Simple fractions: Introduction

Objective:

  • To learn to read and write simple fractions.
  • To master the concept of simple fractions.

This virtual activity is designed for use in math lessons on the following topics:

  • Grade 5. “Simple Fractions. Reading and writing simple fractions”
  • Grade 5. “Proper and improper simple fractions”

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 in which the numerator is greater than or equal to the denominator.

Virtual experiment

Modeling the construction of a fraction allows students to predict and understand how changing the numerator of a fraction affects its value, and how changing the denominator of a fraction affects its value. The correspondence between numbers and pictures allows for flexible exploration of fractions.

The figure below shows the functions each button performs.

Progression:

Learning to build simple fractions

Step 1. Start the simulation: you will be offered 3 different modes: “Intro”, “Game” and “Lab”. Open the “Intro” section.

Step 2. In the working area you will be presented with:

  • Different types of fractions: circles, squares, cylinders, cakes and segments;
  • The empty frame of the fraction model;
  • The forms that make up fractions;
  • A button that increases the amount of the empty frame of the fraction model;
  • Buttons to change the numerator and denominator;
  • Reload button.

Step 3. On the empty frame of the fraction model, hover the mouse over the shape that makes up the fractions. You will have both the numerator and denominator equal to 1. That is, the fraction 1/1 – forms a complete shape.

Step 4. Increase the fraction section by 2. You have gotten ½ – a semicircle. Hence, it turns out that ½ represents half of the shape.

Step 5. Increase the fraction section by 3. You will get ⅓ – one third of the shape.

Step 6. Increase the numerator of the fraction by 2. You will get 2/3 – two-thirds of the shape.

Step 7. So you can see how the fraction looks on the shape by changing the numerator and denominator. Try to construct several types of fractions.

Step 8. Click the button that increases the number of empty skeletons of the fraction model and display 3-4 empty skeletons. Match the fraction with the number of empty skeletons.

Step 9. Fill the empty skeletons using different shapes of fractions.

Step 10. You can repeat these experiments with other shapes.

A game for learning fractions

Step 11. Select the “Game” section. Different levels will be available to you.

  • Some levels present pictures of figures with numbers, by which you will collect fractions from the figures.
  • Other levels present fractions in the form of shapes by which you have to write the fractions.

Choose one level to your liking.

Step 12. 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 are the items from which you need to collect the fractions.

Step 13. Collect the first fraction.

Step 14. To check for correctness, move the cursor over an empty space next to the given fraction, left-click and drag the fraction into it. If the fraction is assembled correctly, it will occupy the space. If you made a mistake, the fraction will return to the place where it was assembled.

Step 15. Assemble the other types of fractions as well.

Step 16. Once you have correctly assembled all the fractions, you can move on to the next level and complete other tasks.

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 an empty space to write the fraction and an empty frame. Underneath the pattern are the numbers to use for the numerator and denominator of the fraction.

Step 18. Form the fraction using the numbers.

Step 19. Place the shapes on the empty frame, following the given fraction.

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 mouse over 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 next fraction from the numbers and form the corresponding shape.

Step 23. Try building a few more fractions. In this lab section, you can improve your fraction skills by creating different fractions.

Conclusion

By creating this virtual activity, students will reinforce their knowledge by experimenting with the topic of simple fractions that they have been studying in math.The simulation demonstrates how fractions relate to shapes, which promotes a deeper understanding of the concept of fractions.