Adding Fractions Using a Cardboard Circle

By Tara Mason on Apr 24, 2017

Students will learn how to add and subract fractions using a cardboard circle. 


2 Carboard circles cut into four parts. 


This lesson will use tactile materials to help reinforce the concepts of adding and subtracting fractions. Students need to have a solid foundation in how to add and subtract fractions and the use of manipulatives will help promote understanding. These materials can be built upon as information and problems become more complex. If students need to work on circles divided into more segments, teachers can modify this lesson to include circles in 6,8, or 10+ parts. 


  1. Teachers can go over a problem verbally explaining the parts of the fraction and how we add/subtract fractions by finding a common denominator. Suggest that you use a circle with four segments to practice adding and subtracting fractions. 
  2. With your student, add 3/4 and 1/2, with the 2 cardboard circles cut into 4 segments. Three pieces from one circle represent the 3/4 and the two pieces from the other circle represent 1/2. Bring the three pieces with the two pieces with results in a total of five pieces, 5/4. Have the student reassemble the pieces to create one circle with one additional piece remaining. The answer to the problem is "1 circle (whole) and 1/4" 
  3. Practice this two more times. Ask your student to add 1/4 and 2/4. What does that equal? Next, ask your student to add 3/4 and 3/4, what does that equal? 
  4. Once your student reports feeling confident about addition, use the same circles to go over subtraction. Ask your student to subtract 1/2 from 3/4. He/she will remove two of the three pieces being displayed. How many pieces are left? (1/4). Practice this one more time, asking your student to subtract 1/4 from 3/4 (= 1/2). 
  5. To reinforce what you have gone over with the manipulatives, ask your student to complete a series of word problems jotting his/her answers down on their media of choice. He/she can use the circles to help go through problems with concrete objects. 

Word Problems: 

  • If I am trainng for a race and I run 1/2 a mile today and 1 and 1/2 miles tomorrow, how far will I have run in two days? 
  • I would like to double a recipe I am using for cookies. The recipe calls for 1/2 cup of flour, how much would I need if I want to double the recipe? 
  • I am on the food committee for the end of the year party. We have ten students who want pizza. Each student can eat 1/4 of a small pizza which has eight slices. How many slices total do I need to feed 10 students? How many pizzas do I need to feed everyone? 


Lesson steps adapted from Koenig and Holbrook, Foundations of Education (2000)


circles collage


Read more about: Math, STEM