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### Algebra in Motion™

Description

An Algebra course designed to help students supplement, replace, or preview. Focused on concepts so that students leave with fundamental mathematical ideas.

Mathematics is best learned in context. To this end Algebra in Motion uses the Laws of Motion and simple geometry to naturally describe the fundamental concepts of Algebra that many high school and college students lack:
• variables - operations and their inverses, rational expressions, distributing/factoring
• formulas - how to derive a formula, how to algebraically manipulate formulas
• functions - theory of functions, application of functions
• graphing - graphical interpretation, slope-intercept form, parabolas
This course was designed to exceed all of the normal algebra standards at the state and national levels. Algebraic thinking is a conceptualization of arithmetic properties and as such requires students to be proficient in fractions, decimals, and percents to be successful.
Sequence

Algebraic Relationships
Students will explore the mathematics of motion and other various physical phenomena in order to attain mastery over variables and the methods of solving equations of single variables.
• Mathematics: unit conversion, fraction-decimal conversions, ratios, simple linear relationships, solving for a variable, inverse operations, slope of a line, graphing, substitution, simplifying rational expressions, simple quadratic relationships, similar polygons, monomials and terms.
• Science: metric and british units for length and mass, linear density, rate, speed, velocity, acceleration, gravity, temperature units and conversion formulae, unit analysis.

Linear Systems
In this quarter students will study a wide range of linear systems from 1-D motion, to composite motion, and other co-linear physical systems. Students will be working to master linear functions and linear graphs.
• Mathematicsgeneral linear relationships, slope-intercept form, substitution, general quadratic form, monomials, binomials, graphing inequalities, x- and y- intercepts, point-slope form and creating a linear equation, intersecting lines, system of linear equations, functions, simple function manipulation, simple distribution and factoring, graphing inequalities.
• Science: acceleration, equations of motion, prediction of points of collision, projectile motion, physical interpretations of polynomial mathematics, analysis of 2-d motion, volumetric fill rates.

In this final quarter students will be working to understand the mathematics of acceleration, projectile motion and gravity. Students will be working to master quadratic functions and quadratic graphs.
• Mathematics: polynomial arithmetic, simplifying rational expressions, factoring polynomials, completing the square, quadratic equation, solving a system of equations, solving polynomial equations, fractional powers, graphing inequalities, distribution of binomials, factoring of trinomials, completing the square, geometric representations of monomial terms, quadratic formula, discriminate.
• Sciencehorizontal projectile motion, Galileo's Laws of Motion, using mathematics to predict physical events, independence of horizontal and vertical motion, projectile motion.
Information

Each Algebra in Motion course is a 30-hour laboratory workshop for a total of 90 hours of in-class material. Academic year sequences are held in 10 week classes each 3 hours long. Summer camps are held in a single week and cover 30 hours of material.

Classes consist of hands-on activities, lecture, and practice problems. Academic year students are required to complete a minimal amount of practice problems.

#### Prerequisites

Students should have mastery over fractions, decimals, and percents. The document at the bottom of this page is a 38 question Algebra Readiness Assessment that will help determine whether your student is ready for Algebra (Algebra in Motion) or Pre-Algebra (Applied Mathematics).

#### Satisfied CDE Algebra I Standards

1. number classification
2. opposite, reciprocals, fractional power, roots, rules of exponents
3. absolute value
4. solve linear equations
5. linear equation word problems
6. x,y intercepts
7. point slope formula
8. parallel and perpendicular slopes
9. system of linear equations
10. monomial and polynomial arithmetic
11. polynomial factoring
12. simplify rational expressions
13. rational expression arithmetic
14. complete the square
15. rate, work, % mixture
16. functions
17. domain and range
18. function definition