Writing Equations from Real-World Problem Situations
Engage
Students work on their own to write an equation to represent the Wonka Bar problem. After 2 minutes of
work time, come back together as a class and go through the following question sequence:
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What do we know in this problem?
Do you know how many candy bars you can buy? So what do we call the part of an equation that is
unknown?
What should we use for the variable? Let's be sure to define the variable with our work.
Why can you represent this situation with an equation?
How can you represent this situation an equation?
Frame the Lesson: In the last lesson, we were discussing how to represent verbal expressions with
algebraic equations. Today we are going to continue this work but with real-world scenarios. We will
translate them using equations so that we can make meaning of them, and eventually solve the
equations. We will use everything we learned yesterday.
Explore/Explain
Students have experience translating expressions and simple equations. Today's lesson gives students
practice with translating from real-world connections. We walk through the problems in this section
together.
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For the first example, Eleni is x years old. In thirteen years she will be twenty-four years old, first read
and annotate the equation.
What does the x represent?
What does the 24 represent?
What variables/numbers/operations do we have?
What does this equation represent?
What are we starting with?
What amount are you ending with?
Are there any terms or operations that are grouped?
Is there any division or multiplication performed on the starting amount?
Is there any addition or subtraction performed on the starting amount?
What do we need to include for this to be an equation?
So what is this equation?
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Check for reasonableness: Now that we have our equation, let’s make sure we know that the equation
is correct. To do this, we will use substitution. Let’s look at the verbal expression. What would make the
equation true?
Great. Now, we have the equation x + 13 = 24. If we plug substitute 11 for x, does it make the equation
true?
In groups, have students work through the next three problems, in the same way. In problem number 2
it's important to make sure kids use .25, rather than 25. It's a great place to ask kids why that's important
After the 4th example, students help me to fill in the words in our notes.
Students work in pairs on the Partner Practice problems.
As they are working, circulate and look for:
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Are students selecting the correct operation?
Are students ordering the terms correctly in the equation?
Are students able to justify their equation using substitution of a value in the problem and their
equation?
Ask groups:
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How do you know this is the correct equation to represent the problem?
Why did you select that variable?
How can you justify that your equation correctly represents the context?
Elaborate
For the class discussion in this lesson, allow students to decide which problems we talk about. Pick one
person who decides which problem from the Partner Practice to look at first. The partner of that person
talks through how the pair came up with their equation. Pick a second pair to go through the same
process for a second problem.
Problem 4 is a good problem for conversation. There may be more than one equation that students have
written to represent the scenario. Talk about all of them, so that students have the chance to see multiple
representations of the information.
Students can be given time to use reasoning to solve for the variables in some of the problems from
partner practice. Ask for the solution to Problem 9, because it gives students the chance to practice with
multiplication of decimal numbers. It also allows you to talk about being quick and fluent with mental
math.
Before moving on to the independent practice, students complete the final check for understanding
(found here, at the start of the Independent Practice problems).
Students work on the Independent Practice problems.
As they are working, look for and ask the same questions used during the Partner Practice:
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Are students selecting the correct operation?
Are students ordering the terms correctly in the equation?
Are students able to justify their equation using substitution of a value in the problem and their
equation?
Ask:
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How do you know this is the correct equation to represent the problem?
Why did you select that variable?
How can you justify that your equation correctly represents the context?
Problem 3 is one to watch out for. Students may try to express the relationship as 58 divided by onethird, rather than 58 divided by 3 (or some other form of this).
Evaluate
Before students begin work on their Exit Ticket, discuss two problems from the independent work
problem set.
For Problem 6, have students 'clap out' their answers - say a, b, c, d and students clap when you get to the
letter of the answer choice they've picked. This allows me to hear where students are with mastery of a
relatively simple problem.
We also discuss problem 10. Pull a Popsicle stick and have a student put his/her work up on the
document camera. The student explains how (s)he worked through the problem. Then open it up for
feedback from the class. Students complete their exit tickets to end class.
Name: ______________________
Date: ______________________________
Writing One-Step Equations
Think About it!
Wonka Candy bars cost $1.50 each.
You have a total of $18 to spend on Wonka bars!
Write an algebraic equation to represent this problem.
________________________________________
Writing Algebraic Equations:
Verbal Description
Eleni is x years old. In thirteen
years she will be twenty-four
years old.
Each piece of candy costs 25
cents.
The price of h pieces of
candy is $2.00.
Suzanne made a withdrawal
of d dollars from her savings
account.
Her old balance was $350,
and her new balance is $280.
A large pizza pie with 15 slices
is shared among p students
so that each student's share is
3 slices.
Algebraic Equations
Steps for Writing Equations
1) Read and _______________________.
2) Define the variable to represent _________________ and
digits/operations for different values.
3) Define the __________________- what does it tell you?
4) Identify what amount you are ________________with and
the amount you are ________________ with.
5) Identify the ____________________:
6) Include an ___________________ between the
start/change and the end.
7) Check by restating and comparing to the written
expressions.
Steps for Writing Equations
1) Read and annotate.
2) Define the variable to represent the unknowns
and digits/operations for different values.
3) Define the equation- what does it tell you?
4) Identify what amount you are starting _with and
the amount you are ending with.
5) Identify the operations:
6) Include an equal sign between the start/change
and the end.
7) Check by restating and comparing to the written
expressions.
Teamwork!
Complete the board below with your shoulder partner. Write an algebraic equation for each
word problem in the space on the next page.
1. Carly is 15, which is four
years younger than
Samantha’s age. Write an
equation to represent
Samantha’s age.
4. A supply closet has 1,821
pencils. The principal orders
more pencils so that there
are a total of 2,500 pencils.
Write an equation to
represent the number of
pencils the principal orders.
7. A beaver is floating on a
log that is 4 5foot long. It
crashes into a rock and is
now only foot long. Write
an equation to represent the
change in the length of the
log after crashing into the
rock.
10. Molly reads x words a
minute. Lauren reads 82
words a minute, which is
twice as fast a Molly reads.
Write an equation to
represent the pace that
Molly reads.
2. Gary used 32 pieces of
paper and Randy used m
pieces of paper. Together,
they used 94 pieces of
paper. Write an equation to
represent the amount of
paper Randy used.
5. Andy lifts weight every
day to build muscle strength.
Today, he decides to
increase the amount of
weight he lifts by 8 pounds to
lift 92 pounds. Write an
algebraic equation to
represent the original
amount of weight Andy lifts.
3. Kayla has four candy bars.
She will give ¼ of a bar to
each of her friends. Write an
equation to represent the
number of friends Kayla can
give ¼ of a candy bar to.
6. Diamond used four times
as many paperclips as Jade,
who used 25 paperclips.
Write an equation to
represent the number of
paperclips Diamond used.
8. Cinthia spends 13 minutes
on each phone call she
makes. If she makes 9 phone
calls, write an equation to
represent the total amount
of time Cinthia spent on the
phone.
9. Tanya spends $0.25 on
each pack of gum she buys.
If she bought a total of 8
packs of gum, write an
equation to represent the
total amount of money
Tanya spent.
11. Frances spent $42.50 on
a pair of shoes. This was half
of the original price. Write an
equation to represent the
original price of the shoes
12. Fatimah has 46 quarts of
ice cream to distribute
amongst the four grades at
her school. Write an
equation to represent the
number of quarts each
grade will receive.
Work Space:
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Equation
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Equation
Final CFU:
Eric had $197 in his savings account before he was paid his weekly salary. He saved money
for one week and his current savings is $429. Which equation represents how much money
Eric earns each week?
a.
b.
c.
d.
197 + 429 = n
197 + n = 429
197n = 429
429/n = 197
Explain how you determined the correct equation.
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Independent Practice
1. A teacher started her day with 64 pieces of chocolate candy. By the end of the day,
she had 12 remaining. Write an algebraic equation to represent this scenario.
_____________________________________
2. Stephanie’s water bottle had 6 ounces of water in it. She took her bottle to the
fountain and filled it until it had 32 ounces of water. Write an algebraic equation to
represent this scenario. Explain your reasoning.
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3. A computer program used one-third of the computers total memory. The computer
had a memory of 58 gigabytes. Write an algebraic equation to represent this scenario.
____________________________________
4. A baker sells a dozen cupcakes for $12.50. A customer buys d dozen cupcakes for a
total of $50. Write an algebraic equation to represent this scenario. Explain your
thinking.
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5. For Christmas, Karl’s grandparents decide to split up $500 amongst their six
grandchildren. Write an algebraic equation to represent the amount of money each
grandchild receives.
_______________________________________
6. Frederick bought 6 books that cost d dollars each. He spent a total of $48. Which
equation below represents the scenario?
a.
= 48
b. 6 + = 48
c. 6d = 48
d. 6 – d = 48
7. The $48 that Frederick spent on books is equal to the amount that he spent on books
last week. Write an equation to figure out how much he spent on books last week.
_______________________________________
8. The rectangle below has a total area of 40 square feet. Write an equation that can
be used to determine the width of the rectangle.
10ft
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9. There are m months in a year, and on average, 30 days in a month. A certain number
of months have a total of 210 days. Which equation below represents this scenario?
a. 210 = 30 + m
b. = 210
c. 210 − = 30
d. 30m = 210
10. Ten years ago, Ms. LePage was 13 years old. Write an equation that represents
Ms. LePage’s current age.
____________________________________________
11. Kwame goes to a store that sells rose bushes and maple trees. Each rose bush costs
$15 and maple trees cost $45. Kwame spent a total of $90 on only rose bushes. Let (t)
Which equation is one way to represent this situation?
a.
b.
c.
d.
45r = 90
15t = 90
45 + t = 90
15 + t = 90
12. The perimeter of the square below is 18 feet. Write an equation that can be used to
find the length of each side.
x
13. Challenge! On an algebra test, the highest grade was 42 points higher than the
lowest grade. The sum of the two grades was 138. Find the lowest grade. After, check
to see if your answer makes sense.
_______________________________
For each expression or equations, write a verbal statement that could have been translated
into the expression. BE CREATIVE!
Example: n + 5 = 8
Five dollars more than my allowance is 8 dollars.
1. t + 9 = 11 _________________________________________________________________
2. p – 25 = 10 _________________________________________________________________
3. 7r = 49 _________________________________________________________________
4. 12 = t – 8 ______________________________________________________________
5.
22 = t ÷ 3 ______________________________________________________________
6. n ÷ 16 = 160_________________________________________________________________
7. 5k = 15 _______________________________________________________________
Name: ______________________________
Date: ________________________
Exit Ticket: Simple One-Step Equations
1. Julia spent $10 on school supplies. This was of the total amount of money she earned
for the week. Write an algebraic equation to represent the total amount of money
Julia earns in a week.
How did you know to choose the operation you chose?
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2. Carly jumped 45 times in double-dutch during recess. This was 12 more than she
completed last week. Choose the algebraic equation that represents the amount of
jumps Carly did at recess last week.
a.
b.
c.
d.
45 = j + 12
45 = j – 12
45 = 12j
12 = 45 + j
How did you determine which equation to choose above?
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3. Write an equation that can be used to find the length of a square with a perimeter of
40.
x