Algebraic+Expressions+8

=Algebraic Expressions= Grade 8 Algebra AOI Link: //The emphasis in this unit is on translating word problems into algebraic expressions.//

Textbook reference: MYP Book 3 Chapters 2 Algebraic Operations

**Guiding Questions**

 * 1) How can a real world situation be translated into a mathematical problem in order to find a solution

Benchmarks

 * 1) Demonstrate understanding of each of the following terms: variable, term, coefficient, like terms, constant, polynomial, monomial, binomial, trinomial, simplify, evaluate, expand, expression.
 * 2) Write algebraic expressions to represent word phrases or simple real life situations
 * 3) Evaluate algebraic expressions and formulas which require the use of order of operations with rational numbers
 * 4) Understand what it means to simplify expressions and understand that expressions in different forms are equivalent but some are more compact
 * 5) Simplify algebraic expressions by collecting like terms.
 * 6) Add and subtract algebraic expressions.
 * 7) Multiply and divide monomial expressions by using laws of exponents.
 * 8) Understand and use the distributive property to multiply a monomial by a polynomial, two or more binomials or two or more polynomials.
 * 9) Divide a polynomial by a monomial using distributive property.
 * 10) Develop understanding of factoring as the reverse of expanding and then factor algebraic expressions using: a) greatest common factor; b) perfect trinomial square; c) difference of squares; d) simple trinomials of the form

Unit Assessment Tasks

 * **Task/Criteria** || **A** || **B** || **C** || **D** ||
 * Investigating Magic Squares ||  || x || x ||   ||
 * Frogs ||  || x || x || x ||
 * Test || x ||  ||   ||   ||

**Knowledge and Understanding** ﻿ ||
 * **Concepts** || **Extension** ||
 * * algebraic expressions
 * substitution
 * factorizing || * complex factorizing ||
 * # <span style="font-family: Verdana,Geneva,sans-serif;">Define the following terms - variable, term, coefficient, like terms, constant, polynomial, monomial, binomial, trinomial, simplify, evaluate, expand, expression.
 * 1) <span style="font-family: Verdana,Geneva,sans-serif;">Simplify algebraic expressions by combining like terms.
 * 2) <span style="font-family: Verdana,Geneva,sans-serif;">Show that there are alternative and equivalent forms of an algebraic expression.
 * 3) <span style="font-family: Verdana,Geneva,sans-serif;">Use substitution to find the value of an algebraic expression.
 * 4) <span style="font-family: Verdana,Geneva,sans-serif;">Use the distributive property to multiply monomials by polynomials, binomials by binomials, and binomials by trinomials.
 * 5) <span style="font-family: Verdana,Geneva,sans-serif;">Divide polynomials by monomials using the laws of exponents. || # <span style="font-family: Verdana,Geneva,sans-serif;">Factorize a trinomial with leading coefficient other than 1.

Links and Resources

 * [|Combining like terms] || Purplemath explanations with worked examples ||
 * [|Translating] || Learn the important words that help you translate English phrases into algebraic expressions ||

Lesson Sequence
Factorizing
 * **Lesson** || **Description** ||
 * Introduction to Algebra || * [|Math 08 - Algebra - Introduction to Algebra.pdf]
 * [|Wallwisher]can be used collaboratively to research the key algebra terms
 * Exercise 2A, 2B - Notation and terminology associated with algebra ||
 * Algebraic Expressions || *
 * [|Math 08 - Algebra - Algebraic Expressions Worksheet.pdf]
 * Magic squares can be a great application of manipulating algebra and consolidate the key skills of combining like terms and number susbstitution
 * [|Math 08 - Algebra - Magic Squares and Algebraic expressions.xls]
 * [|Math 08 - Algebra - Algebraic Expressions Task.pdf] ||
 * Number Tricks || * investigate the algebra behind number tricks - Investigation page 104
 * [|Math 08 - Algebra - Number Tricks.pdf]
 * [|Math 08 - Algebra - More Number Tricks.pdf] ||
 * Translation || * translating simple phrases and other real life situations into algebraic expressions
 * [|Math 08 - Algebra - Translating word phrases into algebraic expressions.pdf]
 * exercise 2C ||
 * Algebraic Expansion || * multiplying using the distributive property - a(b+c);
 * multiplying using the rule (a+b)(c+d). Use a geometric approach similar to the one on page 106
 * expanding the square of a binomial
 * multiplying conjugate pairs
 * [|Math 08 - Algebra - Algebraic Expansion.pdf]
 * Select appropriate exercises from chapter 4 ||
 * Dividing algebraic expressions || * divide polynomials by monomials ||
 * Review and testing knowledge and understanding || * notation and terminology
 * operations on polynomials
 * review set 4A ||
 * factorizing algebraic expressions by removing a common factor
 * factorizing a difference of two squares
 * factorizing perfect square trinomials
 * factorizing easy trinomials with leading coefficient of 1
 * Select appropriate exercises from chapter 17
 * See investigation on page 359

<span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; line-height: normal;">Use the Algebra tiles applet here to help students visualize the concept of factorization

Algebraic fractions simplify algebraic fractions by factorizing and canceling common factors
 * <span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; line-height: normal;">
 * begin to perform operations on simple algebraic fractions
 * Select appropriate exercises from chapter 21

<span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; line-height: normal;"><span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; border-collapse: separate; line-height: 19px;">Review and testing knowledge and understanding
 * factorizing
 * algebraic fractions
 * review set 17A, 21A