learn alberta – video essons&lesson=m6lessonshell11.swf solving equations… (unit
TRANSCRIPT
![Page 1: Learn Alberta – video essons&lesson=m6lessonshell11.swf Solving Equations… (Unit](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e595503460f94b53627/html5/thumbnails/1.jpg)
Learn Alberta – video
http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell11.swf
Solving Equations… (Solving Equations… (Unit Unit 1111))
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Questions:1. What is the difference between an “equation” and
an “expression?”
2. What do equations use when solving problems?
(hint: What are some key words we use to represent operations?)
Solving Equations… (Solving Equations… (Unit Unit 1111))
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What do the models below have in common?
How are they different?
ExpressionsExpressions & & EquationsEquations……Student Outcome: Understand the difference between an
expression and equation
x x=
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• A single constant (1,2,3…any number)• A single variable (x,y,x…any letter)• A numerical coefficent (2y, 5x, 9/x…)• A combination of operations with constants,
variables or numerical coefficients. (2y + 4…)
An An ExpressionExpression can be written can be written as a…as a…
Student Outcome: Identify constants, numerical coefficients and variables.
2y - 7
numerical variable constantcoefficient
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Investigate the Investigate the ExpressionExpression below…below…
Student Outcome: Identify constants, numerical coefficients and variables.
Model Expression Constant Variable Numerical Coefficient
+ 4 Z 6(multiply)
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Write the expression for the models below.
1.
2.
3. +
Write the “Write the “ExpressionExpression”…”…Student Outcome: Identify constants, numerical coefficients and
variables.
x x
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Model or write a phrase for the expressions below.
1. Three times a number minus five
2. A number divided by two plus four
3. +
Identify the “Identify the “ExpressionExpression”…”…Student Outcome: I will learn how to model and solve problems
with equations
x x
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• Mathematical statement with two expressions that have the same value
• Both expressions have equal value and are separated by an equal sign (=)
• Write the mathematical statement (2 expressions).
• Write the equation in a phrase.
An “An “EquationEquation” is a…” is a…Student Outcome: I will learn how to model and solve problems
with equations
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• What are the two expressions that make up this equation?
• What is the equation?
1.
2.
Write the Write the ExpressionExpression & the & the EquationEquation
Student Outcome: I will learn how to model and solve problems with equations
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• Page 393: # 5, 7, 9, 10ab
• Page 394: # 11ab, 12ab, 14, 15
Practise & Apply Practise & Apply
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Practical Quiz #1Practical Quiz #1
On the front
On the back
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Example:Aaron and his mother spend $56 to take the ferry from Vancouver to
Victoria, Aaron knows that the cost for each person is $11. So, the cost for
two people is 2 x $11 = $22, but they must pay for their truck to go on
the ferry as well. He decides to model the situation with the equation..
t + 22 = 56Where t is the cost of the truck to be on the ferry. How could he determine
the cost of the truck?
One-Step Equations:1. Model it (pictures & numbers)
2. Solve it: remove the numbers from one side to leave the variable alone… do the same to the other side.
Solve One-Step Equations: Solve One-Step Equations: x + x + a = ba = b
Student Outcome: I will learn how to solve and model problems with equations.
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C + 22 = 56
+ $22 (- $22) = 56 (- $22)
= $34
Solve One-Step Equations: Solve One-Step Equations: x + x + a = ba = b
Student Outcome: I will learn how to solve and model problems with equations.
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You Try It:Hilda’s grandmother gives her $5 for her birthday. Hilda puts this in per
piggy bank and now has $12. How much did she have before her birthday?
One-Step Equations:
1. Write the equation (including a variable, which is what you’re looking for)
2. Model It (pictures and numbers…5 loonies, 12 loonies, and a piggy bank)
3. Solve it: remove the numbers from both sides to until the variable is left alone.
Solve One-Step Equations: Solve One-Step Equations: x + x + a = ba = b
Student Outcome: I will learn how to solve and model problems with equations.
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Hilda’s grandmother gives her $5 for her birthday. Hilda puts this in per
piggy bank and now has $12. How much did she have before her birthday?
Solve One-Step Equations: Solve One-Step Equations: x + x + a = ba = b
Student Outcome: I will learn how to solve and model problems with equations.
Write it Model it Solve it (remove from both
sides)
P + 5 = 12 =
=
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• An operation that “undoes” another operation
• The opposite operation of subtraction is ______________
• The opposite operation of division is ______________
• Remember…to keep the equation balanced, whatever operation is used on one side of the equation must be done on the other.
• “Isolate the variable,” means to
get the variable by itself.
• Another name for opposite
operation is called …
“inverse operations”
Apply the “Apply the “opposite operationopposite operation””Student Outcome: I will learn how to solve an equation using opposite
operations
Example:
1. x + 34 = 55
x + 34 - 34 = 55 – 34
x = 21
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Complete the examples below:
1. X - 24 = 48
2. 17 + 35 = y - 31
Find & Use the “Find & Use the “inverse inverse operationoperation””
Student Outcome: I will learn how to solve an equation using inverse operations
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3 Ways to 3 Ways to SOLVESOLVE……
Solve by “Inspection”
Solve by
“Modelling”
Solve by
“Isolating The Variable”
- Using mental math…- inspect what number
minus 24 is equal to 48
Draw a picture…use dots and then cross out on both sides.
Use “opposite operations” to isolate
the variable!
X - 24 = 48
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• Page 399: # 6, 7, 8, 10cd, 12ab
• Page 400: # 14, 16, 17
• EXTEND #19, 21, 22
Practise & Apply Practise & Apply
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Practical Quiz #2Practical Quiz #2
On the front
On the back
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Don’t be afraid of multiplication or division operations
Just remember to use the inverse operation
to get the number or variable to the other side.
Remember: try to get the variable on its own!
Example: 5g = 25
Solve One-Step Equations: Solve One-Step Equations: ax ax = b= b
Student Outcome: I will learn how to solve and model problems with equations.
Operation Inverse Operation
Division (÷) Multiplication (x)
Multiplication (x) Division (÷)
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3f = 21Use “mental math” to solve each
equation.
Use cups and marbles to model this
equation.
=
Solve One-Step Equations: Solve One-Step Equations: ax ax = b= b
Student Outcome: I will learn how to solve and model problems with equations.
Ask yourself: “3 times what number gives
21.”
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Divide to apply theDivide to apply the “Inverse “Inverse Operation”Operation”
Student Outcome: I will learn how to solve and model problems with equations.
7 = d
5Re write the equation
d = 7
5
Use the “opposite operation” to get
the variable by itself.
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Divide to apply theDivide to apply the “Inverse “Inverse Operation”Operation”
Student Outcome: I will learn how to solve and model problems with equations.
• Sylvie and Murray earn money delivering groceries. Last weekend, Murray earned $29. This was one third of the amount Sylvie earned. How much money did Sylvie earn?
Questions to answer:
1. What are we looking for (this is the variable)?
2. What is the algebraic equation?
3. Solve the equation using opposite
operations. (Show your work)
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Divide to apply theDivide to apply the “Inverse “Inverse Operation”Operation”
Student Outcome: I will learn how to solve and model problems with equations.
Answers:
1. What are we looking for (this is the variable)?
Sylvie’s earnings
2. What is the algebraic equation?
S = $29
3
3. Solve the equation using opposite
operations. (Show your work)
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• Page 406: # 9ab, 10, 12ab,
14ab, 15ab
• Page 407: # 17, 18
Practise & Apply Practise & Apply
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Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c
Student Outcome: I will learn how to solve and model problems with 2-step equations.
A clothing store is having a sale. Jake pays $19 in total for two
T-shirts and a pair of $5 sunglasses. How much does Jake pay
for each T-shirt?
Model Two-Step Equations:
• All Boys: use simple drawings
(t-shirt, sunglasses and $19)• All Girls: use the balance scale with algebra tiles
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Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c
Student Outcome: I will learn how to solve and model problems with 2-step equations.
Model Two-Step Equations:
• All Boys: use simple drawings
(t-shirt, sunglasses and $19)
+ + = $19
$5.00
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Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c
Student Outcome: I will learn how to solve and model problems with 2-step equations.
Model Two-Step Equations:
• All Girls: use the balance scale
S S
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Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c
Student Outcome: I will learn how to solve and model problems with 2-step equations.
A clothing store is having a sale. Jake pays $19 in total for two
T-shirts and a pair of $5 sunglasses. How much does Jake pay
for each T-shirt?
Everyone Solve It: 2S + 5 = 19
HINT: get rid of values before your divide/multiply…in other words apply the
“REVERSE” order of operations
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Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c
Student Outcome: I will learn how to solve and model problems with 2-step equations.
Maurie saw this sign advertising T-shirts and socks. He pays
$30 in total for two T-shirts and four pairs of socks (2$/pair).
What is the price of one T-shirt?
• All Girls: use simple drawings
(t-shirt, socks and $30)• All Boys: use the balance scale with algebra tiles
• Everyone: Solve it and show your work!
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Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c
Student Outcome: I will learn how to solve and model problems with 2-step equations.
Maurie saw this sign advertising T-shirts and socks. He pays $30 in total for
two T- shirts and four pairs of socks (2$/pair).
What is the price of one T-shirt?
• All Girls: use simple drawings
(t-shirt, socks and $30)
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Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c
Student Outcome: I will learn how to solve and model problems with 2-step equations.
Maurie saw this sign advertising T-shirts and socks. He pays $30 for two T-
shirts and four pairs of socks (2$/pair). What is the price of
one T-shirt?
• All Boys: use the balance scale with algebra tiles
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Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c
Student Outcome: I will learn how to solve and model problems with 2-step equations.
Maurie saw this sign advertising T-shirts and socks. He pays $30 for two T-
shirts and four pairs of socks (2$/pair). What is the price of one T-shirt?
• Everyone: Solve it and show your work!
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• Page 411: # 4ab, 5a
• Page 412: # 8, 11ab, 12d, 16
Practise & Apply Practise & Apply