Download Algebra II Solving Linear Equations Unit Plan

Algebra II Solving Linear Equations Unit Plan
Vocabulary: Linear, equivalent
linear – an equation is said to be linear if all variables have an exponent of 1, and no variables are
coefficients of other variables (x + y = 5 is fine, but x*y=5 is not.)
equivalent equations – two equations with the exact same solution or solution set.
I. One-variable linear equations
Key idea: To solve for x, get x alone.
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To do that, we must have a single x term, so combine like terms first.
Key idea: Then, solving is PEMDAS in reverse
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Start outside parentheses (or distribute to get rid of them.)
Get rid of separate terms first
Then, get rid of coefficient
Lastly, deal with powers.
Key idea: Nothing crosses the equals sign
Key idea: Law of Solving – “what you do to one side, you must do to the other.”
Key idea: For multiply and divide, you must do to all terms on both sides.
Key idea: Solutions can always be checked!
1.) “x” on one side
Examples:
o
o
o
One simple example
One example that involves combining like terms
One example that involves “x” on the top of a fraction
HW: “X” On One Side Topic Practice
Optional HW (extra practice): 3.3 worksheet
p. 29 #1-3, #5 – 9 odds; #23-35 odds
p. 29 #4-8 evens; #22-36 evens
p. 59 #30, 31, 34, 37
p. 778 #23-27
2.) “x” on both sides
- examples of how to solve when “x” is on both sides of the equation
Identities and Contradictions:
An equation where any number is a solution is called an identity
[Construct an example in class.]
An equation with no solutions is called a contradiction
[Construct an example in class.]
Key Idea: When you are solving for “x,” and all the variables disappear, and you’re left
with a true statement, the original equation is an identity.
When you are solving for “x,” and all the variable terms disappear, and you’re left with a
false statement, the original equation is a contradiction.
HW: “X” On Both Sides Topic Practice
Optional HW (extra practice): 3.4 worksheet
p. 30 #37-50, skip 47
p. 59 #32,33,35,36
p. 778 #27-30
3.) Linear Proportions
Proportion – An equation with a fraction on both sides
Recall that a fraction bar is a grouping symbol: All the numbers and variables on both the
top and bottom of a fraction bar are assumed to be in parentheses, even if they are not
written. Remember this when plugging things in to your calculator!
HW: Linear Proportions Topic Practice
Optional HW (extra practice): p. 747 #13-24
Solving Linear Equations Numerical Problems Quiz
II. One-variable equations word problems
Key Idea: Common sense check – does your answer make sense in the context of the word problem?
Key Idea: “Comparison” problems usually have an “x” on both sides. “Totals” problems usually have an
“x” only on one side.
Key Idea: Sometimes using a table or making a diagram is a better way to answer some word problems
than writing a formal equation.
HW:
Solving Linear Equations Word Problems Worksheets #1, #2 [use the first few as examples.]
III. Multi-variable linear equations
Vocabulary: Multi, formula, isolate
“Multi” – more than one
“Formula” – an equation with more than one variable that describes the relationship between
real-life quantities
“Isolate” – to get a variable alone without necessarily finding a numerical value for it
Discuss: Can anyone think of some famous formulas? [Write on board.]
Key Idea: Multi-variable equations tend to have an infinite number of solutions.
We want to be able to do three things with multi-variable equations:
1.) Isolate a variable within the equation.
2.) Solve for a given variable by substituting in values for all the other variables.
3.) Make a solution table out of the solution set of the equation.
1.) Isolate a variable
Key Idea: We have to modify the law of solving: “For multiply and divide, you must do to all terms
on both sides…”
[Show example from the famous formulas.]
[Show a second example using 3x + 2y = 6.]
[show an example involving reciprocals, such as the area of a triangle formula.]
2.) Substitute and solve
[Show an example plugging (-3) in for x in 3x + 2y =6.]
Show the check.
3.) Make a solution table
Key Idea: Most multi-variable equations have an infinite number of solutions. We can organize a
“sample” of these solutions using a solution table.
[Show an example using 3x + 2y = 6]
Integrating word problem skills:
p. 35 examples #4,5; checkpoint #2
HW: Multi-variable equations Topic Practice
Optional HW (extra practice):
p. 36 #3-9, #12-17;
p.37 #19-21;
p.39 #57-60;
Quiz 2 #13,14,16
p.59 #39-46;
p. 61 #16-18
p. 778 #31-33
IV. Unit Review
Solving Linear Equations Worksheets #1-4
Solving Linear Equations Blockbuster
Solving Linear Equations Test