Table multiplication and division

Table multiplication and division

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

Objective:

  • Familiarity with the multiplication table and memorization;
  • The operation of division;
  • Relating the operation of division and multiplication.

This virtual activity is designed to be used in math lessons in the next chapter:

  • Grade 2. “Multiplication and division”

Theoretical part

Multiplication Operation

Imagine you are a baker and you want to bake lots of delicious pies. How many pies will you get if you use 2 cups of flour for each pie?

That’s where multiplication comes to our rescue!

Multiplication is the addition of identical groups.

In our case:

1 pie = 2 cups of flour

2 pies = 2 cups of flour + 2 cups of flour = 4 cups of flour.

3 pies = 2 cups flour + 2 cups flour + 2 cups flour + 2 cups flour = 6 cups flour

Let’s write it down like this:

2 x 3 = 6, where:

2 is the multiplier (what we are multiplying) – the amount of flour for 1 pie

3 is the multiplier (how many times we multiply) – the number of pies

6 is the product (the result of multiplication) – the total amount of flour.

Division operation

The more pies we bake, the more flour we use!

Now let’s imagine that you have 8 delicious apples and you want to put them equally into 2 baskets. How many apples will be in each basket?

Division will help us with that.

Division is dividing a number into equal groups.

In our case:

8 apples / 2 = 4 apples in each basket

We write it like this:

8 : 2 = 4, where:

8 is the divisor (what we are dividing) – the total number of apples

2 is the divisor (how many groups we divide into) – the number of baskets

4 is the quotient (the result of division) – the number of apples in each basket.

Let’s write it like this:

8 : 2 = 4, where:

8 is the divisor (what we are dividing) – the total number of apples

2 is the divisor (how many groups we divide into) – the number of baskets

4 is the quotient (the result of division) – the number of apples in each basket.

The more apples, the more baskets with the same number of apples you get!

Multiplication and division are like two sides of the same coin:

  • By multiplying, we increase the quantity several times (bake more pies).
  • By dividing, we break the quantity into groups (arranging the apples in baskets).

Virtual experiment

The “multiplication” simulation is an aid for students to familiarize themselves with the multiplication table. The screen introduces the multiplication operation in the form of the Pythagoras table. By manipulating the numbers, he gets the results of multiplication.

Course of Work:

Step 1. Start the simulation: You will be offered 3 different modes: “Multiply”, “Factor” and “Divide”. Open the “Multiply” section. 

Part 1. “Multiply”.

Step 2. You are given 3 levels: Level 1 performs multiplication of numbers 1-6, Level 2 1-9, and Level 3 1-12. Choose Level 1. In the workspace, you are given:

  • The Pythagorean table (1);
  • A product (2);
  • Level and number of points (3);
  • An eraser (4);
  • A place to write the result of the multiplication (5);
  • Check button (6);
  • Return button (7).

Step 3. The Pythagoras table displays an expression that is colored and multiplied below the table. Write the value of the multiplication in the box where you write the result of the multiplication.

Step 4. Click the “Check” button. If the result is correct, the expression of the next product is given. If there is an error, the “try again” button will appear. If there is an error, click the same button and write the result of the product from the beginning.

Step 5. You can complete all the level 1 productions and go to the next level, or you can complete some more level 1 productions from the beginning. 

Part 2. “Factor”.

Step 6. Open the “Factor” section. There are 3 levels: Level 1 does multiplication of numbers 1-6, Level 2 does multiplication of numbers 1-9, and Level 3 does multiplication of numbers 1-12.

Step 7. You are given in the work area:

  • Pythagorean table (1);
  • Product (2);
  • Level and number of points (3);
  • Eraser (4);
  • Return button (5).

Step 8. The expression below the table gives the result of the product. In the Pythagoras table, mark the two numbers you need to multiply.

Step 9. If the result is correct, the expression for the next product is given. If there is an error, a “try again” button appears. If there is an error, press the same button and write the result of the product from the beginning. 

Step 10. You can complete all level 1 pieces and go to the next step, or you can complete some more level 1 pieces from the beginning.

Part 3. “Divide”. 

Step 11. Open the “Divide” section. There are 3 levels: Level 1 does multiplication of numbers 1-6, Level 2 does multiplication of numbers 1-9, and Level 3 does multiplication of numbers 1-12. The work area is similar to the “Multiply” section.

Step 12. The expression below the table gives one of the multiplication numbers and the result of the product. Find the second number to multiply. Check the second number by marking it on the Calculator bar.

Step 13. If the result is correct, the expression of the next product is given. In case of an error, the “Try again” button will appear. If there is an error, press the same button and write the result of the product from the beginning.  

Step 14. You can finish all level 1 productions and go to the next step, or you can do some more level 1 productions from the beginning.

Conclusion

Students will learn how to multiply using the Pythagorean table through this virtual activity. This is interesting for students because they work with the multiplication operation visually and it makes it easier to memorize the multiplication table.