Review and extend previous understandings of algebraic concepts and processes Simplify numerical, linear and quadratic expressions and solve simple first-degree equations and inequalities
Conceptual Framework
form representation, simplification, generalization in the context of Scientific and Technical Innovation
Statements of Inquiry
Students will appreciate the many forms of algebraic representation through an inquiry into algebraic patterning
Factual
How can we generate and identify patterns in numbers so that we can describe them as algebraic rules?
Conceptual
How do we represent generalized numbers?
How do we solve real world problems using algebra?
Debatable
Is algebra a useful tool?
Description
Students begin the unit by reviewing important algebra skills from Year 9, generalizing number concepts into algebraic forms. Then, using different forms of representation including pictorial patterns and area models, students generate and manipulate quadratic expressions. The concept of simplification allows students to understand that there are different forms of quadratic expressions which are equivalent.
Learning Outcomes
Demonstrate understanding of each of the following terms: variable, term, coefficient, like terms, constant, polynomial, monomial, binomial, trinomial, simplify, evaluate, expand, expression
Translate expressions into words and words into algebraic expressions
Use substitution to find the value of an algebraic expression that requires the use of the order of operations
Add and subtract directed numbers (integers) with confidence
Simplify algebraic expressions by combining like terms
Write algebraic expressions from a given word problem
Understand exponential notation as repeated multiplication
Apply shortcuts relating to exponents to simplify expressions
Multiply and divide simple, monomial expressions with integer and rational exponents
Expand algebraic expressions using the distributive property
Factorize algebraic expressions by removing a common factor