Definitions
What is an algebraic expression made up of? How does it differ from an algebraic equation?
Coefficient, variable, constant, terms & operation. It does not have an equals sign.
Five more than twice a number equals 31.
Write this sentence in an algebraic expression.
2n + 5 = 31
A number divided by 4.
Write this sentence in an algebraic expression.
n/4
x + 25 = 74
x = 49
2y - 6 = 10
y = 8
Linear vs Nonlinear Patterns
Linear pattern, the value increases or decreases by the same number creating a constant change and a straight line when graphed. Nonlinear pattern, the change is not constant and numbers vary, causing a crooked line.
2 + b - 1 = 5
Write this equation in words.
Two plus a number, subtract a number equals 5.
5x+3
Write this equation in words.
A number multiplied by 5 plus 3.
y - 9 = 8
y = 17
6y+9=45
y = 6
Independent vs Dependent Variables
Independent Variables-The variable that affects what happens in the situation.
Dependent Variable – The variable that changes because of the independent variable. It depends on it.
A player scored 2 points each shot. By the end of the game he had 36 points.
How many shots did he make? Write the equation and solve it.
2x = 36
x = 18
He made 18 shots that game.
1, 4, 16, 64, ...
What is the pattern rule?
4n
3x = -15
x = -5
b/5−3=5
b = 40
Functional vs Recursive Relationships
Functional Relationship- You can find any number in the pattern right away. You don’t need the numbers before it. Ex.) “Double a number and add 3.”
Recursive Relationship- Each number in the pattern is found by using the number before it. You can’t skip ahead—you need the previous number. Ex.) Start with 2, then add 3 each time.
Clara is driving to her cottage in Alberta. The total distance is 950 km. She has driven 537 km so far. How much more distance (d) does she need to drive? Write the equations and solve it.
537 + d = 950
d = 413 km
She has 413 km left to go until she arrives at her cottage.
Admission to Fun Haven is $10. For each ride in Fun Haven, it costs an additional $2.
2r + 10
m ÷ 6 =8
m = 48
1.2y−3=9
y = 10
Means keeping both sides of an equation equal at all times. Anything you do to one side must also be done to the other side (add, subtract, multiply, or divide)
Preservation of Equality
A cook prepares 4.2 dishes per hour and has already prepared a total of 33.6 dishes. How many hours (h) did the cook work? Write the equations and solve it.
4.2h = 33.6
h = 8
The cook has worked for 8 hours.
At Bella's bookstore, a notebook costs $3. Each additional sticker costs $0.25. Write the algebraic expression to represent the cost of the notebook with (s) extra stickers.
0.25s + 3
2.4y=12
y = 5
−3x+7=25
x = -6