Pre-Algebra


(Mathematics Cluster)

COURSE DESCRIPTION

This integrated, collaboratively taught Pre-Algebra Core class will provide all students an opportunity to study numeration, mathematical symbolism, algebraic operations, problem-solving techniques, and related subjects, so they will know about, understand, and better appreciate mathematical facts, concepts, and applications through textbook lessons, calculator exercises, mental arithmetic, and manipulative laboratories. By satisfying requirements of this study, all students will become more informed, skilled, productive, employable, and socially responsible citizens.

SWRSD OUTCOMES

Outcome 6: Students exhibit a positive attitude and self-initiative.
Outcome 7: Students use a variety of ways to think and to reason when solving problems and making thoughtful decisions.
Outcome 9: Students use technology for adapting to and initiating productive change.
Outcome 11: Students demonstrate skills and attitudes that will enable them to achieve post high school education.

COURSE OUTLINE

CONTENT (Essential course facts, concepts, and basic skills; assessed with teacher -made tests and rubrics )

Major Components of Study

A. Textbook Lessons

Alaska Content Standard(s):
Standard A: Mathematics
(A student should understand mathematical facts, concepts, principles, and theories.)

Key Elements: Students will know about, understand, and demonstrate the ability to:

understand and use numeration from all number sets (counting, whole, integers, rationals, irrationals) and work effectively with fractions, decimals, and percents;
Students will:
construct whole numbers using blocks of various number bases
add, subtract, and simplify whole numbers using blocks of various number bases
multiply, divide, and simplify whole using blocks of various number bases
make the correlation between simplifying block manipulations and carrying in the place value number system
construct rational numbers using fraction tiles
add, subtract, and reduce rational numbers using fraction tiles
multiply, divide, and reduce rational numbers using fraction tiles
construct signed integers using appropriate manipulatives
add and subtract signed integers using appropriate manipulatives
multiply and divide signed integers using appropriate manipulatives
apply four operations (addition, subtraction, multiplication, division) with pencil and paper to all number sets

select and use appropriate systems, units, and tools of measurement, including estimation;
Students will:
measure lengths, volumes, and weights in English and metric systems
round off measurement and estimate error
convert within the metric and English systems

perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools for computation or estimation including mental arithmetic, paper and pencil, calculator, and computer;
Students will:
solve problems by trial and error
represent, analyze, and use mathematical patterns, relations, and functions using methods such as tables, equations, and graphs;
Students will:
find the range, mean, median, and mode of data sets
make line plots, stem and leaf plots, and scattergrams from data sets
identify and use data points from a graph
determine odds and probability and make predictions based on them
make tables of solutions for relations and functions
graph solutions for relations and functions from a table of solutions
construct, draw, measure, transform, compare, visualize, classify, and analyze the relationships among geometric figures.
Students will:
calculate areas and perimeters of triangles, quadrilaterals, and other polygons
calculate volumes and surface areas of prisms, cones, pyramids, cylinders, and spheres
use the vocabulary of polygons
find missing values of polygons
draw conclusions using geometric principles
solve problems using geometric principles

Standard B: Mathematics
(A student should understand and be able to select and use a variety of problem solving strategies.)

Key Elements: Students will know about, understand, and demonstrate the ability to

use computational methods and appropriate technology as problem-solving tools;
Students will:
find and use formulas for perimeter, area, volume, etc.
use problem solving to investigate and understand mathematical content;
Students will:

formulate mathematical problems that arise from everyday situations;
Students will:
know key words from standard English for the four arithmetic operations
write expressions from standard English descriptions of mathematical problems
identify the unknown quantities in a problem presented in standard English
write equations from problems presented in standard English
develop and apply strategies to solve a variety of problems;
Students will:

use common sense to help interpret results;
Students will:

apply what was learned to real life situations;
Students will:
determine profit and loss and commission and gratuity
determine original price, sale price, discount, sales tax, and unit cost
determine interest, principal, and balance
use mathematics with confidence.
Students will:

Standard C: Mathematics
(A student should understand and be able to form and use appropriate methods to define and explain mathematical relationships.)

Key Elements: Students will know about, understand, and demonstrate the ability to

express and represent mathematical ideas using oral and written presentations, physical materials, pictures graphs, charts, and algebraic expressions;
Students will:
plot points on coordinate plane
relate mathematical terms to everyday language;
Students will:

develop, test, and defend mathematical hypotheses;
Students will:

clarify mathematical ideas through discussion with others.
Students will:

B. Calculator Activities

Alaska Content Standards: Standard C: Technology
(A student should be able to use technology to explore ideas, solve problems, and derive meaning.)

Key Elements: Students will know about, understand, and demonstrate the ability to

use technology to observe, analyze, interpret, and draw conclusions.
Students will:
use and manipulate the calculator's order of operations to solve problems
utilize the calculator's memory input and output functions to store, retrieve, and use values in the problem solving process
utilize selected special operation keys (squaring function, square root function, inverse function, fraction/decimal conversion, and parentheses) to enhance the problem solving process
use technology to solve problems both individually and with others.
Students will:
engage in explorative calculator activities (individual and group games) that promote calculator skills and numerical literacy
use technology to create new knowledge by evaluating, combining, or extending information.
Students will:

C. Mental Arithmetic

Alaska Content Standards: Standard A: Mathematics
(A student should should understand mathematical facts, concepts, principles, and theories.)

Key Elements: Students will know about, understand, and demonstrate the ability to
understand and use numbers, number systems, counting numbers, whole numbers, integers, fractions, decimals, and percents;
select and use appropriate systems, units, and tools of measurement, including estimation;
perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools for computation or estimation including mental arithmetic, paper and pencil, a calculator, and a computer.


D. Manipulative Laboratories

Alaska Content Standard(s):
Standard B: Mathematics
(A student should understand and be able to select and use a variety of problem solving strategies.)

Key Elements: Students will know about, understand, and demonstrate the ability to

use computational methods and appropriate technology as problem-solving tools;
use problem solving to investigate and understand mathematical content;
formulate mathematical problems that arise from everyday situations;
develop and apply strategies to solve a variety of problems;
use common sense to help interpret results;
apply what was learned to new situations; and
use mathematics with confidence.

SKILLS (Essential processes or skills, universally taught by all teachers in all courses; assessed with teacher -made rubrics and/or tests )

Major Categories of Skills

A. Cross-curricular and/or Integrative Skills

Key Elements: Student will know about, understand, and demonstrate the ability to

1. effectively communicate (listen, observe, read, write, discuss, present, explain, persuade, defend)
3. use a variety of higher order thinking skills (hypothesizing, estimating, analyzing, classifying, synthesizing, evaluating,inferring, generalizing) to solve common day-to-day problems
Key Elements: Student will know about, understand, and demonstrate the ability to

C. Life and/or Employability Skills

Key Elements: Student will know about, understand, and demonstrate the ability to

respect and treat others equally, from the perspective of the needs and rights of all people
D. Cultural Relevance:



Alaska Content Standards for Culturally Responsive Schools: Student Standards A-E

Key Elements: Student will know about, understand, and demonstrate the ability to

INSTRUCTIONAL RESOURCES AND MATERIALS


A. Community Resources Related to Course

Each individual and/or team of instructors, with the help of long time staff, students, parents and other concerned community members should cooperatively compile and periodically update a list of village elders, parents, local government leaders, business persons, and other concerned, active members of the community willing to share their wealth of experiences, knowledge and skills. If available, specific examples should be included now.

B. Major Internet Web Site Addresses Related to Course (a tiny sample)

Free Federal Resources for Academic Excellence: www.ed.gov/free/subject
ITO Interdisciplinary Projects: www.fred.net/nhhs/html/ito
PBS Mathline www.pbs.org/learn/mathline
National Council of Teachers of Mathematics www.nctm.org
Mega-Mathematics www.c3.lanl.gov/mega-math/
Math games,toys, puzzles www.sal.cs.uiuc.edu/~Jeffe/mathgames
Appetizers and lessons for math and reason www.cam.org/~aselbui/lesson
Geometry forum forum.swarthmore.edu
AIMS education foundation 204.161.33.100/aims
Project mathematics www.projmath.caltech.edu
Annenburg/CPB math/science project www.learner.org
Geometry center www.geom.umn.edu

C. Media Center: Southwest Region School District
Contact Roz Goodman, the Southwest Region Media Specialist, for help. She has lists of materials related to specific subject areas and will help you find Internet resources or other materials
D. Itinerant Travel Kits and/or Permanent Core Skills Instructors' Materials

Donald in Mathemagics Land; Stand and Deliver; Life by the Numbers.






A History of Mathematics; Journey through Genius; A Brief History of Time; An Old Man's Toy; Science for All Americans.

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(Assessment Guidelines and Grading still "under construction" and awaiting additional in-put)

Teacher-made tests of content units will be required: pretests, quizzes, Unit Tests, Final Exams

Processes/Skills will be assessed Rubrics, checklists, et.al.

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(The Following Still Needs Input, Thought, and Work)

ASSESSMENT GUIDELINES AND GRADING



The primary goal of this class is to give all students an opportunity to gain essential new knowledge, comprehension, and skills. To determine if all students are actually attaining this goal, regular, in-progress assessment of student progress will be part of daily in-progress activities and final student projects.

CONTENT KNOWLEDGE TESTS

Minimum Requirements : At the very least, course Content will be regularly assessed with traditional
Teacher-made Tests (multiple choice, completion, true/false, matching, short essay).
Suggestions:
CRITERION-REFERENCED TESTS (CRT's)
STUDENT PERFORMANCE RUBRICS

EXTRA CREDIT WORK

In order to encourage students to pursue high level performances and quality products, all students who have completed required work, including any expected revisions, should be given an opportunity and encouraged to do Extra Credit work that might increase the depth and/or breadth of their understanding.
GRADING

All students will be held accountable for meeting the minimum requirements of all courses and will earn grades based on their ability to demonstrate the acquisition of basic content knowledge and comprehension, and their ability to apply specific essential skills to produce quality finished products. Final Grades in all courses will follow on a traditional "A", "B", "C", "D", "F", "I", system.
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