Tasks for Finding the Whole from the Part

Tasks for Finding the Whole from the Part

Fraction Matcher by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC-BY-4.0 (https://phet.colorado.edu)

Objective:

  • To learn how to compare and equate prime numbers, mixed numbers.

This virtual work is designed for use in mathematics lessons on the following topics

  • Grade 4. “Tasks to find the whole from the parts”

Theoretical part

Problems to find the whole from parts

In these problems we are given a part of a whole and we know what that part is. Our task is to find this whole.

Example: Nazgul has 5 apples. This is 1/3 of all the apples in the basket. How many apples are in the basket?

Answer:

  • If we know that 1/3 of a fraction is 5 apples, then to find the whole, we need to divide 5 apples by 1/3.
  • Dividing by a fraction is the same as multiplying by the inverse fraction: 5 ÷ 1/3 = 5 * 3/1 = 15 apples.

Comparing and balancing fractions and mixed numbers

Compare fractions:

  • If the denominators of fractions are the same, compare the numerators: the larger the numerator, the larger the fraction.
  • If the denominators are different, make the fractions have a common denominator and then compare the numerators.

Compare mixed numbers:

First compare the whole numbers. If they are equal, compare the fractional parts.

Criteria for making fractions equal

  • Equality of the numerators and denominators: The simplest case: two fractions are equal if their numerators and denominators are equal. For example, 3/4 = 3/4.
  • Fraction reduction: A fraction can be reduced by dividing its numerator and denominator by the same number (other than zero). The resulting fraction is equal to the original fraction. For example, a fraction 6/8 can be reduced by 2, resulting in a fraction 3/4. So 6/8 = 3/4.

Virtual Experiment

In the Aligning Simple Fractions virtual experiment, students learn to find and align fractions using numbers and pictures. Performs fraction calculations in a fun way to easily master the topic of simple fractions. Align the same fractions using different numbers and fraction representations.

Progression:

Part 1. Play with correct and incorrect simple fractions

Step 1. Start the simulation: You will be presented with 2 different modes: “Fraction” and “Mixed Numbers”. Open the “Fraction” section.

Step 2. In the workspace you will be presented with 8 different levels of problems. Levels 1-2 use less than 1 fraction. Levels 3-6 use fewer than 2 fractions. Levels 7-8 use only more than 1 and less than 2 fractions. 

Step 3. Open the first level. In the work area you are provided with: 

  • Windows that collect correctly aligned fractions (1);
  • Scales for comparing fractions (2);
  • Fractions passed for comparing and balancing (3);
  • Buttons to “return to levels” and “update fraction types” (4); 
  • Level and number of points (5).

Step 4. Bring any fraction to the scales by left-clicking and dragging it. 

Step 5. Among the remaining fractions, find a fraction that is equal or proportional to the fraction on the scale. Place it on the second scale. 

Step 6. Check for correctness by clicking on the “Check” button. If the fractions are equal, click “OK” and perform the next alignment. If there is an error, click “Try again” and align the fractions from the beginning. 

Step 7. Complete the tasks in a level and move on to the next level.

Part 2. The Mixed Numbers Game

Step 8. Open the “Mixed Numbers” section. In the workspace, you will see 8 different levels of problems. Levels 1-6 use less than 2 mixed number fractions. Levels 7-8 use more than 1 and less than 2 fractions.

Step 9. Open the first level. This section also provides a workspace like the first section. This is where you will do mixed number problems.

Step 10. Move any fraction to the scales by left-clicking and dragging. From the remaining fractions, find one that is equal to or proportional to the fraction on the scale. Place it on the second scale. Check your work by clicking on the “Check” button. 

Step 11. Complete the tasks of one level and move on to the next levels. 

Conclusion

In this simulation, students used the basic property of fractions to reduce fractions by comparing and making fractions equal to each other. Understanding the equality of fractions can be the basis for further learning about fractions and performing various mathematical operations with them.