Transcript Solve One-Step Equations

Solving Equations… (Unit 11)
Learn Alberta – video
http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=l
essons&lesson=m6lessonshell11.swf
Solving Equations… (Unit 11)
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?)
Expressions & Equations…
Student Outcome: Understand the difference between an expression and
equation
What do the models below have in common?
x
How are they different?
x
=
An Expression can be written as a…
Student Outcome: Identify constants, numerical coefficients and variables.
•
•
•
•
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…)
2y - 7
numerical
coefficient
variable
constant
Investigate the Expression below…
Student Outcome: Identify constants, numerical coefficients and variables.
Model
Expression
Constant
Variable
Numerical
Coefficient
+4
Z
6
(multiply)
Write the “Expression”…
Student Outcome: Identify constants, numerical coefficients and variables.
Write the expression for the models below.
1.
2.
3.
x
x
+
Identify the “Expression”…
Student Outcome: I will learn how to model and solve problems with
equations
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.
x
x
+
An “Equation” is a…
Student Outcome: I will learn how to model and solve problems with
equations
• 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.
Write the Expression & the Equation
Student Outcome: I will learn how to model and solve problems with
equations
•
•
1.
2.
What are the two expressions that make up
this equation?
What is the equation?
Practise & Apply
Page 393-394
12,13,14,15
9
1,5,10,11,12
1,3,4,5,7
Show Me What You Know #1
On the front
On the back
Activity
Guess My Number
(see handout)
Alien Invasion
(see handout)
Solve One-Step Equations: x + a = b
Student Outcome: I will learn how to solve and model problems with equations.
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 = 56
Where 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.
2.
Model it (pictures & numbers)
Solve it: remove the numbers from one side to leave the variable
alone… do the same to the other side.
Solve One-Step Equations: x + a = b
Student Outcome: I will learn how to solve and model problems with equations.
C + 22 = 56
+ $22 (- $22) = 56 (- $22)
= $34
Solve One-Step Equations: x + a = b
Student Outcome: I will learn how to solve and model problems with equations.
You Try It:
Hilda’s grandmother gives her $5 for her birthday. Hilda puts this in her
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: x + a = b
Student Outcome: I will learn how to solve and model problems with equations.
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?
Write it
Model it
Solve it
(remove from both
sides)
P + 5 = 12
=
=
Apply the “opposite operation”
Student Outcome: I will learn how to solve an equation using opposite
operations
•
•
•
•
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”
Example:
1.
x + 34 = 55
x + 34 - 34 = 55 – 34
x = 21
Find & Use the “inverse operation”
Student Outcome: I will learn how to solve an equation using inverse operations
Complete the examples below:
1.
X - 24 = 48
2.
17 + 35 = y - 31
3 Ways to SOLVE…
X - 24 = 48
Solve by
“Inspection”
Solve by
“Modelling”
- Using mental math… Draw a picture…use
dots and then cross out
- inspect what number
minus 24 is equal to 48 on both sides.
Solve by
“Isolating The
Variable”
Use “opposite
operations” to isolate
the variable!
Practise & Apply
• Page 399-400
3,18-22
14
3,4,6,8,9,15-18
1,3,4,6,8,9,12,13
Show Me What You Know #2
On the front
On the back
Solve One-Step Equations: ax = b
Student Outcome: I will learn how to solve and model problems with equations.
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.
Operation
Inverse Operation
Division (÷)
Multiplication (x)
Multiplication (x)
Division (÷)
Remember: try to get the variable on its own!
Example:
5g = 25
Solve One-Step Equations: ax = b
Student Outcome: I will learn how to solve and model problems with equations.
3f = 21
Ask yourself:
“3 times what
number gives
21.”
Use “mental math” to solve each
equation.
Use cups and marbles to model this
equation.
=
Divide to apply the “Inverse Operation”
Student Outcome: I will learn how to solve and model problems with equations.
7=d
5
Re write the equation
d =7
5
Use the “opposite operation” to get
the variable by itself.
Divide to apply the “Inverse 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)
Divide to apply the “Inverse 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)
Practise & Apply
• Page 405-407
3,16,17,18,19,20,21
13
3,6,8,10,15,16,17,18
3,4,8,10,11,14,15
Solve Two-Step Equations ax + b = 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
Solve Two-Step Equations ax + b = 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
Solve Two-Step Equations ax + b = 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
Solve Two-Step Equations ax + b = 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
Solve Two-Step Equations ax + b = 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!
Solve Two-Step Equations ax + b = 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)
Solve Two-Step Equations ax + b = 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 $30 for two Tshirts and four pairs of socks (2$/pair). What is the price of
one T-shirt?
•
All Boys: use the balance scale with algebra tiles
Solve Two-Step Equations ax + b = 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 $30 for two Tshirts and four pairs of socks (2$/pair). What is the price of one T-shirt?
•
Everyone: Solve it and show your work!
Practise & Apply
• Page 411-412
3,16,17,18,20,21
15
3,7,11,14,17,18
3,4,6,7,8,11,14
Unit Review Questions:
Pages 414-416
#3,5,6,11cd,12,16,19,20,21,22
http://www.quia.com/ba/143047.html