Students practice the addition and subtraction of fractions by making fraction squares out of a folded piece of paper.

Students will learn to add and subtract fractions with the aid of a fraction square.

 

• The students will create a fraction square.

• The students will use the fraction square to demonstrate addition of fractions.

• The students will use the fraction square to demonstrate subtraction of fractions.

Mathematics
Number, Number Sense and Operations

Benchmark D:
Use models and pictures to relate concepts of ratio, proportion and percent.

Benchmark I:
Using a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.

Indicators
Grade 5
Number and Number Systems
1. Use models and visual representations to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.

2. Use various forms of the number 1 to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6.

Grade 6
Number and Number Systems
5. Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than one and greater than 100.

• Construction paper or tag board cut into 8-inch-by-8-inch squares (or use the Fraction Tool template)

Steps for making a fraction tool

1. Start with a piece of paper, thin cardboard or tag board. Cut it into 8 inches square.

2. Fold all four corners into the center so that you have four triangles with the apexes pointing into the center.

3. Mark two of the folded triangles as 1/4.

4. On the third folded triangle make a perpendicular cut from the apex of the triangle to the fold.

5. Mark the two subsections of this triangle three as 1/8.

6. On the fourth triangle make a perpendicular cut from the apex of the triangle to the fold. Next, divide each of the two sections with another partial cut (if you cut too far, you will cut the sections off). You should now have four sections in the fourth triangle.

7. Mark the four subsections of this triangle as 1/16.

Day 1

1. Using the fraction tool, begin with simple computations:

   a. 1/4 + 1/4 = ? Have the students lay down the identified flaps to determine the answer. Answer: 2/4 = 1/2.
   
   b. 1/4 + 1/8 = ? How can that be expressed so that denominators are the same? Answer: Another way of saying 1/4 is 2/8, so 2/8 + 1/8 = 3/8.

2. Offer progressively more difficult problems, ultimately leading to students creating equations for the class to solve.

3. Based upon students’ progress and understanding, write 10 addition problems on the board for students to copy and solve using their fraction square. You may also use the included addition student worksheet.

Day 2

1. Follow the same procedures as above, but subtract fractions with like denominators.

2. Move onto a higher level by having the students subtract fractions with unlike denominators (example: 1/4 – 1/8 = ?, 2/4 – 4/16 = ?).

3. Based upon students’ progress and understanding, write 10 subtraction problems on the board for them to copy and solve using their fraction square. You may also use the included student worksheet.

4. Have the students use the tool to solve the equations on the subtraction student worksheet.

Use the number of correct problems divided by 10. Introduce the students to percentage, e.g., 8/10 = 80 percent.