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LCCS students are expected to demonstrate their understanding
in each subject area through content rich real life projects.
Students must demonstrate their ability to solve problems using
multiple strategies, communicate an understanding of mathematical
logic in the problem solving process, and apply mathematical concepts
to real world scenarios. By the end of their LCCS experience,
students will have amassed a portfolio composed of varied projects
that demonstrate their degree of understanding. LCCS students
will complete projects that integrate content from the California
State Math Standards and projects will be selected from the following
types:
- Data study
- Mathematical model of a physical system or phenomenon
- Design of a physical structure
- Management and planning analysis
- Pure mathematics investigation
- History of a mathematical idea
The LCCS curriculum is one founded upon academic rigor. Student
development of specific skills will be measured in each project.
The skill areas measured in Mathematics are:
- Content Understanding
- Problem solving
- Mathematical Skills and Tools
- Mathematical Communication
SKILL CRITERIA
Problem Solving
The student demonstrates problem solving by using mathematical
concepts and skills to solve non-routine problems that do not
lay out specific and detailed steps to follow, and solves problems
that make demands on all three aspects of the solution process
– formulation, implementation, and conclusion.
Formulation
The student participates in the formulation of problems; that
is, given the statement of a problem situation, the student:
- Fills out the formulation of a definite problem that is to
be solved; ð Extracts pertinent information from the situation
as a basis for working on the problem
- Asks and answers a series of appropriate questions in pursuit
of a solution and does so with minimal "scaffolding"
in the form of detailed guiding questions
- Implementation
The student makes the basic choices involved in planning and
carrying out a solution; that is, the student:
- Chooses and employs effective problem solving strategies
in dealing with non-routine and multi-step problems;
- Selects appropriate mathematical concepts and techniques
from different areas of mathematics and applies them to the
solution of the problem;
- Applies mathematical concepts to new situations within mathematics
and uses mathematics to model real world situations involving
basic application of mathematics in the physical and biological
sciences, the social sciences, and business.
Conclusion
The student provides closure to the solution process through summary
statements and general conclusions; that is the student:
- Concludes a solution process with a useful summary of results;
- Evaluates the degree to which the results obtained represent
a good response to the initial problem;
- Formulates generalizations of the results obtained;
- Carries out extensions of the given problem to related problems.
MATHEMATICAL SKILLS AND TOOLS
The student demonstrates fluency with basic and important skills
by using these skills accurately and automatically, and demonstrates
practical competence and persistence with other key skills by
using them effectively to accomplish a task, perhaps referring
to notes, or books, perhaps working to reconstruct a method; that
is the student:
- Carries out numerical calculations and symbol manipulations
effectively, using mental computations, pencil and paper, or
other technological aids, as appropriate.
- Uses a variety of methods to estimate the values, in appropriate
units, of quantities met in applications, and rounds numbers
used in application to an appropriate degree of accuracy.
- Evaluates and analyzes formulas and functions of many kinds,
using both pencil and paper and more advanced technology.
- Uses basic geometric terminology accurately, and deduces
information about basic geometric figures in solving problems.
- Makes and uses rough sketches, schematic diagrams, or precise
scale diagrams to enhance a solution.
- Uses the number line and Cartesian coordinates in the plane
and in space.
- Creates and interprets graphs of many kinds, such as function
graphs, circle graphs, scatter plots, regression lines, and
histograms.
- Sets up and solves equations symbolically (when possible)
and graphically.
- Knows how to use algorithms in mathematics, such as the Euclidean
Algorithm.
- Uses technology to create graphs or spreadsheets that contribute
to the understanding of a problem.
- Writes a simple computer program to carry out a computation
or simulation to be repeated many times.
- Uses tools such as rulers, tapes, compasses, and protractors
in solving problems.
- Knows standards methods to solve basic problems and uses
these methods in approaching more complex problems.
MATHEMATICAL COMMUNICATION
The student uses the language of mathematics, its symbols, notation,
graphs, and expressions, to communicate through reading, writing,
speaking, and listening, and communicates about mathematics by
describing mathematical ideas and concepts and explaining reasoning
and results; that is, the student:
- Is familiar with basic mathematical terminology, standard
notation and use of symbols, common conventions for graphing,
and general features of effective mathematical communication
- Uses mathematical representations with appropriate accuracy,
including numerical tables, formulas, functions, equations,
charts, graphs, and diagrams.
- Organizes work and present mathematical procedures and results
clearly, systematically, succinctly, and correctly.
- Communicates logical arguments clearly, showing why a result
makes sense and why the reasoning is valid.
- Presents mathematical ideas effectively both orally and in
writing.
INCORPORATION OF RELEVANT TECHNOLOGY
Online Research
The student will be able to utilize the internet as a research
tool. More specifically, the student will be able to:
- locates and cite relevant research located on the internet;
- use email to correspond with peers and specialists in the
subject matter of their projects;
- incorporate into email correspondance data of different file
types and applications.
Word Processing
The student will be able to utilize word-prcessing software to
produce a multi-page document. The student will also be able to:
- use features of the software to create and edit the document;
- use features of the software to format the document;
- use features of the software to insert tables, charts, and
graphics;
- use features of the software to track and highlight editing
for other students.
Spreadsheets
The student will be able to create, edit, and analyze a spreadsheet
that appropriately presents, evaluates, and manipulates data.
The student will also be able to:
- create a spreadsheet that uses of formulas and functions
to evaluate data for a specific purpose;
- use features of the software to sort, and arrange data for
specific purposes;
- use features of the software to create multiple spreadsheets
when appropriate;
- Use features of the software to create tables, graphs or
charts to represent numeric data.
PROJECT CRITERIA
Data study, in which the student:
- Carries out a study of data relevant to current civic, economic,
scientific, health, or social issues;
- Uses methods of statistical inference to generalize from
the data;
- Prepares a report that explains the purpose of the project,
the organizational plan, and conclusions, and uses an appropriate
balance of different ways of presenting information.
Mathematical model of a physical system or phenomenon, in which
the student:
- Carries out a study of a physical system or a phenomenon
by constructing a mathematical model based on functions to make
generalizations about the structure of the system;
- Uses structural analysis (a direct analysis of the structure
of the system) rather than numerical or statistical analysis
(an analysis of data about the system);
- Prepares a report that explains the purpose of the project,
the organizational plan, and conclusions, and uses an appropriate
balance of different ways of presenting information.
- Design of a physical structure, in which the student:
- Creates a design for the physical structure;
- Uses general mathematical ideas and techniques to discuss
specifications for building the structure;
- Prepares a report that explains the purpose of the project,
the organizational plan, and conclusions, and uses an appropriate
balance of different ways to present the information.
Management and planning analysis, in which the student:
- Carries out a study of a business or a public policy situation
involving issues such as optimization, cost-benefits projections,
and risks;
- Uses decision rules and strategies both to analyze options
and make balance tradeoffs; and brings in mathematical ideas
that serve to generalize the analysis across different conditions;
- Prepares a report that explain the purpose of the project,
the organizational plan, and conclusions, and uses an appropriate
balance of different ways of presenting information.
Pure mathematics investigation, in which the student:
- Carries out a mathematical investigation of a phenomenon
or concept in pure mathematics;
- Uses methods of mathematical reasoning and justification
to make generalizations about the phenomenon;
- Prepares a report that explain the purpose of the project,
the organizational plan, and conclusions, and uses an appropriate
balance of different ways of presenting information.
- History of a mathematical idea, in which the student:
- Carries out a historical study tracing the development of
a mathematical concept and the people who contribute to it;
- Includes a discussion of the actual mathematical concept
and its place in the curriculum of the current day;
- Prepares a report that explain the purpose of the project,
the organizational plan, and conclusions, and uses an appropriate
balance of different ways of presenting information.
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