Concepts in Middle School Algebra
Variables and Expressions
Variable
Communications
What is a variable ?
- A variable in math is a symbol, usually a letter like x or y, that represents an unknown or changeable value.
Examples of variables: x, y, n, k, a, A, b, B, i
What is an algebraic term
What is an expression
What does it mean when a variable is attached to a number?
- It means multiplication
Examples:
Algebra page 5
Expectations
Be able to identify variables, terms, and expressions
Exercises
Expression
What is an Term ?
A single number, variable, or a product of one or more numbers and variables
Examples:
5
111
x
12A
23K
4AB
110xy
What is an Expression
- A math sentence containing having two or more terms
Examples:
2k + 3
-2k 1 3
3x - 4y - 7
5a - 2a + 1
Unit 1 test
Substitution and Evaluation
Comunications
What does substitute or substitution mean?
- It means replacing a variable by some given value, and simplify
Examples:
Algebra page 4
What does evaluate mean?
- It means replacing a variable by some given value, and simplify
Examples:
Algebra page 4
What does it mean to evaluate an expression ?
- It means to replace the variables by numerical values, then simplify
Examples and exercises:
Expectations
Use substitution to evaluate (or simplify expressions)
What does evaluation mean?
Exercises
Simplifying expressions part 1
Communications
What is collection like terms?
What does it mean to simplify an expression
Expectations
Be able to perform operations with positive integers
Evaluate expressions with positive terms and values
Negative integers
Communications
A negative imteger is an imteger that is less than zero.
Expectations
Be able to perform operations with negative integers
Evaluate expressions with negative values
Simplifying expressions part 2
Expectations
Be able to perform operations with positive and negative integers
Evaluate expressions with positive and negative terms and values
Equations Part 1
Math Modelling
Divisors, Multiples and Remainders
Prime Numbers
Prime factor tree
Prime factorization
Divisibility
Background
Know the timetable well
Factors and multiples
Prime numbers
Divisibility rules
Goals
Prime factor tree
Prime factorization of a number
Divisibility rules
List the factors (divisors) of a number
Find common factors of two or more numbers
Find the GCF (Greatest Common Factor) of two or more numbers
List some multiples of a number
Find some common multiples of two or more numbers
Find the LCM (Least Common Multiple) of two or more numbers
Real world problems
Common Divisors and Multiples
Fractions
Unit 3: Powers
Unit 4: Orders of Operations
Unit 6: Integers
Unit 7: Ratios and Percents
Unit 8: Math Modelling of Real World Problems