Name: Leslie Daughtry
Subject Area/Grade Level* of Lesson Plan: 7th grade math
Adding and Subtracting Fractions with a Twist
55 minutes
Lesson Rationale/Overview:
This lesson plan is designed to help students have a better understanding of fractions and how to add and
subtract them. The goal is for this knowledge to help benefit students who will have to be able to make these
calculations throughout their lives.
Objectives:
Students will be able to:
 Find the greatest common factors between two numbers.
 Find the multiples of numbers and be able to describe what a multiple is.
 Simplify fractions.
 Describe how to simplify fractions.
 Add and subtract various fractions.
 Determine between two fractions which is greater.
 Explain why you must find the common denominators of two fractions in order to add or subtract them.
 Explain why the numerator must change when the denominator is changed .
 Explain why multiplying or dividing the top and bottom of a fraction by the same number does not change
the overall amount the fraction represents.
TEKS:
§111.23. Mathematics, Grade 7.
(b) Knowledge and skills.
(1) Number, operation, and quantitative reasoning. The student represents and uses numbers in a variety of
equivalent forms. The student is expected to:
(A) compare and order integers and positive rational numbers;
(B) convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator
(2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve
problems and justify solutions. The student is expected to:
(A) represent multiplication and division situations involving fractions and decimals with models, including
concrete objects, pictures, words, and numbers;
(B) use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals;
(C) use models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide
integers and connect the actions to algorithms;
(D) use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes,
and student-teacher ratio;
(E) simplify numerical expressions involving order of operations and exponents;
Name: Leslie Daughtry
Subject Area/Grade Level* of Lesson Plan: 7th grade math
(F) select and use appropriate operations to solve problems and justify the selections; and
(G) determine the reasonableness of a solution to a problem.
Prior Knowledge:
Students will have used fractions before in previous classes.
Materials / resources / equipment needed:
Teacher:
 Either a chalk board with chalk or a dry erase board with markers depending on what the school
provides
 Access to a projector and paper for the projector
 Enough work sheets and handouts for each student and me along with an extra just incase
 30 pennies
 30 nickels
 30 dimes
 30 quarters
 4 plastic jars to hold the coins
 30 sheets of blank colorful paper
 Tape
 Bag full of fun prizes relating to math with enough of the same prize for each student
Student:
 Pens
 Pencils
 Paper
Daily Agenda:
(What I will write on the board so that the students’ know what is going to happen during this lesson plan).
1. Objective and standard met: The student is expected to use addition, subtraction, multiplication, and division to
solve problems involving fractions and decimals (taken directly from TEKS cited in lesson).
2. What they should be able to do to show their understanding by the end of the lesson: The student is expected to
use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals (taken
directly from TEKS cited in lesson).
3. Major activities for lesson: Use coins to help get an understanding of how to add and subtract fractions .
4. Homework: Generate a list of 10 problems subtracting and adding various fractions with one bonus question.
Name: Leslie Daughtry
Subject Area/Grade Level* of Lesson Plan: 7th grade math
Activities:
(Includes descriptions of warm-up/hook, details about what the teacher and student are doing, and a breakdown
of the estimated time interval for each activity).

Before students arrive to class, the teacher must set up the four jars of coins, separated by difference in
value, on her desk in order from pennies to quarters.
Introduction:
Part 1(6 minutes):
 Teacher will begin by saying, “How is everyone doing today? Is anything new going on in your lives.”
o Here the teacher should let the students have an opportunity to talk briefly about things going on
in their lives.
 Teacher: “Today we are going to learn how to add and subtract fractions with the help of these coins (the
teacher will point to the 4 jars of coins placed on her desk). Now I would pay attention closely if I were you
because there may be an opportunity to win a prize at the end of class if you have paid close enough
attention to the lesson.”
o Focus on learning and not the prize. The teacher should get the students full att ention.
 Teacher: “Can anyone tell me why I separated these coins into four separate jars?”
 The teacher will call on students who have their hand raised and encourage the students to answer. If no
one raises there hand the teacher will wait seven seconds and then give them a clue by asking how many
types of coins there are and what they are.
 After they successfully answer this question, the teacher will read out the list of objectives and state, “by
the end of the day, you will all be able to answer these seemingly tricky questions. Don’t worry, this
concept will be a lot easier to understand with the help of the coins we have.
 While the teacher proceeds to write the word “fractions” on the board, students will be asked what they
know about fractions and what some examples are.
 After the teacher calls on a student she will write down what they say on the board. Here the teacher will
state if the student is right or wrong explaining why either way.
o The teacher needs to ask the students what the top of a fraction is called (numerator) and what the
bottom part of a fraction is called (denominator). If the students are unable to answer these
questions, the teacher needs to write the answer on the board in the form of
numerator/denominator.
o If the students do not come up with the idea of part/whole (write this on the board). The teacher
must explain: the numerator represents the part of a whole, which is the denominator.
 After all of this, the teacher should ask the students what the worth of each of the four coins are and
proceed by writing the coins and their worth down on the board .
Part 2 (6 minutes):
 Teacher: “Before we learn how to add and subtract fractions, we need to learn how to find the least
common denominator of each fraction. Fractions such as 2/4 and 1/4 are easier to add because they
already have a common denominator. You simply add the two top numbers (numerator) together and keep
the bottom number (denominator) the same.”
o The teacher should demonstrate this addition on the board by usin g a circle cut into four pieces with
two pieces shaded in and then showing how to add 1/4 by shading anoth er piece of the circle, leaving
you left with 3/4.
 Teacher: “Fractions such as 1/3 and 1/2 are not as easy to add because their denominator is not the same.
Why could you not simply add the top numbers together like you did before? ”
o The teacher should listen to the student’s reasons, while encouraging people who have not yet spoke
up to answer.
 Teacher: “You cannot do the same process we did before because of the part to whol e ratio we discussed
before. The numerator represents the part of the whole, which is the denominator.”
o The teacher should proceed in showing what would happen if you tried to add 1/3 and 1/4 together
using the same method as before except using two separate circles; explain how the one piece shaded
in the circle divided into three parts was bigger than the one shaded in the other.
 Teacher: “Does this mean we should just give up? No, let’s think about it for a little bit. How could we get
1/3 and 1/4 to have the same denominators? Let’s just look at the numbers in these denominators right now
and figure out there multiples. You can think of multiples as being x times the number. X is a number
representing how many times you multiply that number. So basically if you can divide a number by three
and get an integer it is a multiple of three.”
Name: Leslie Daughtry
Subject Area/Grade Level* of Lesson Plan: 7th grade math
o
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The teacher should show all of this on the board and write down all of the multiples of three and four,
while explaining why they are the multiples . The teacher also should involve the student in this process
by asking them what X times a number is, such as what 3 times 3 is to give you one of the multiples of
three which is 9.
Teacher: “Well now that we know how to find the multiples of the denominators, the least common
denominator is going to be easier to find. All you have to do when finding the least common denominator is
find the least common multiple of the two numbers in the denominator.”
o Here the teacher should circle 12 and explain how this was the first multiple t hat these two numbers
have in common.
Teacher: “Great! Now we just have to multiply the denominator of each fraction by a number that will
make it equal to 12. The tricky part is we must NEVER forget to multiply the numerator and denominator
by the same number!”
o The teacher should show how to do this on the board and explain why you must multiply the top and
bottom by the same number. When you multiply the top and bottom by the same number they can
cancel out to get you your original fraction, which is why we are allowed to do this step.
Teacher: “Here comes the easy part. Just add the two numerators together and keep the denominator to
give you 7/12. Now that we have a common denominator, we can use the same technique we did before by
dividing the circle into equal pieces.”
o Here the teacher should end by shading in 7 pieces of the circle cut into 12 pieces explaining the
process as she goes.
Teacher: “Any questions, concerns, or comments with the lesson so far (wait and answer any questions)?
Do not worry. You will be able to understand this concept better with more practice. So if something is not
as clear now to you, with more practice it will all get cleared up.”
Transition (1 minute):
 The teacher should now begin to hand out the sheets of homework due tomorrow, the blank sheets of
colorful paper (one to each student and place the leftovers on the front of the teacher’s desk), and an even
amount of each different coin for each of the students.
 Teacher: “Put away your homework for now. We are going to start the first part of activity for today with
the use these two sheets of paper along with these different coins to help us figure out first how add
fractions. We will use what we learned about having a common denominator in this activity as well.”
Activity 1 (15 minutes):
 Teacher: “Let’s begin by turning our papers with the shorter side as our height and the longer side as our
length (demonstrate this). Next two vertical lines, like so. Now draw a long horizontal line through the
middle of the paper.”
o The teacher should demonstrate this to them with the projector.
 Teacher: “Let’s start off on the left hand side by placing a penny above the line and a nickel below the line.
Whatever is above the line is the numerator and whatever is below the line is the denominator, just like
regular fractions.”
o The teacher should proceed in doing the activity as well on the projector.
 Teacher: “Since a penny represents one cent write this somewhere on the top left box of your paper in
pencil. Since a nickel represents a five cents write this somewhere on the bottom left box of your paper in
pencil.”
o The teacher should now begin to pass around the tape and allow her students to tape down their
coins.
 Teacher: “Now for the upper and lower boxes in the middle put one penny on top and let’s make it a dime
on the bottom this time. Proceed in writing the amount each coin is just like you did last time. Then pass the
tape around and tape down your coins also like you did before. Feel free to help each other or ask me a
question if you are confused.”
o During this time the teacher should be walking around giving encouragement and help if needed.
o Once everyone is finished, the teacher should walk around again and make sure that they have all
done it correctly.
 Teacher: “What are the fractions that we made up using the values of the coins? Are they the same as the
number of coins in the numerator and denominator? ”
o The teacher should see what the students say and describe the importance of remembering that the
value of the coin and the quantity of coins are different, which is why the students were asked to write
the value of the coins in each the numerator and denominator to the side.
Name: Leslie Daughtry
Subject Area/Grade Level* of Lesson Plan: 7th grade math
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Teacher: “After what we learned about the importance of having a common denominator, how could you
make 1/5 and 1/10 have a common denominator? ”
o Now is when the teacher should have the students answer this question in a step by step process, giving
hints when needed.
o The teacher should also be recording the answers and processes on the board throughout this entire
activity.
Teacher: “So we figured out that the least common denominator is ten. This means we must make both
denominators equal ten, and since one of them is ten already this makes it easier. What do we have to do to
1/5?”
o The teacher should call on students randomly, trying to call on students who have n ot yet answered. If
the student does not know what to do the teacher should help by giving h ints and if this does not work
call on someone else. The students should be able to explain that you must multiply the numerator and
denominator of 1/5 by two to get 2/10 and why.
Teacher: “We know what we must multiply the numerator and denominator by 2 t o get 2/10. So to get a
visual of this, for the boxes that represent your 1/5 fraction with coins taped on it, add coins to it
accordingly to get 2/10. Do not tape these coins down.”
o Let the students complete this task.
Teacher: “Now I want you to take off the coins that are not taped down. This fraction is the same value as
it was with these extra coins. Just think about it for a while. What is 2/2 (let students answer)? What is one
times 1/5 (let students answer)? This is why we can multiply the top and bottom numbers by the same
number because when you simplify the number you will end up with the same starting value.”
o Let the students ask questions and demonstrate examples on the board as needed.
Teacher: “Now that we have found a common denominator, what is 2/10 plus 1/10?”
o A student should answer this question while also explaining the process they did to come up with the
answer of 3/10. The teacher should check the answer by using the circle technique.
Teacher: “Can anyone tell me what coins you can have in the numerator and what you could have in the
denominator that would give you 3/10?”
o There should be two different answers. Three pennies are always on top but there could be either a
dime or two nickels on the bottom.
o Have the students answer and make sure they say both of these different answers explained above.
Teacher: “Choose either of these coin combinations and tape the coins accordingly to get a fraction value
of 3/10 consuming the right upper and lower boxes on your sheet of paper. Write the values of these coins
in the boxes somewhere, just like before.”
Teacher: “Now I want you all to take out a sheet of paper and solve this problem. (write this on the board)
If we were to find to sum of these two fractions based off of the number of each coin in the numerator and
denominator what would these two fractions add up to be? Would the answer change if instead of using a
dime for the second fraction we used two nickels instead? ”
o The teacher should stress how important it is to read directions because if you do not pay close
attention you could wind up solving the wrong thing.
o The teacher should go around the room helping people when needed. When it looks like everyone has
attempted to answer the question, the teacher should ask a volunteer to come up and exp lain how
he/she got the answer and their thought process throughout solving it.
Transition (1 minute):
 Teacher: “Now that we have successfully found out how to add fractions using coins as a visual, our next
activity will involve the same steps except we will be subtracting these fractions instead.”
o The teacher should proceed to write on the board 3/4 minus 1/4.
 Teacher: “Can anyone make an educated guess as to how you solve this equation?”
o The teacher will proceed by calling on a student and explaining that you do the exact same steps as
how you add fractions except instead of adding the numerators together you will subtract them to get
2/4.
o The teacher will then explain how 2/4 simplifies to 1/2 when you divide the top and bottom by two.
o The teacher should stress that you can multiply or divide the numerator and denominator without
changing the value of the fraction as long as you multiply or divide by the same number to both.
 Teacher: “This being said let us learn how to subtract better with the same activity.”
Activity 2 (15 minutes):
 Teacher: “I want each of you to split up into groups of 3 or fewer and, based on how we solved adding
Name: Leslie Daughtry
Subject Area/Grade Level* of Lesson Plan: 7th grade math
fractions using the coins and sheets of paper, do the same process on the back side of these sheets of paper
except subtract these values. Make sure to choose fractions with different denominators. I want each of you
to do one example together as a team. Once you have successfully solved a problem grab another sheet of
paper from my desk and create a new equation using the same process. I will also be walking around
answering any questions that you might have.”
o The teacher should walk around at this point answering any questions. The teacher should also make a
note that students may want to think about multiples before attempting to subtract fractions such as
1/25 minus 1/10 that will have much larger least common multiple; however students are encouraged
to do these harder problems that will take more time once they understand the concept better.
o The teacher should go around and check each group’s examples one by one as they finish.
Transition (1 minute):
 Teacher: “You all showed great progress during these activities and encourage all of you to attempt the
bonus question on your homework only after you have attempted all the homework.”
o The teacher should answer any further questions.
Conclusion (10 minutes):
 Teacher: “For our final minutes of class I would like to give all of you an opportunity to win a prize like I
said at the beginning of class. I will be walking across the room and asking each one of you to briefly
either tell me a fact or something interesting you found out today relating to this lesson . Don’t be nervous.
This is not meant to be hard I just want to make sure that you each have paid attention and learned
something from today’s lesson. If you have any questions at this time you were too shy to ask before please
feel free to ask me. While I am talking to each person everyone else should start to look over their
homework and see if there are any questions or concerns you have about any of the problems. Also, do not
worry, there are plenty of the same prizes to choose from so the order I go in will not make a difference.”
o The teacher should proceed walking around the room letting each student pick a prize after they
have spoken about the lesson.
o The teacher should also answer any questions.
 Teacher: “Great job everyone! Hope you had fun in class today and learned a lot. Have a great day and
don’t forget to finish all your homework.”
Homework:
Homework will be handed out at the beginning of each class by the teacher.
Assessment (Be sure to make sure assessment reflects TEKS objectives cited above):
Formative:
During the activity, students will be asked:
 What are the fractions that we made up using the values of the coins? Are they the same as the number of
coins in the numerator and denominator?
 How do you make a number have a common denominator?
 Why do you have to have a common denominator when adding or subtracting fractions?
 Why do you have multiply or divide a numerator and denominator by the same thing?
 What is the top and bottom of a fraction called?
 Do you subtract or add fractions the same way you add regular integers? Why?
Name: Leslie Daughtry
Subject Area/Grade Level* of Lesson Plan: 7th grade math
Summative:
Students will be tested at the end of the chapter through a written, land mark test provided by the Math Department.