Solving Equations
Solve for g:
4g = 12
g = 3
Determine the TIMES TABLE shown in the (y) column:
Determine the equation that relates x to y
x y
1 6
2 12
3 18
4 24
5 30
Times Table: 6
Equation: y = 6x
Function (rule): x2 - 6
Input (x): 0, 1, 5, 10, 14
Output (y): -6, -4, 4, 14, 22
Write the following as an equation with (y) as the variable:
Eight plus a number is 13
8 + y = 13
What is a variable? How do we write a variable in algebra?
A variable is an unknown value / number. We usually use a letter to represent a variable (x, y, n, etc.)
Solve for e:
13 = 28 - e
e = 15
Determine the TIMES TABLE shown in the (y) column:
Determine the SHIFT up/down:
Determine the equation that relates x to y:
x y
1 0
2 3
3 6
4 9
5 12
Times Table: 3
Shift: down 3
Equation: y = 3x - 3
Function (rule): /4 + 1
Input (x): 16, 8, 0, 40, 100
Output (y): 5, 3, 1, 11, 26
Write the following as an equation with (s) as the variable. Then solve.
Sophie's mom makes some sandwiches for a trip to the beach. Her family eats 5 of the sandwiches at lunch, and there are 3 left over. How many sandwiches did she make?
s = 8
What is the difference between an expression and an equation. Give an example of each.
An equation has an equals sign (=). It has a left side and a right side. An expression does not have an equals sign.
Expression: 4x - 2 Equation: x + 5 = 21
Solve for r:
5 + 4 + r = 12 - 2
r = 1
Determine the TIMES TABLE shown in the (y) column:
Determine the SHIFT up/down:
Determine the equation that relates x to y:
x y
1 9
2 11
3 13
4 15
5 17
Times Table: 2
Shift: up 7
Equation: y = 2x +7
Function: y = x + 7
Input (x): 0, 1, 2, 3, 4
Output (y): 7, 8, 9, 10, 11
Write the following as an equation with (c) as the variable:
Sahib buys some cookies to share with 4 of his friends. Each person (including Sahib) gets 6 cookies. How many cookies did he start with?
c / 5 = 6
c = 30
What does RPR stand for? What is an RPR? Give an example.
Recursive Pattern Rule
It is the description of a pattern using words.
Ex: start a 5, add 3 each time
Solve for n:
6n - 11 = 7
n = 3
Determine the TIMES TABLE shown in the (y) column:
Determine the SHIFT up/down:
What goes in the blank?
x y
1 -7
2 -3
3 1
4 5
5 __
Times Table: 4
Shift: down 11
Blank: 9
Function: y = 2x - 2
Input (x): 5, 2, 7, 10, 0
Output (y): 8, 2, 12, 18, -2
Daily Double!!!
How many years old is Mr. Pohanka?
37 (I know, he looks so much younger!)
What does EPR stand for? What is an EPR? Give an example.
Explicit Pattern Rule
An equation that can be used to determine any value in a pattern through substitution.
y = 2x or y = x - 9
What is the value of b?
6a = 54
a + b - 7 = 12
b = 10
Fill in the Blanks:
x y
1 -2
2 __
3 4
4 __
5 10
Blank 1: 1
Blank 2: 7
Function: y = x/2 - 6
Input (x): 6, 24, 100, 66, 15
Output (y): -3, 6, 44, 27, 1.5
Daily Double:
How old are Mr. Pohanka's kids?
In the following expression, which is the "Numerical Coefficient", which is the "Variable", and which is the "Constant"?
3p + 2
Numerical Coefficient = 3
Variable = p
Constant = 2