Algebra+9

=All Things Straight=

Grade 9 Algebra AOI Link: Human Ingenuity //The emphasis in this unit is on how Mathematics can be a powerful tool in solving real life problems.//

Textbook reference: MYP Book 4 Chapters 1, 8, 17, 21

Guiding Questions

 * 1) How can real life problems be described Mathematically? How can I go about solving this?
 * 2) How can technology aid us in solving these problems quickly and efficiently?

Benchmarks

 * Master understanding of the following terms: variable, term, coefficient, like terms, constant, expression, simplify, polynomial, monomial, binomial, trinomial, degree of a term or of a polynomial, writing a polynomial in descending order
 * Simplify, add, subtract, multiply and divide polynomials
 * Use mental math to simplify special products quickly including difference of squares and square of a binomial
 * Master understanding of the terms equation, inequality and system of equations and what it means to solve an equation, an inequality or a system of equations or inequalities
 * Solve linear equations containing fractions and decimals using a variety of methods including clearing the fractions and/or the decimals
 * Investigate and develop understanding of what it means if an equation has an infinite number of solutions or no solution and solve linear equations with infinite or no solution
 * Check the validity of a solution of an equation by substituting the solution back into the original equation
 * Solve a wide variety of literal equations for a given variable including those which come from real-life applications
 * Solve linear inequalities (simple and compound) containing parentheses, fractions and decimals including those with infinite or no solution
 * Solve a system of equations in two variables using: a) Graphing method (manually and graphing calculator); b) Substitution method; and c) Elimination method
 * Determine the number of solutions that a system has by examining the relationships between the equations
 * Use appropriate concepts and skills related to equations, inequalities and simultaneous equations to solve a variety of problems in both familiar and unfamiliar situations including those in real-life contexts
 * Make appropriate deductions and then select and apply general rules correctly to solve problems involving equations, inequalities and simultaneous equations including those in real-life contexts
 * Represent and interpret relationships using multiple representations including equations, table of values and graphs and master understanding of relationships as linear (constant rate of change) or nonlinear (not a constant rate of change)
 * Develop understanding of the meaning and significance of the terms relation, function, domain, and range with emphasis on linear functions
 * Master understanding of the meaning and significance of a relationship which is linear and key characteristics of linear functions including slope and x and y intercepts
 * <span style="font-family: Verdana,Geneva,sans-serif;">Master ability to graph linear functions using a variety of methods including: table of values, intercepts, y=mx+b, graphing calculator
 * <span style="font-family: Verdana,Geneva,sans-serif;">Master understanding of characteristics of special lines including vertical, horizontal, parallel, perpendicular
 * <span style="font-family: Verdana,Geneva,sans-serif;">Represent the equation of a line using a variety of forms including y=mx+b, standard form and point-slope form, convert from one form to another, and understand that the forms are equivalent but feature different information
 * <span style="font-family: Verdana,Geneva,sans-serif;">Find the equation of a line using y=mx+b or point-slope form given: the graph of the line, a point and the slope, two points on the line, parallel or perpendicular to another line and passing through a certain point
 * <span style="font-family: Verdana,Geneva,sans-serif;">Represent a relation as a scatter plot, determine the line of best fit (manually, using a GDC and/or statistical software) and interpret the results
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use graphs to analyze nature of change in quantities in linear relationships
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use linear functions as tools for mathematical modeling to solve a variety of problems in both familiar and unfamiliar situations including those in real-life contexts
 * <span style="font-family: Verdana,Geneva,sans-serif;">Make appropriate deductions and then select and apply general rules correctly to solve problems involving linear functions including those in real-life contexts

Unit Assessment Tasks

 * **Task/Criteria** || **A** || **B** || **C** || **D** ||
 * Points of Intersection ||  || x || x || x ||
 * Test || x ||  ||   ||   ||

**Knowledge and Understanding**
 * **Content:** || **Extension** ||
 * * Basic Polynomials
 * Linear Equations
 * Linear Functions
 * Linear Inequalities ||  ||

**Skills:**
 * * Factorizing algebraic expressions
 * Using substitution to evaluate expressions
 * Using algebraic equations to solve problems in unique contexts ||

**Links and Resources**

Lesson Sequence
Polynomials


 * Understanding the basic polynomial terms
 * Adding and subtracting polynomials
 * Multiplying and Adding polynomials

<span style="border-collapse: separate; font-family: Verdana,Geneva,sans-serif; line-height: 19px;">Difference of squares and square of a binomial
 * Investigate and understand special products: difference of squares and square of binomial
 * Use mental math to quickly simplify these products
 * IBMYP 4 Text Book Page 76 - 86 (Chapter 3 - Algebra)

Linear Equation
 * Understand the terms equation, inequality and and systems of equation.
 * What it means to solve and equation, inequality or systems of equation
 * Solve linear equations containing fractions and decimals
 * IBMYP 4 Text Book Page 34 - 49 (Chapter 1 - Algebra)
 * Investigate and develop understanding of linear equations with infinite solution or no solutions