Efficient Calculations: Properties of Multiplication

Efficient Calculations: Properties of Multiplication

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

Objective:

  • Simplifying expressions by combining like terms.

This virtual work is intended for use in math lessons in the following chapter:

  • Grade 3. “Multiplication and Division Outside the Table”

Virtual Experiment

The virtual work “Efficient Calculations” is intended for students to learn how to make calculations with different coins and reduce expressions.

Workflow:

Step 1. Run the simulation. You have 4 different modes. “Basics”, “Explore”, “Negatives”, “Game”. You will work in the “Explore” and “Game” sections. Open the “Explore” section.

Step 2. In the work area, you are provided with:

  • Coin types (1);
  • Button for switching a coin to variables x,y,z (2);
  • Value of expression (3);
  • Board “My Collection” (4);
  • Buttons for displaying coin values ​​and coefficients (5);
  • Reset button (6).

Step 3. Pull out some coins to the work area. When you hold the coins in one row, part of the screen turns whitish, forming a sum. You can see the sum on the board, where the value of the expression is shown.

Step 4. Activate the buttons to display the values ​​​​and coefficients of the coin.

Step 5. Build the next expression. Build several expressions using coins.

Step 6. You can replace the coin with the variables x, y, z.

Step 7. Open the “Game” section. You are given 8 levels. In this lesson, you will work on the first 4 levels.

Step 8. Open the first level. In the work area you are provided with:

  • Types of coins (1);
  • A table of expressions given for assembly (2);
  • Back and refresh buttons (3).

Step 9. Build expressions by looking at the expression panel given for assembly and drag them to the empty space under the expression.

Step 10. After you have completed the entire expression on the board, you can move to the next level by clicking the “Next” button.

Conclusion

Students, working on the simulator, made calculations on the topics: generalization of expressions by similar members, coefficient.