Name________________________
Extended Response Practice #4
/4 points
Respond completely
in your Answer Document. (2
points)
Jen is paddling a canoe from one side of a
lake to the other. She is paddling at a rate of
35 yards per minute.
In your Answer Document, write an equation
to find y, the number of yards she paddles in
x minutes.
Use your equation to determine how long it
will take her to paddle the 840 yards from
one side of the lake to the other.
Learning Target:
I can…
Visually represent and solve equations
To Draw an Equation
1. Identify what will represent a
_____________________ and
what will represent
______________________
2.Make sure each side of your equation
is a side of your
_____________________
Solving Equations Symbolically
Both sides of an equation are the same
2c + 5 = 9
One way we can show this is by using a scale
x represents variables and o represent numbers
2) If X’s represent variables and O’s
represent the known amounts, draw a model of
the equation 10 = 4a + 2
Variables: ________
Numbers: ________
3) Draw a representation of the equation 3a – 7 = 8
Variables: ________
Numbers: ________
Which picture represents 3x + 3 = 2
4) If X’s represent variables and O’s
represent the known amounts, which of the
following pictures represents 3x + 2 = 2x + 3?
Other ways to represent
equations
*assume the unit tiles are numbers
2x + 1 = 7
What equation does this model
represent?
What equation does this
model represent?
OAA PRACTICE
What is the value of
?
To Solve Equations
Visually:
1. Anything that appears on both side
of the scale _________________
2.Isolate the
____________________________
Solving Equations Visually
What is the value of
?
What is the value of
?
What is the value of
?
EXIT
Write the equation that this
model represents.
What is the value of
?
Visual Representation Activity
Word Problems
Justin bought 2 apples and 1 pear for
$4.00. The pear was $1.78. Write
an equation and solve to find the cost
of the apples.
Word Problems
Mark bought 4 pens and 1 notebook for
$3.25. The notebook was $2.25.
Write an equation and solve to find
the cost of the apples.
Example
Sara bought 2 bags of chips and a coke
for $7.50. The coke was $1.50. How
much were the chips?
Equation _______________
Answer ________________
The fair costs $3 to get in and $2 for
every ride. If John spent $21, how
many rides did he go on?
Equation _________________
Answer ______________
Logo Shirts, Inc. is going to charge
General Sherman $6 for each t-shirt
they make for the school. The company
will also charge the school a flat fee of
$35 to set up the design. The school
spent $575 all together. Which
equation represents this situation?
A.35x + 575 = 6
B.6x + 575 = 35
C.-6x + 35 = 575
D.6x + 35 = 575
331 students went on a field trip. Six
buses were filled and 7 students
traveled in cars. How many students
were in each bus?
a.6x + 7 = 331
b.7x + 6 = 331
c.331x + 6 = 7
d.7 + 331x = 6
You bought a magazine for $5 and four
erasers. You spent a total of $25.
How much did each eraser cost?
A.5x + 25 = 20
B.5x + 4 = 25
C.4x + 5 = 25
D.-4x + 5 = 25
Aliyah had $24 to spend on seven
pencils. After buying them she had
$10. How much did each pencil cost?
Equation: ___________________
Answer:_________________
Representing Equations
2x – 6 = 4
+
+
=
-
-
You try
3x + 1 = 7
+
+
=
-
-
You try
4x – 2 = -6
+
+
=
-
-
4. -3x + 8 = -1
5. 2x – 3 = -7
6. Challenge*
2(x + 4) = 2
Solving Equations - Example
15
16
Solving Equations – Example 2
Uses of a variables
A variable can be used for :
1.
An unknown that can change.
2. A generalization of a pattern
Example: Find the nth term with the
rule 2n + 1
3. A formula
The formula to change from Celcius to
Fahrenheit is
C = 5/9(F – 32)
Simplifying Expressions
COMBINE LIKE TERMS
Example: 2a + 6b – 5 + 4a – 2b + 1
1. Circle one term (and each sign before
the term!)
2. Square the next term (and signs!)
3. Underline the last term
4. COMBINE!
18p + 13p + p
Simplify the expression
18p + 13p + p =
a.
b.
c.
d.
22p
32p
31p
32p²
CANNOT COMBINE
Different powers (x + x²)
Different letters (2a + 3b)
Plain numbers with variables (2a +
5)
3x + 2y – 6x + 7y
8f + 2t + 3f + t
11f + 3t
-3x + 9y
You try!
a.
b.
c.
d.
13x + 9
2x
5x – 3
5x + 3
Simplify 2x + 4y + 2 – x + 9y + 6x 5
a. 9x + 13y - 3
b. 21xy – 3
c. 7x + 13y
d. 8xy - 11
a. 6x² - 2x
b. 6x² - 2
c. -2x² - 2x
d. -4x²
Simplify and solve for x
3x – x + 4x = 54
Simplify
6x = 54
Solve
x=9
What is the simplified
equation? What is x?
4x – 10x + x = 45
a.
b.
c.
d.
-6x = 45;
-5x = 45;
-7x = 45;
-5x = 45;
x = -7.5
x = -9
x = -6.42
x=9
What is the simplified equation?
What is x?
2x – 4 + 4x + 2 – x = -17
a. 5x – 4; -2.6
b. 6x + 6; -3
c. 5x – 2; 3
d. 5x – 2; -3
Problem of the Day
(Tuesday)
Calculate your class average for the
problem of the day. Round to the
nearest tenth and answer
numerically.
Review
Simplify the expression.
a. 7x² -3x -1
b. 8x² -4x
c. 8x² - 3x
d. 7x² - 4
Distributive Property
Multiply the outside number by
everything in the parenthesis
4(a + 5) =
4a + 20
-3(b + 6) =
-3b – 18
2(3c + 12 + a) =
Simplify and solve
3(x + 10) = 90
2(b – 12) = 8
Problem of the Day
(Wednesday)
Simplify the expression 4(k + 7) + 2k
a.
b.
c.
d.
4k +
6k +
6k +
4k +
9
28
7
28
Review – Simplifying
Expressions
1. Always do the Distributive Property
first!
Multiply the outside number by
everything in the parenthesis
2. Simplify the rest of the expression by
combining like terms
3a + 5(a – 6)
3a + 5a – 30
7 + 5(a – 6)
7 + 5a – 30
Simplify 28k + 36(7 + k)
a.
b.
c.
d.
64k + 252
29k + 252
29k + 36
28k + 252
Signs!
Simplify –(x + 10)
a.
b.
c.
d.
-x + 10
-x – 10
x – 10
-x – 1
Simplifying Expressions
Multiplying variables
 m ∙ m = m²
 3m² ∙ 2m³ = 6m⁵
 2a ∙ b² ∙ 4a ∙ b⁵
Example:
2c ∙ 3c = 864
Simplify
2x² ∙ x ∙ -4x³
3(a + 7 – b)
c(4 + c – d)
9x² ∙ 9x
Solve with variables on both sides
2x + 10 = -4x – 2
1. Get the variable
2x + 10 =
+ 4x
6x + 10 =
on one side
-4x – 2
+4x
-2
2. Solve the two step equation
6x + 10 = -2
-10 -10
6x = -12
x = -2
8x + 9 = 3x + 49
1. Get the variable on one side
8x + 9 = 3x + 49
-3x
-3x
5x + 9 = 49
2. Solve the two step equation
5x + 9 = 49
-9 -9
5x = 40
x=8
Problem of the Day
(Thursday)
CPS Learning Series Question
Problem of the Day
(Monday)
Writing Algebraic Expressions
1. Identify the variable
Remember the variable is the unknown
or element that changes in the problem.
Example:
Justin is x years old. Jackie is two
years younger than twice Justin’s age.
How old is Jackie?
2. Identify what’s WITH the variable
Justin is x years old. Jackie is two
years younger than twice Justin’s age.
How old is Jackie?
3. Write the expression
Jackie’s age = 2x – 2
You try!
Jeremy did 2 fewer than
3 times the hours of
work that Haley did.
A. 2x – 3
B. 2 – 3x
C. 3x – 2
D. 3 – 2x
1. Identify the variable
h = number of hours
2. Write the expression
Total Cost = 12 + 2h
Using your expression 12 + 2h, how much
would it cost to rent the bicycle for 4
hours?
$20
If Katie spend $26, how many hours did
she rent the bicycle for?
12 + 2h = 26
h=7
You try!
First half
Total
8
+
+
Second half
=
3x
23
=
1. Identify the variable
x = how much they need to save per month
2. Write the equation
Already saved + Need to Save = Total
80
+
6x
= 200
3. Solve for x
They need to save $20 a month
1.
Identify the variable
x = number of paperbacks
2. Write the equation
Admission + paperbacks bought = Total spent
2.50
+
.25x
= 4.50
3. Solve for x
You bought 8 paperbacks
Problem of the Day (Friday)
Relating a Table to an
Equation
Problem of the Day
(Tuesday)
Equations to Boot
Example:
Sam’s boots are 3 sizes less than twice
the size of Toni’s.
(s = Sam’s boot size, t = Toni’s size)
s = 2t – 3
Example 2
Sam‘s socks have one more than twice
the number of holes as Zoey’s.
A. s = 2(z + 1)
B. 2z + 1 = s
C. z = s + 1 x 2
Example 3
Matt’s right sock has 2 less than 6
times the holes as his left sock.
A. 6L – 2 = R
B. 2(L + 6) = R
C. R = (6 x 2)
1. Basha’s boots cost $80 more than Chad’s.
A. b + 80 > c
B. c = b + 80
C. c + 80 = b
2. Yolanda’s boots cost $5 less than twice the cost of Sam’s.
A. 2s – 5 = y
B. y + 5 = 2s
C. 5 + s = y
3. Zoey’s new boots cost $8 more than Toni’s and Chad’s combined.
A. z = t + c + 8
B. 2(t + c) = z – 8
C. z + 8 = c + t
4. Toni dried out her boots 4 hours more on Friday than on
Thursday.
A. f + t = 4
B. 4f = t
C. t + 4 = f
5. On Monday, Mike’s boots traveled 3 times longer than on
Tuesday.
A. mt = 3
B. t = 3m
C. m = 3t
6. On Sunday, Chad’s boots traveled 6 miles less than on
Wednesday.
A. w + 6 = s
B. s + w = 6
C. w – 6 = s
7. Yolanda’s boot size is one less than ½ the size of Chad’s
A. c = y – 1½
B. y + ½ + 1 = c
C. y = ½c - 1
8. Sam has 8 more than 4 times as many blisters on his left foot as
on his right.
A. L = 8R + 4
B. 4R + 8 = L
C. L + R = 4 x 8
Writing Expressions
Stations
6
Justin went to the store to buy snacks for his class at
school. He bought soda for $2.00. He bought cookies for
$0.45 a piece. If he spent $11.00, how many cookies did
he get?
1. On my last birthday I weighed 125 pounds. One year later
I have put on x pounds. Which expression gives my weight
one year later?
A. 125 + x
B. 125x
C. 125 – x
D. 125/x
2. Jane and her three college friends are going to be sharing the
cost of a 3 bedroom apartment. The cost of rent is n dollars.
What expression can you write that will tell you what Jane's
share is?
A. n/3
B. n/4
C. 4n
D. 3n