Fractions: Mixed Numbers

Objective:

  • To know the definition of a mixed number.
  • Displaying ordinary fractions, mixed numbers in a coordinate ray.
  • Comparison of ordinary fractions, mixed numbers.

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

  • Grade 5. “Mixed numbers”
  • Grade 5. “Display of ordinary numbers and mixed numbers on the coordinate ray”
  • Grade 5. “Comparison of ordinary fractions and mixed numbers”.

Theoretical part

Ordinary fractions are numbers represented as fractions where the numerator and denominator are integers and the denominator is not zero.

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.

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 of a mixed number:

  • 1 ½ is a mixed number.
  • 1 is the whole part.
  • 1/2 is the fractional part.

Writing a mixed number:

  • A mixed number is written as two numbers separated by a space.
  • The first number is the whole number.
  • The second number is the fractional part.

Converting fractions to mixed numbers:

  • Divide the numerator by the denominator. Example: 7 / 3 = 2 (remainder 1).
  • Write down the mixed number. Example: 7/3 = 2 ⅓

Virtual experiment

The “Fraction: modeling mixed numbers” simulation allows students to become familiar with and compare several representations of fractions, including mixed numbers. The correspondence between numbers and representations allows for flexible exploration of fractions.

The figure below shows the functions each button performs.

Progress:

Part 1. 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;
  • An empty frame of the fraction model;
  • The shapes that make up the fractions;
  • Button that increases the amount of the empty fraction model frame;
  • Buttons to change the numerator and denominator;
  • Button for mixed numbers;
  • A reload button.

Step 3. Start the mixed numbers button. Select the appearance of the fraction to your liking.

Step 4. 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 5. Increase the fraction section by 2. You have gotten ½ – a semicircle. Hence, it turns out that ½ represents half of the shape.

Step 6. Click the button that increases the amount of empty frame of the fraction model. You will have 2 wireframes.

Step 7. Fill the first skeleton completely and the second one halfway. You will have a mixed number.

Step 8. Increase the section of the fraction by 3. You will have a fraction of 3/3.

Step 9. Create another mixed number by completing the skeletons.

Step 10. Click the button that increments the empty frame of the fraction model and pull the third empty frame onto the screen.

Step 11. Form mixed numbers by collecting and filling the frames with different fractions from the shapes.

Step 12. You can also repeat the experiments for other types of shapes.

Part 2. A game for learning fractions

Step 13. Select the “Game” section of the simulator.

Step 14. You will be presented with different levels. Drawing figures on the given levels fractions are represented as numbers, by which you will construct fractions from the figures. And in levels given by numbers, fractions are represented as figures by which you will write fractions by numbers. Choose the type of level to your liking.

Step 15. On the right side of the screen, you will find a list of fractions 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. On the left side are the back and restart buttons.

Step 16. Collect the first fraction. If you have selected a level that has an image of shapes, you can add as many more empty wireframes as needed using the “Add” button to express a mixed number.

Step 17. To check for correctness, move the cursor 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 its place of assembly.

Step 18. Assemble the other types of fractions as well.

Step 19. Once you have correctly assembled all the fractions, you can move on to the next level and complete other tasks.

Step 20. You can complete other levels by clicking the “Back” button above left and returning to the “levels” section.

Part 3. Lab part

Step 21. 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 22. Construct a mixed type of number from the numbers.

Step 23. Place the shapes on the empty frame following the given fraction. You can add more empty skeletons as needed using the “Add” button.

Step 24. Move the fraction and shape to the left side of the screen by holding down the left mouse button.

Step 25. 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 26. Build the correct type of fractions from the numbers and form the corresponding shape.

Step 27. Try to build some more mixed and proper fractions.

Conclusion

In the course of the work, students not only learned theoretical information about fractions, but also acquired practical skills of working with them. They learned how to create, analyze and work with ordinary fractions using virtual tools and modeling. This experience enriched the knowledge in the field of mathematics and will come in handy for further learning.