Box-and-whiskers plots. Choosing a data display. Analyzing misleading graphs.

Unit IV

Coordinates for locations. Introduction to coordinate geometry. Translations. Rotations. Scatter plots. Graphs and functions. Functions and equations.

Unit V

Modeling problem situations. Opposites and the distributive property. Variables on both sides. Inequalities with one variable. Rewriting equations and formulas. Using reciprocals. Area formulas. System of equations in geometry.

Unit VI

Ratios and rates. Investigating probability. Solving proportions. Sampling and making predictions. Similar polygons.

Unit VII

Direct variation, slope and tangent. A direct variation model. Circumference and Arc length. Direct variation with y = kx. Using dimensional analysis. Areas of circles and sectors.

Unit VIII

Linear growth and decay. Linear combinations. Horizontal and vertical lines. Writing equations for lines. Graphing systems of linear equations. Graphing linear inequalities. Systems of linear inequalities.

Unit IX

The Pythagorean Theorem and reasoning. Investigating properties of square roots. If-then statements and converses. Geometric probability. Surface area of space figures. Volumes of prisms and cylinders. Volumes of pyramids and cones. Similar figures: Area and volume.

Unit X

Reflections. Transforming parabolas. Factors and intercepts. Working with powers. Factored form and x-intercepts. Expanded form and line of symmetry.

ASSESSMENT TECHNIQUES AND TEACHING METHODOLOGIES

1. Assessment Techniques
   1. Projects and Investigations (20% - 30%)

      Given once a quarter, requiring 1 - 3 weeks preparation. Done individually or in small groups. Q1: Checkerboard Investigation (ind.). Q2: Business Survey Project (small group). Q3: Painted Cube Investigation (ind.). Q4 - (option): Search and Rescue Project (ind.), or Sports Arena Project (small group). Each project or investigation is graded according to a specific rubric.

   2. Tests and Quizzes (60% - 70%)
      1. Quizzes: Given every 2 - 4 lessons, 10 - 15 minutes, covering basic skills and applications.
      2. Tests: Given after every unit, 60 - 90 minutes. Content: basic skills and applications (70%), higher level/critical thinking applications ( 30%).
   3. Homework/Classwork (10%): Evaluated on effort and completion.
2. Teaching Methodologies
   1. Explorations: Students, individually or in pairs, follow a series of directions leading to a conclusion that supports a concept or procedure to be studied further. Generally used at the beginning of a lesson. Discussion following formalizes conclusions and elaborates other applications. Can be followed by further direct instruction or student practice and application.
   2. Direct Instruction: Presentation of a new idea or concept which requires teacher explanation, definitions of new terms or procedures. Includes student involvement through discussion to bring out connections to their prior knowledge and responses to questions that use the new material. Followed by student practice.
   3. Review and extension: Prepared materials which students can work on their own that usually cover material from several lessons, and can preview ideas and skills needed in future lessons.

KEY RESOURCES

1. Texts
   1. Integrated Mathematics 1; McDougal Littlell/Houghton Mifflin, 1995.
   2. Support and Practice materials; Study Guide; Practice Bank; Problem Bank; Project Book, Explorations Lab Manual. McDougalLittlell/Houghton Mifflin, 1995.
2. Materials
   1. Algebra Tiles, unifix cubes, 3-dimensional solids, spinners, 2-pan balance, number line
   2. Overhead Projector
3. Technology
   1. Scientific calculators
   2. Graphics calculators
   3. Computer word-processing and spreadsheet applications.

ESL STRATEGIES/CONSIDERATIONS

1. ESL Supplemental teachers are given outline of lessons and vocabulary to prepare students in advance of a lesson.
2. Assistance is given during preparation of projects and investigations pertaining to writing and organization.
3. On occasion, a student will complete math work during a supplemental period with that teacher’s supervision and appropriate assistance.

FUTURE CHANGES / NEEDS

An effort must be made to continually improve the project/ investigation component of this course so that students are focused on the application of their learning in a way that demonstrates the skills that they have learned and requires clear and effective communication.