CIC Mathematics Curriculum Documentation
Honors/Integrated Mathematics 2
Integrated Math 2:
For tenth grade students this course represents the final year of preparation of the IGCSE core syllabus. These students will continue the following year with integrated math 3 and, as seniors, fulfill the IB group five requirements with IB math studies (standard level)
For ninth grade students this course represents the first year of preparation of the IGCSE extended syllabus. The students will continue the following year with integrated math 3 and will then be prepared to enter the IB program in IB math methods (standard level). In some cases an exceptional student may be recommended for honors integrated math 3 in the tenth grade.
Through investigations, group work, activities and direct instruction, students in this course will build on their knowledge of topics introduced in Integrated Math I and prepare IGCSE coursework. Students will move from making inductive conclusions to the use of deductive reasoning. This will be done through the study of coordinate geometry, logic and introductory topics in plane geometry. In addition, students in the course will study various variation models including direct, inverse, linear, exponential and quadratic, use of statistics including polling methods and sampling, algebraic applications of geometry and theoretical probability for compound events. Other specific topics will include matrix operations, transformations, and basic vectors.
Honors Integrated Math 2:
This course is designed for ninth grade students who show high ability in mathematics and possess a capability for making connections. It represents the first year of preparation of the IGCSE extended syllabus. These students are expected to complete their IB group five requirements with IB math higher level or, in some cases, IB math methods (standard level).
While the philosophy and teaching methods are similar, this course offers a more in depth study of the topics in Integrated Math 2. Students will be expected to exhibit higher level thinking skills in making connections between the topics as well as between the pure math and its applications. Less time will be spent in direct instruction and more in investigation. Treatment of certain subjects may be more rigorous than in the non-honors level course.
Students will be able to:
(Note: Items in Italics are required only of Honors section)
- 2x2 Systems of linear equations by graphing, substitution and linear combinations and matrix methods without technology and 3x3 systems with technology and quadratic systems by graphing and substitution
- Quadratic equations by graphing, undoing, factoring, and quadratic formula.
- Algebraic problems derived from geometric figures using congruence, similarity, parallel line theorems, right triangle trigonometry, surface area and volumes.
- Probability and counting problems including permutations, combinations, simple and compound events which may be dependent or independent, Pascals triangle and binomial experiments.
- Graph linear functions, relations that include direct variation, inverse variation, exponential growth/decay, and quadratic function, and systems of linear inequalities.
- Simplify expressions that include rational and integer exponents, matrices, complex numbers and radicals. Differentiate between exact solutions and estimated solutions.
- Make inductive conclusions and then prove algebraic and geometric statements using coordinate methods and deductive techniques with a high degree of rigor.
- Make conclusions based on others experiments and then investigate individually, a situation or problem and come to a conclusion or solution and then write about the problem, process and conclusion to the level required by the IGCSE extended coursework rubric.
- Use proper vocabulary in all facets of mathematics and specifically to
- make a critical analysis of surveys designed by others
- describe graphs, number sets, symmetry and transformations
- discuss geometric situations
- Write equations for graphs and situations that can be modeled by linear or quadratic functions, direct and inverse variation, doubling and halving and exponential growth and decay.
- Draw nets, cross sections, loci and figures under transformations.
|Core Topics||Honors Topics|
|Samples and Sampling Methods, Surveys, Making Conclusions Inductively and Deductively, Critical Reading of Statistical Results, Proportions, Percent Error, Venn Diagrams||Data Trends|
|Vocabulary of functions: Domain, Range, Increasing, Decreasing, Linear, Non-Linear, Constant; Models of Variation: Linear, Direct, Inverse, Direct with Powers, Doubling and Halving; Simplifying with Exponents including Integer and Rational Exponents, Surface Area and Volume of a Sphere;||Exponential Variation; Simplifying Radicals;|
|Solving Linear Systems by Graphing, Substitution, Linear Combination and Matrix Methods, Graphing Systems of Linear Inequalities, Parallel and Perpendicular Lines, Dilations and Translations, Matrix Algebra;||Inverse of a 2x2 Matrix, Solution of 3x3 Systems Using Technology;|
|Parabolas and Quadratic Equations, Solutions by Factoring, Graphing, Quadratic Formula and Undoing; Translations, Discriminant, Complex Numbers, Solving Quadratic Systems ||Simplifying with Complex Numbers|
|Classifying Quadrilaterals, Distance, Midpoint, Reflections over the axes, Rotations, Coordinate Methods including basic proofs||Rigorous Use of Coordinate Methods, Reflection of y = x and y = -x|
|Counting, Permutations, Combinations, Probabilty, Odds, Compound Events, Independent and Dependent Events, Mutually Exclusive Events, Binomial Experiments, Pascal's Triangle, Binomial Theorem||Non-Mutually Exclusive Events, Combinations with Repeated Letters|
|Implications, And, Or, Not, Venn Diagrams, Valid Arguments, Biconditionals, Proof, Angle Relationships, Parallel Lines, Algebraic Postulates||Truth Tables, Euclidean System|
|Parallel Lines, Triangle Sum Theorem, Simlarity and Congruence of Triangles, Isosceles Triangle Theorem, SImilarity in Right Triangles, Geometric Means, Right Triangle Trigonometry, Emphasis on Applications||Greater Emphasis on Formal Proof|
|Unit Nine (as time allows)|
|Figures in Space, Cross Sections, Nets, Locus, Review of Surface Area and Volume|
ASSESSMENT TECHNIQUES AND TEACHING METHODOLOGIES
- Assessment Techniques
- Coursework (20% per quarter): Designed to meet the needs of the IGSCE coursework option. It is suggested that 2 open-ended problems and one project be completed during 1st quarter, two investigations be completed during 2nd quarter, one project be completed during 3rd quarter and that grade 9 students complete 2 open-ended problems or one investigation during 4th quarter.
- Open-ended Problems: Short problems requiring mathematical investigation; assessed based on the criteria: problem restatement 10%, investigation 30%, analysis 30%, solution 15% and overall flow and quality 15%
- Investigations: Longer investigations graded using the IGCSE rubric; 1998 1999 investigations were "Frogs" and "Games."
- Projects: Also graded using the IGCSE rubric; 1998 1999 projects were "Biased Survey" and "Professions."
- Quizzes and Tests (70%)
- Quizzes: at least one per chapter covering the material in the first half of the chapter. Weaker classes may require one quiz short quiz per section or two sections and/or frequent open notes or homework quizzes. Quizzes assess the lower part of Bloom's Taxonomy and are graded based on 90% - 100% is an A and 60% is the lowest passing score.
- IGCSE control elements: all submitted IGCSE coursework must be accompanied by work done on similar subject matter under controlled circumstances. Generally takes the form of a quiz and is graded using a 4 on the IGCSE rubric as an A, a 3 as a B, and so on.
- Tests: One per unit studied; usually 2 per quarter. Should include both basic knowledge and further applications as well as one sample IGCSE question (from a past paper) on the material. If the test is designed in such a way as 75% of the material is considered necessary to achieve a level satisfactory and only 10% is above the level deemed excellent, then a standard scale is used to set marks. If this is not the case, the teacher may select the tests that illustrate the minimum knowledge necessary to be labeled "passing," "satisfactory," and "excellent" and use the scores to create a valid scale.
- Homework/Classwork (10%): This component should not be lower than the test and quiz component. In other words, I student should not be penalized for not doing homework or for lack of understanding at the time the assignment was graded. Homework is generally assessed as excellent, satisfactory or incomplete and may be assessed using homework consensus or individual checking. In weaker sections, notebooks may be collected daily and each problem checked. This is not the case in average or strong sections.
- Teaching Methodologies
- Investigations: Students work in small groups following a step-by-step process and answering thought questions in order to create an understanding about a mathematical concepts. Generally includes a follow-up discussion and/or assignment designed to check for understanding.
- Reading Response Sheets: Teacher designed worksheets containing questions that can be answered by the students through a careful reading of the section. Used when the book explains a concept fully and clearly and the teacher could not add much to the topic. Used for the purpose of teaching students how to read a math book critically and take notes from it. Another opportunity to promote critical reading is by having the students write a summary of the material found in the unit before the unit is begun.
- Direct Instruction: Used in conjunction with investigations or on its own when a topic requires teacher explanation or a dialogue between teachers and students in order for the students to fully master all aspects of the topic. Never used for a full 90 minute lesson and usually done in a discussion format interspersed with activities designed to further understanding or check for understanding.
- Review Sheets: Used when a class displays a particular difficulty in understanding a concept or before a test. Other review assignments include, but are not limited to, outlining the chapter and writing sample test questions.
- Journals: Students write journal entries at the end of every class. They have traditionally not been communication between teacher and student but not necessarily only about mathematics. In the beginning, students may be given a topic on which to write, but as the year progresses, they tend to free write about the lesson or something else that is going on in their lives.
- Primary Text: Integrated Mathematics 2, Rubenstien, Craine, Butts; (McDougall Little/Houghton Mifflin Inc, Boston, MA, 1995)
- Additional text resources
- Unified Mathematics, Books 1, 2 and 3, Rising; (Houghton Mifflin Company, Boston, MA, 1982)
- GCSE Mathematics., Robert Powell (Letts Educational, London, England 1995)
- Geometers Sketchpad; (Key Curriculum Press, Berkeley, CA, 1994)
- Graphics Calculators
- ESL students are encouraged to seek math help during their supplementary classes.
- ESL and resource teachers aid ESL students in the writing of projects and investigations.
- ESL students are given opportunities to rewrite coursework assignments when language difficulties have caused them to either misunderstand the question or create a poorly worded explanation of their solution.
- If the IGCSE program and its coursework are abandoned, care should be taken not to disregard those assessment components. Mathematical investigations and projects are educationally sound practices and prepare students for the required IB coursework. However, if the coursework is not submitted to the IGCSE, it may be completed in small groups and graded using a teacher designed rubric.
- If the IGCSE program is retained, the department must consider the impact of sections which contain students from both 9th and 10th grades, some of whom are in their first IGCSE year and others of whom are in their second and final year. While it lends flexibility to the master schedule, it does require extra organization on the part of both the teachers and the students.
- More communication between the mathematics department and the ESL department would benefit the few ESL students who remain at this level.
- All students would benefit from greater communication and uniform pacing and assignments among the teachers and sections.