Fractions: Equality

Objective:

  • Comparing and equating ordinary fractions, mixed numbers.
  • Display ordinary fractions, mixed numbers in the coordinate ray.

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

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

Theoretical part

1. Equality of fractions:

Two fractions are considered equal if they denote the same part of a whole.

Example: 1/2 = 2/4

Explanation:

  • Both fractions represent half of a whole.
  • 1/2 is one part of two and 2/4 is two parts of four.
  • These parts are equal to each other, so the fractions are equal.

2. Comparing Fractions:

2.1 Compare denominators.

Example: 1/3 > 1/4

Explanation:

  • The denominator shows how many parts the whole is divided into.
  • 1/3 is a part of 3 and 1/4 is a part of 4.
  • The larger the denominator, the smaller the part.
  • Therefore, 1/3 > 1/4.

2.2 Bring fractions to a common denominator.

Example: 1/2 > 3/8

Explanation:

  • 1/2 and 3/8 do not have the same denominator.
  • Let’s bring both fractions to a common denominator of 8:
  • 1/2 * 4/4 = 4/8
  • 3/8 * 1/1 = 3/8
  • Now both fractions have the same denominator.
  • 4/8 > 3/8, so 1/2 > 3/8.

2.3 Compare the numerators.

Example: 2/3 > 1/3

Explanation:

  • The numerator shows how many parts are taken.
  • 2/3 is two parts of 3 and 1/3 is one part of 3.
  • The larger the numerator, the larger the part.
  • Therefore, 2/3 > 1/3.

3. Equivalent fractions:

Equivalent fractions are fractions that are equal to each other.

Example: 1/2, 2/4, 3/6-equivalent fractions.

Explanation:

  • All these fractions represent the same part of a whole.
  • 1/2 is half of the whole, 2/4 is two-fourths of the whole, and 3/6 is three-sixths of the whole.
  • All these parts are equal to each other, so the fractions are equivalent.

Virtual experiment

The simulation game “Fraction: Equality” allows students to explore equivalent fractions with different denominators and then test their concepts on the game screen.

The figure below shows the functions each button performs.

Progression:

Part 1. Equality Lab

Step 1. Start the simulation: you will be presented with 2 different modes: “Equality Lab screen” and “Game”. Open the “Equality Lab screen”.

Step 2. In the working area you are presented with:

  • Different types of fractions consisting of two parts: round, rectangular, cylindrical and segments;
  • Empty shot model frames;
  • The shapes that make up fractions;
  • Equality expressions;
  • Buttons that change the numerator and denominator of a fraction;
  • Button that changes the number of parts of an empty fraction model frame;
  • Reload button.

Step 3. Place the mold on the empty skeleton located on the left side of the screen. You will automatically have the empty skeleton on the right side replenished. You will see from the equality below the shapes that 1/1=2/2.

Step 4. Fill the empty skeletons on the left with more shapes. Make it a point to change the equality each time you fill.

Step 5. Click the “Reload” button.

Step 6. Increase the number of parts of the empty frame of the fraction model by 3.

Step 7. Place the shape on the empty frame on the left. You will automatically have the empty skeleton on the right automatically replenished. You will see from the equality under the shapes that 1/1=3/3.

Step 8. Fill the empty skeletons on the left with more shapes. Attribute the change in equality to the change in equality each time you fill.

Step 9. click the Reload button. Increase the denominator of the fraction by 2.

Step 10. Examine the changes to the equality by placing the shapes into empty frames.

Step 11. Explore the changes by replacing the fraction model shapes.

Step 12. Explore multiple types of equality by changing the denominator of the fraction by starting over.

Part 2. A game for learning to balance fractions

Step 13. Open the “Game” mode in the simulator. You are given 8 levels. Select the first level.

Step 14. In the work area you are given:

  • Blank cells at the top of the screen where my balancing matches are located;
  • Scales for balancing fractions;
  • The fractions that need to be balanced;
  • On the right side, the level number and the number of points scored are displayed;
  • On the left are the back and restart buttons.

Step 15. Select one of the fractions to be balanced and place it on the scales.

Step 16. Among other fractions, find a fraction equal to it and place it on the second scale.

Step 17. Check for correctness using the “check” button. If correct, place it in the empty cell above by clicking “ok”. And if there is an error, click the “try again” button and do the equality again.

Step 18. Complete the tasks given by balancing the other types of fractions.

Step 19. Once you have done everything correctly, you can move to the next level by clicking “continue”.

Step 20. You can continue and complete the tasks of each level as you wish to sharpen your knowledge.

Conclusion

In completing this virtual lab activity, students explored different aspects of equality in the context of fractions.

In Part 1 of the experiment, students worked with models of fractions and explored their equality. Part 2 introduced a new game format for learning how to equalize fractions. Here, learners practiced finding correspondence between different parts. This allowed students to put their knowledge and skills into practice, as well as develop their logical thinking skills and work with parts in a playful way.