Understanding the meaning of multiplication

Objectives:

• To vizualize multiplication using different models of conception
• To understand the meaning of multiplication in context and using representative models

Activity 1:

1. Call out a number between 1-10 and ask students to picturize that quantity in their mind in terms of any object. Eg – 7 bananas, pencils, books, chocolates, etc.
2. Now ask children to imagine that those objects are all put in a box and imagine ‘n’(1-9) such boxes
3. Take an example object and two numbers and draw it out on the board to explain the meaning of multiplication. 7X6 would mean 7 items in a box and 6 such boxes. (It can be interpreted in the reverse order as well, but this interpretation is more amenable to Kannada)
4. Explain that any ‘m x n’ would mean ‘n groups of m’. In Kannada, it is ಗುಣ್ಯ x ಗುಣಕ - ಗುಣ್ಯದ ಗುಣಕ ಗುಂಪುಗಳು
5. Take another example and ask students for a sample object and how it can be represented
6. Next, divide children into small groups of 3 or 4 and have them take turns to practice a few examples where they represent multiplication equations pictorially. Chits/start-stop/random number generator can be used for choosing numbers. Note: It is not important for students to calculate the product in this exercise. They only need to understand how it can be represented and interpreted.
7. Array model: Extend the definition of m x n to demonstrate what an array arrangement would look like. Eg - 3 x 4 and 4 x 3 would be as shown in the figure.
8. Number line: Also demonstrate that multiplication m x n can also be understood as n jumps of size m on a number line.
9. In the same groups formed before, have students practice representing a few multiplication equations of numbers <10 in these formats.

Activity 2: Constructing multiplication tables

1. Demonstrate how the multiplication tables can be constructed using the array model and have children construct it themselves. Make sure they write the equation, representation and the product. Example shown in figure. It can be written in other ways as well.
2. Students can work on constructing the tables in sets - [2, 4, 8]; [3, 6, 9]; [10 & 5] and ask them to identify patterns in it
3. Once students have constructed one set of tables, ask them to highlight equations having the same product. For eg – 2x8, 8x2, 4x4, etc. This will help reinforce the relationships as well.

Multiplication Practice:

Objectives:

• Recalling multiplication facts in random order

Activity 1: Grid game

(refer https://drive.google.com/file/d/1tboNhoViapac1S9OkrWhqEKue5RHWt38/view)

• 1. Ask students to draw a grid of any size and in the 1^st cell, they write the multiplication symbol.
  2. In the top most row and left most column, numbers are written. Numbers can be given by the facilitator, chosen at random by the students via dice/chits, chosen based on specific conditions, etc.
  3. The products of the numbers corresponding to each cell need to be filled up
  4. Different variations can be done depending on the abilities of the students and need for targeted practice. Can be played individually, or in groups where 2 or more groups compete to complete the grid first, the grid can initially have numbers in order in the row/column and progressively get more random