Writing Equations with One Variable Part 2
Michigan Department of Education Standards for High School:
Standard 1: Write equations and inequalities with one or two variables to represent mathematical or
applied situations, and solve.
Set:
As the students are entering the classroom, have them pick up a bell work sheet. The bell work sheet
will have a variety of problems like how to solve single variable equations. It will also have a couple brain
teaser questions that will be about today’s lesson. The students will have five minutes of class time to
finish the bell work, and I will randomly pick students to come up to the board and write their work
along with the answer to the problems. If the student’s answer is correct, I ask if anyone has questions
and then move on to the next problem. If not correct we go over the problem and find out what went
wrong. (We will not review the brain teaser questions, since they will be used to help associate the
equations with story problems in information and modeling #2.)
(Note: make sure you tell students that they may be able to do none, one, or all of the brain teaser
questions and whatever they can do is ok. The brain teaser questions are ones that will be taught in that
days lesson. )
The bell work sheet will look like:
Name: _____________________________
Solve:
1) 3x=12
2) 4x +2 = 14
3) 3 (x-1) = 15
Brain Teasers:
4) I went to Kroger with $12 and bought three notebooks, how much were each notebook?
5) The next weekend I went to Target with $14 and bought 4 notebooks, but this time there was a
2 dollars stocking fee (for all notebooks purchased). How much did I end up paying for each
notebook?
6) I left Target and went to Wal-Mart, and they had notebooks a dollar off the original price. I had
$15 and bought 3 notebooks of each notebook. What is the original price of 1 notebook?
7) If all the prices are still the same as when I bought the notebooks, where should I have bought
all 10 notebooks for the cheapest price?
The solutions to the bell work are:
1) 3x=12
a. X = 12 / 3
b. X = 4
2) 4x +2 = 14
a. 4x = 14 – 2
b. 4x = 12
c. X = 12 / 4
d. X = 3
3) 3 (x-1) = 15
a. (x-1) = 15/3
b. X-1 = 5
c. X = 5+1
d. X = 6
Objectives:
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Students will be able to write a correct single variable equation after reading a story problem.
Students will be able to solve the single variable equation appropriately (defined by the story
problem)
Information and Modeling #1 (only complete if the student had problems with the Pre- Assessment):
1) Problems with Pre-Assessment part 4
a. White Board Review
i. Give each student a personal white board, marker, and cloth (to erase answers).
ii. Remind them that if they are doing anything other than working on the problem
on the board, then we will put the boards away and they will complete the
problems individually.
iii. Using Pre- Assessment worksheet #1, write the problems on the board, have the
students solve the problem, and then hold up their board (facing the front of
the room).
Check for understanding #1:
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If the students got too rowdy or didn’t do what they were supposed to then give them the PreAssessment worksheet #1 for homework. This will show their ability to solve single variable
equations, which they need to know how to do in order to solve single variable story problems.
If the students did not get rowdy, then their ability to solve the problems in the game is the
understanding that they know how to complete the problem.
Information and Modeling #2:
1) Now let’s go over the brain teaser problems:
a. Use the “common knowledge” to solve them.
i. I went to Kroger with $12 and bought three notebooks, how much were each
notebook?
1. Since you have $12 and you want to buy 3 then you take 12 / 3 and your
answer is 4. Therefore each book was four dollars
ii. The next weekend I went to Target with $14 and bought 4 notebooks, but this
time there is a 2 dollars stocking fee (for all notebooks purchased). How much
did I end up paying for each notebook?
1. Since there was a 2 dollar fee you can subtract 14 – 2 = 12, so now you
only have $12 to buy notebooks.
2. Then just like the example above you again have $12 but now I bought 4
notebooks so you take 12/ 4 and get 3. Therefore each book was three
dollars.
iii. I left Target and went to Wal-Mart, and they had notebooks a dollar off the
original price. I had $15 and bought 3 notebooks. What is the original price of 1
notebook?
1. This is just like the first one, we have $15 and 3 notebooks so we take
15/3 = 5.
2. Then we had a $1 off each notebook, so to get the original price we
have to add 1 to the sale price = 5+1=6. Therefore each notebook was
six dollars.
iv. If all the prices were the same as when I bought the notebooks, where should I
have bought all 10 notebooks for the cheapest price?
1. We know that Kroger had notebooks for $4, Target had notebooks for
$3, and Wal-Mart had notebooks for $6. Target would have the best
price for all 10 notebooks.
b. Make the connection.
i. Now if you were to look at the problems from your bell work, question 1 is the
equation from number 4, question 2 is the equation from number 5, and
question 3 is the equation for number 6.
c. Writing equations.
i. I went to Kroger with $12 and bought three notebooks, how much was each
notebook?
1. They give you how many dollars spend and how many notebooks you
have. Since we don’t know the price of 1 notebook, label that x.
2. Let’s say we don’t know how much money we have but want to know
how much we need. Then we take the price of books (x) times the
number of notebooks (3), which would give you the total amount of
money needed to buy 3 notebooks at x dollars.
3. But they told us that we have 12 dollars. So the equations looks like 3x
= 12
ii. The next weekend I went to Target with $14 and bought 4 notebooks, but this
time there is a 2 dollars stocking fee (for all notebooks purchased). How much
did I end up paying for each notebook?
1. Same thing have x be the price of one notebook. Then to get the total
amount of money needed = we take x (price of one book) times 4
(number of notebooks) but we have to add the fee which is 2 dollars :
4x +2
2. And once again we know how much money we have 14 so : 4x +2 = 14
iii. I left Target and went to Wal-Mart, and they had notebooks a dollar off the
original price. I had $15 and bought 3 notebooks. What is the original price of 1
notebook?
1. We don’t know how much each notebook is, so label that x.
2. Say we don’t know how much money we need/have:
a. To get the total amount of money we need to buy 3 notebooks
= 3 times the price x. 3x= total money needed
b. But the price for each notebook was $1 off the original price so
we have to subtract 1 from the price of one notebook: x-1.
Therefore we have 3(x-1) = total money needed.
3. Now we have $ 15 total to spend, therefore: 15 = 3(x-1).
2) More Examples (Came from: (Z a c c a r o 2 5 - 3 4 ) :
a. “Larry weighs 50 pounds more than Steve. Together they weigh 130 pounds. What does
Steve weigh?” (, p27-28).
i. Larry weighs= 50 +Steve
ii. Steve +Larry = 130
iii. Steve = x
iv. Equation: x+ (x+50)= 130
v. Answer: 40 pounds
b. “The sum of three consecutive numbers is 264. What is the smallest number?” (p29).
i. Let say the number we start with is x, so the first number is x, second is x+1, and
third is x+2.
ii. Equation: x+ (x+1)+ (x+2) = 264
iii. Answer : 87
c. A horse is 45 pounds more than 6 times its rider’s weight. If both weigh a total of 710
pounds, how much does the horse weigh?” (p29).
i. Horse weight = 45 + 6 (rider’s weight)
ii. Riders weight = x
iii. Equation: x + (45+6x) = 710
iv. X = 95 pounds
v. Horse weight = 45 +6(95)
vi. Answer: horse weights 615 pounds
Check for understanding 2:
Problems from: (Z a c c a r o 2 5 - 3 4 )
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Read the students a story problem and have them tell you what steps to take to solve the
problem.
Problem 1:
o “A truck, its driver and its load weight 43,320 pounds. The truck weights 230 times the
weight of the diver and the load is 30 pounds more than three times the driver’s weight.
What is the weight of the load?” (p29).
 Equation: x + (230x) +(30+3x) = 43,320
 The driver weights 185
 Answer: The load is 585 pounds
Problem 2:
o “Dan had twice as much money as Scott. Steve had $8 more than Dan. If their money
added up to $108, how much money did Scott have?” (, p27 -28).
 Equation: n +(2n)+ (2n+8) = 108
 Answer: 20
Problem 3:
o “A class of 34 students has two more girls than triple the number of boys. How many
girls are there in the class?
 Equation: (2+3x) +x = 34
 X=8
 Answer: 8 boys and 26 girls
Problem 4:
o “Because the moon’s gravity is much less than the earths, an individual standing on the
earth would weigh 6 times what she would weigh on the moon. Kate weights twice as
much as Stephanie when they stand on the moon. If the total of their weights on the
moon is 36 pounds, what does Stephanie weigh on the earth?” (p29).
 Equation: 3x = 36
 Answer: 72 pounds on earth
Guided Practice:
1) Group time
a. Place the students into groups based on their abilities in the cookie worksheet.
b. Give the ability group the work sheet that corresponds to their ability.
c. There are two sets of worksheets to choose from (depending on the level of the
students).
i. Worksheets:
1. Descriptions:
a. Worksheet A has: all single step word problems
i. Came from: ( " F r e e - P r e A l g e b r a W o r k s h e e t s " )
b. Worksheet B has: 2 single step and 8 two step word problem
i. Came from: ( " F r e e - P r e A l g e b r a W o r k s h e e t s " )
c. Worksheet D: Level 1
i. Came from: Problems from: (Z a c c a r o 3 1 )
d. Worksheet E: Level 2
i. Came from: Problems from: (Z a c c a r o 3 2 )
e. Worksheet F: Einstein Level
i. Came from: Problems from: (Z a c c a r o 3 3 - 3 4 )
(Note: depending on the abilities of the class you may have to make more worksheets for the higher or
lower level students).
d. While the students are working on their worksheet in groups, help the lowest group first
with their questions and work your way up to the higher level groups (start with the
lower groups because they will probably need more help than the higher level groups)
Formative Assessment:
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The students will turn in the worksheet they were completing in groups. This worksheet again
will be taken for a completion/effort grade and if necessary show what they did wrong and how
they can fix it.
Although they completed this in groups, it will still show how well each student understands the
material by what the group needs help on. It will also show how well each student completes
the worksheet and if the group/student finished each problem.