Constructing fractions

Objective:

  • To learn to read and write simple fractions.
  • Distinguish between proper and improper fractions.
  • Know the definition of a mixed number.

This virtual activity is designed to be used in math lessons on the following topics:

  • Grade 5. “Simple Fractions. Reading and writing common fractions”
  • Grade 5. “Proper and improper fractions”.
  • Grade 5. “Mixed numbers”

Theoretical part

Fractions are numbers represented as fractions where the numerator and denominator are integers and the denominator is not equal to zero. In mathematics, ordinary fractions play an important role, used to describe fractions, parts of a whole, and to perform various arithmetic operations.

Writing a fraction:

  • A fraction is written as two numbers separated by a line.
  • The number above the line is called the numerator.
  • The number below the line is called the denominator.

Example:

  • 1/2 is an ordinary fraction.
  • 1 is the numerator.
  • 2 is the denominator.

Meaning of the fraction:

  • The denominator shows how many parts the whole has been divided into.
  • The numerator shows how many such parts have been taken.

Example:

  • A pizza is divided into 8 equal parts.
  • We took 3 parts.
  • 3/8 is a fraction that represents 3 parts out of 8.

Reading fractions:

  • 1/2 is one second.
  • 3/4 – three fourths.
  • 5/8 – five eighths.

Types of fractions:

  • A proper fraction is a fraction that has a numerator less than the denominator.
  • An improper fraction is a fraction that has a numerator greater than or equal to the denominator.

A mixed number is a number that consists of a whole part and a fractional part.

Example:

  • 1 1/2 is a mixed number.
  • 1 is the whole part.
  • 1/2 is the fractional part.

Constructing fractions:

An integer must be divided into equal parts. For example, divide a circle into 4 equal parts. If we color 2 parts of the 4, we get 2/4.

Virtual experiment

The Build a Fraction virtual activity allows students to create fractions from differently shaped parts by playing games and conducting lab experiments. Modeling the construction of a fraction allows them to predict and understand how changing the numerator of a fraction will affect its value, and how changing the denominator of a fraction will affect its value.

The figure below shows the functions each button performs.

Progression:

Part 1. Learning how to construct proper fractions

Step 1. Start the simulation: you will be given 3 different modes: “Build a fraction”, “Mixed numbers”, “Lab”. Select the “Build a fraction” section.

Step 2. You will be given different levels. Drawing figures on the levels given fractions are presented as numbers, by which you will construct fractions from the figures. And on levels given by numbers, fractions are represented as shapes by which you will write fractions with numbers. Select level 1, represented by a picture of shapes.

Step 3. On the right side of the screen, you will find a list of fractions that you need to collect. You can collect these fractions in the center area. At the bottom of the screen, you will find the elements from which you need to collect the fractions. On the left side are the back and restart buttons.

Step 4. Collect the first fraction.

Step 5. To check if it is correct, hover over the empty space next to the given fraction, left click and drag the fraction into it. If the fraction is correct, it will occupy the space. If you made a mistake, however, the fraction will return to the assembly space.

Step 6. Assemble the other types of fractions as well.

Step 7. Once you have correctly assembled all the fractions, you can move on to the next level and complete the other tasks.

Step 8. Go back to the levels section by clicking the back button at the top left.

Step 9. Choose the first of the levels given by the numbers and complete the tasks.

Part 2. Learning to build mixed fractions

Step 10. Select the “Mixed numbers” section.

Step 11. You will be given different levels as in the “Build a fraction” section. Select level 1, represented by a picture of shapes.

Step 12. Build the first type of fraction. Because of the mixed number, the shapes do not correspond to a single empty skeleton. Therefore, click the “Add” button next to the empty skeleton to display the number of skeletons you will need.

Step 13. Collect the fraction and place it by dragging it to the empty space next to the given fraction. In case of an error, the fraction will be returned to the place where it was assembled.

Step 14. Assemble the other types of fractions as well.

Step 15. Once you have done everything correctly, you can move on to the next level and complete the other tasks.

Step 16. You can also complete the levels given by the numbers if you want. To do this, go back to the levels section by clicking the back button at the top left. Select the first of the levels given by numbers and complete the tasks.

Part 3. Laboratory part

Step 17. Select the “Lab” section. You are given shapes to create fractions. You can choose a shape: round or rectangular. Here you see a blank space to write the fraction and an empty frame. Underneath the template are the numbers to use for the numerator and denominator of the fraction.

Step 18. Construct a mixed type of number from the numbers.

Step 19. Place the shapes on the empty frame following the given fraction. You can add more empty skeletons as needed using the “Add” button.

Step 20. Move the fraction and shape to the left side of the screen by holding down the left mouse button.

Step 21. Pull a copy into the workspace by dragging the empty space next to the numbers. And in the same way, move the empty wireframe next to the shapes to the same workspace.

Step 22. Build the correct type of fractions from the numbers and form the corresponding shape.

Step 23. Try to build some more mixed and proper fractions.

Conclusion

Using a virtual experiment is an effective and interactive way to learn how to create different types of fractions. This tool allows students not only to visualize the process of building fractions from different shapes, but also to conduct laboratory experiments to better understand their properties. With the ability to check the correctness of assignments in real time and instant feedback, students can effectively progress in mastering this math topic.