March Through
Equations
Lessons & Activities for writing
and solving equations.
© 2013 Lindsay Perro
Clipart by Scrappin Doodles
March Through Equations
Lesson Overview:
o Week One
• Writing Equations and Expressions
 Writing Equations and Expressions Notes
 Practice Worksheets
o Week Two
• Solving One & Two Step Equations
 Solving Equations Notes
 Practice Worksheet
o Week Three
• Solving Multi Step and Integer Equations
 Practice Worksheets
o Week Four
• Equations in the Real World
 Practice Worksheet
 Solving Equations PowerPoint Practice
© Lindsay Perro
http://www.beyondtheworksheet.com
Week One
Writing Equations & Expressions
To get the most out of this lesson, use the resources in the order listed below.
All activities for this week are print & practice.
1. Writing Equations and Expressions Notes
2. Writing Equations Practice Worksheet
3. More Practice Writing Equations
Worksheet
Writing Equations Notes
Fill in each box with the key words that signal each operation/symbol.
Addition
Subtraction
Multiplication
Division
Equal Sign
Let’s review writing expressions.
5 more than the sum of a number and 12.
______________________________
4 times of the sum of a number and 8.
______________________________
6 more than the quotient of a number and 15.
______________________________
10 less than the sum of a number and 2.
_ _____________________________
Writing equations is very similar! All you have to include is an equal sign. Let’s
practice!
6 less than a number is 18.
______________________________
The quotient of 7 and a number is 28.
______________________________
The sum of a number and 20 is 8.
______________________________
5 less than half a number is 40.
______________________________
25 is four more than a number.
______________________________
13 less than a number is 4 more than a different number. _____________________________
© Lindsay Perro
http://www.beyondtheworksheet.com
Writing Equations Practice
The sum of 21 and a
number is 30.
You download music for
$1.99 per song (s) and
spend a total of $15.92.
The product of 8 and the
sum of a number m and 2
is 16.
Admission to the circus
costs $4 plus $0.50 per
ride. Ella spent $17.50 at
the circus.
Strawberries are $3.50 per
pound. You bought $18.25
worth of strawberries.
The quotient of a number
X and 2 is 20.
5 less than the product of 5
and a number y is 22.
The product of 10 and the
difference of a number X
and 14 is 90.
4 less than a number X is 2.
Three times the difference
of a number y and 9
is 5.
Ernie has 3 more than half
the amount of trucks (n)
that Al has. Ernie has 45
trucks.
Abby purchased $150
worth of cookies, which
was $30 more than half of
what Ann spent.
You’re getting a pay raise!
You are going to be
making $9 per hour plus a
$100 a day sales bonus.
You make $190 per day.
15 plus the difference of 10
and a number X is 15.
Shipping a package costs
$1 per pound (X) and a
$5.00 shipping fee. You
spent $15 to ship your
package.
Jose’ is joining a gym. He
pays $20 each month plus
$3 for each aerobic class.
He spent $35 last month.
2 more than the sum of a
number X and 3 is 15.
The difference of 6 and a
number X is 14.
Aiden has four less than
triple the amount of
baseball cards as Sam.
Aiden has 40 baseball
cards.
The sum of a number X and
42 is 15.
© Lindsay Perro
http://www.beyondtheworksheet.com
More Practice Writing Equations
Write each equation. Find your answer in one of the two answer boxes.
#
Equation
Answer 1
Answer 2
1
The sum of 36 and a number
is 14.
36 + 14 = n
n + 36 = 14
2
Fourteen less than a number
is 5.
n – 14 = 5
14 – n = 5
3
2 more than half a number
is 6.
2n + 2 = 6
n+2=6
4
5 less than the sum of a
number and 4 is 20.
5 – (n + 4) = 20
(n + 4) – 5 = 20
5
The sum of triple a number and
6 is 9.
3n + 6 = 9
3•6 + n = 9
6
12 more than the difference of
half a number and 3 is 45.
n + 12 = 45
( n – 3) + 12 = 45
7
The product of 14 and a
number is 140.
14 • n = 140
14 + n = 140
8
15 less than the quotient of a
number and 6 is 30.
(n ÷ 6) – 15 = 30
(6 ÷ n) – 15 = 30
9
The sum of half a number and
3 is 21.
n + 3 = 21
n + 3 = 21
10
13 less than the product of a
number and 6 is 50.
13 - (n • 6) = 50
(n • 6) - 13 = 50
© Lindsay Perro
http://www.beyondtheworksheet.com
Week Two
Solving Equations
To get the most out of this lesson, use the resources in the order listed below.
All activities for this week are print & practice.
1. Solving Equations Notes & Practice
2. One Step Equations Practice
Solving Equations Notes & Practice
Before we learn how to solve equations, we need to go over inverse operations.
Inverse means opposite!
List the inverse of each operation:
Addition __________________ Subtraction _____________________
Multiplication ________________ Division_______________________
Ok, now let’s look at an example of a one step equation:
x ÷ 6 = 18
x ÷ 6 = 18
Step 1: Isolate the variable.
x6 x6
Step 2: Apply the inverse operation of ÷ 6 to both sides.
x = 108
Step 3: Solve.
Your turn! Be sure to show all of your steps.
1)
X – 9 = 12
2) 5 • X = 60
3) 13 + X = 62
4) X ÷ 11 = 132
Did you know you could check your answers? Let’s check the answer from the example above.
x ÷ 6 = 18
Our answer was x = 108
Substitute the answer you got into the
original equation.
108 ÷ 6 = 18
18 = 18
If you take the time to check your
answers, you can be guaranteed to have
all the correct answers!
How great is that!
Check the answers to the problems you did above.
1)
X – 9 = 12
© Lindsay Perro
2) 5 • X = 60
3) 13 + X = 62
4) X ÷ 11 = 132
http://www.beyondtheworksheet.com
Solving one step equations was easy, right? Let’s try two step!
Look at an example of a two step equation.
3x - 4 = 41 Step 1: Isolate the variable and its
coefficient.
+4 +4
Step 2: Perform the inverse operation of
3x = 45
– 4 to both sides.
÷ 3 ÷ 3 Step 1: Isolate the variable and its
coefficient.
3x = 45
x = 15
Step 3: Isolate the variable.
Step 4: Perform the inverse operation
of • 3 to both sides.
Step 5: Solve.
Your turn! Be sure to show all of your steps.
1) 2x – 10 = 18
x
2) 3 + 4 = 13
3) 10 + 7X = 45
4)
x
- 11 = 10
5
Let’s check the answer from the example above.
3x – 4 = 41
Our answer was x = 15
Substitute the answer you got into the
original equation.
3(15) - 4 = 41
45 – 4 = 41
41 = 41
If you take the time to check your
answers, you can be guaranteed to have
all the correct answers!
How great is that!
Check the answers to the problems you did above.
1) 2x – 10 = 18
© Lindsay Perro
x
2) 3 + 4 = 13
3) 10 + 7X = 45
x
4) 5 - 11 = 10
http://www.beyondtheworksheet.com
Solve.
1) 2 + 5x = 22
2) 5x + 9 = 29
3) x + 2 = 30
4) -2x + 1 = -13
Check your answers from above.
1) 2 + 5x = 22
2) 5x + 9 = 29
3) x + 2 = 30
4) -2x + 1 = -13
Solve.
1) x - 12 = -15
2) x = -8
3) 6 + x = -20
Check your answers from above.
x
x
1) 3 - 12 = -15
2) 5 = -8
3) 6 + 3 = -20
3
Solve AND check.
1) x + 12 = 15
4
© Lindsay Perro
5
2) -3x + 8 = 29
3
x
3) 4 + x = 4
2
4) 8 + x = 5
-10
x
4) 8 +-10 = 5
4) -2x - 10 = 12
http://www.beyondtheworksheet.com
One Step Equations Practice
6 + x = 12
x – 8 = 10
x
= 15
5
3x = 18
x + 4 = 20
x=____
x=____
x=____
x=____
x=____
x–8=3
x
2 =2
x=____
x=____
x=____
x + 5 = 18
x
=2
6
10 + x = 25
x
2= 10
5 + x = 21 x – 3 = 11
x=____
x=____
2x = 12
x
= 20
4
x=____
x=____
x=____
x=____
x=____
x+4=4
9x = 27
x
6 = 12
3+x=5
4x = 24
x=____
x=____
x=____
x=____
x=____
3x = 15
x – 10 = 1
x=____
x=____
x
2 = 16
x=____
©LindsayPerro
x – 9 = 31 x + 10 = 11
x=____
x=____
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Week Three
Solving Multi Step & Integer Equations
To get the most out of this lesson, use the resources in the order listed below.
All activities for this week are print & practice.
1. Solving Integer Equations Practice
2. Solving Multi Step Equations Practice
Solving Integer Equations
-2x + 4 = 2
5x + 7 = -18
X
-7 + 3 = 4
-8x + 2 = 18
- 6 + 4x = 2
8+
-8x + 24 = -16
© Lindsay Perro
X
= -2
-10
X
2 -3=9
6+
X
= -10
3
12x + 12 = -24
-9x - 4 = 14
X - 8 = -12
-4
X
- 6 = -30
4
15 – 3x = 30
-x + 8 = 3
-3x - 4 = 29
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Solving Multi-Step Equations
Use the distributive property and combining like terms to solve each equation
#
Answer 1
Answer 2
Answer 3
1
-16 = -4 - 6x
2
-10
-2
2
3(2x + 5) = 3
0
-2
3
3
½ ( x – 2) = 5
12
3.5
4.5
4
8x – 2 = -9 + 7x
15
-11
-7
5
2(x + 3) + 5 = 25
4
7
-4
6
3(x – 2) = 21
5
71
9
7
12 = -4(-6x – 3)
0
1
2
8
4x – 23 = 29
1.5
-13
13
9
x + 6 = 2x – 8
-2
14
1.5
10
7n – 4n – 6 = 12
6
2
7
© Lindsay Perro
http://www.beyondtheworksheet.com
Week Four
Equations in the Real World
To get the most out of this lesson, use the resources in the order listed below.
1. Writing & Solving Equations Practice
2. Solving Equations PowerPoint Review
Name _________________________________
Date _______________________
Writing & Solving Equations
Write and solve an equation for each situation.
1. You are buying bottles of glue for Mrs. Perry’s class. A bottle of glue is $0.74. Write an
equation relating the total cost (c) to the number of glue bottles (g) you purchase.
________________________
Write the equation: ________________________
Define your variable:
What is the total cost if you purchase 7 bottles of glue?
2. A data plan for your cell phone will cost you $29.99 per month. Write an equation
relating the total cost (c) to the number of months (m) you have the data plan.
________________________
Write the equation: ________________________
Define your variable:
What is the total cost of your cell phone plan for 12 months?
3. Some cell phone companies offer a cheaper data plan, but you have to pay a one time
sign up fee. The sign up fee is $375 and the cost is $25 per month. Write an equation
relating the total cost (c) to the number of months (m) you have this data plan.
________________________
Write the equation: ________________________
Define your variable:
What is the total cost of your cell phone plan for 12 months?
4. You can download songs online for $0.99 each. Write an equation relating the total
cost (c) to the number of songs (s) you download.
________________________
Write the equation: ________________________
Define your variable:
How much would 50 songs cost?
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http://www.beyondtheworksheet.com
5. Another website allows you to download songs for $.75 each, but you pay a sign up
fee of $15. Write an equation relating the total cost (c) to the number of songs (s) you
download.
________________________
Write the equation: ________________________
Define your variable:
How much would 50 songs cost on this website?
6. You and your friends go out to lunch. Each of you buys a soda for $2 and you buy a
plate of nachos for $7.50 that you all share. Write an equation relating the total cost of
lunch (c) to the number of people (p) that go.
________________________
Write the equation: ________________________
Define your variable:
How much would it cost for 5 people to go to lunch?
7. A rental car company charges a fee of $0.50 per mile and a flat fee of $250 for renting
a car. Write an equation relating the total cost (c) of the car rental to the number of
miles (m) driven.
________________________
Write the equation: ________________________
Define your variable:
How much will it cost to drive 850 miles?
8. Your parents are renting a moon bounce for your little sister’s birthday party. It costs
$175 to rent, plus $15 for each day you keep it. Write an equation relating the total
cost (c) of the moon bounce to the number of days (d) you keep it.
________________________
Write the equation: ________________________
Define your variable:
How much will it cost to keep the moon bounce for 5 days?
© Lindsay Perro
http://www.beyondtheworksheet.com