Class 08 Activity – Square of a 3 digit number

 Activity – Square of a 3 digit number

PROJECT

Objective: 

To find the square of a 3-digit number using diagonal method.

Materials Required: 

Drawing sheets, sketch pens, geometry box, etc.

Procedure:

Let us find the square of 345.

Write down the digits 3, 4, 5 in the 3 x 3 square as shown in figure.

2. Now, join the diagonals of all the small squares with the dotted lines as shown in figure. 

3. Multiply each digit on the 1st column of the squares with digit on the row and write the products in the 1st column. Colour them as shown in figure. We write the tens digit on the upper half and ones digit on the lower half of the diagonals. 

4. Complete the squares by multiplying the elements of each column as shown in figure.

5. Starting from the lower square, add the numbers diagonally as shown in figure. 

6. Add the sum of the digits along the diagonal. If the result of addition comes in two digits, add the carry over to the next diagonal. Thus, the square of 345 = 119025

II. Now, let us find the square of 3497. Thus, the square of 3497 = 12229009.

Class 08 Activity – Relationship between the side length and the area of the square.

 Activity – Relationship between the side length and the area of the square.

objective: 

To investigate several squares with different side lengths and review the relationship between the side length and the area of the square.

Procedure: 

Give students the following square pattern and ask them to study the pattern.

If this pattern were to continue, for any number of tiles on the side of a square, we should know what number of tiles is needed to build the entire area of the square. 

Fill in the table below:

How many tiles would be on the side if there are 324 tiles in the area?

How many tiles would be on the side if there are 841 tiles in the area?

Based on what you learned, what is the relationship between the length of side of a square and itself area ? 

If you know the area, how do you find the length of a side?

Class 08 Activity – Exponents and powers

 Activity – Exponents and powers

Objective: 

To find the values of 20, 21, 22 by paper folding activity.

Materials Required:  

Few rectangular paper cutouts, scale, pencil

Preparation for the Activity:

The rectangular pieces of paper represent the base 2.

2. Number of times the rectangular pieces will be folded that will represent the power

Demonstration and Observation:

Take a rectangular piece. This is not folded. So, it is folded zero time.

2. Now take another piece of paper. Fold it into two equal parts along the length. Here, the fold has been made one time. Open the paper. We find two equal parts.

3. Take another piece of paper and first fold it into two equal parts along the length as done in step 2. 

Then, similarly fold it once more along the width. 

We have folded the paper two times. Open the paper. 

We find 4 equal parts of rectangles. Make lines along with it.

Two be Draw the line segment among the creases to get 4 such rectangles.

4. Take another piece of paper and first fold it as done in step 3. 

Then once again fold it along the breadth. We folded the paper three times. 

Open the paper and count the number of equal rectangles.

 Draw the lines along with the creases to get 8 equal rectangles.

 Keep on folding to get further results.

Class 08 Activity – Rational numbers

 Activity – Rational numbers

Objective: 

To show that every rational number 𝑝/𝑞 can be represented on the number line.

Materials Required: 

A drawing sheet, a compass, a scale, a pencil, an eraser, etc.

Let us represent the rational number 17/7 on the number line.

Procedure: 

Draw a number line on the drawing sheet with the help of a scale.

Represent the integer 17 on it.

 Let the point P represent 17. 

1. Divide the segment OP into 7 equal parts.

2. Let us name the first point on the right of O as A. OA represents one-seventh of 17 or 17/7 units. 

Thus, A represents the rational number 7. on the number line.

II. Now let us represent the rational number (−9)/4 on the number line.

Draw a number line.  Represent - 9. (on the left of 0) on the number line. Let the point Q represent the integer -9.  Now divide the segment OQ into four equal parts.

2. Let us name the first point on the left of O as B. 

OB represents one-fourth of OQ, i.e., 1/4of-9 or (−9)/4units.

Thus, the point B represents the rational number (−9)/4  on the number line.

 Similarly, other rational number can be represented on the number line. 

Thus, every rational number can be represented on the number line,  as a line segment can be divided into any number of equal parts.