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.

Class 07 Puzzles - Triangles

 Puzzles - Triangles

1. Here 9 matchsticks have been used to form four congruent triangles. Now arrange only 6 matchsticks to four congruent triangles.

Puzzles – Triangles - Solution

1. Here 9 matchsticks have been used to form four congruent triangles. Now arrange only 6 matchsticks to four congruent triangles.  Tetrahedron

2. Here 12 matchsticks have been used to enclose an area of 9 squares. Draw four diagrams toshow how 12 matchsticks can be used to enclose areas of 8, 7, 6, and 5 squares.

2. Here 12 matchsticks have been used to enclose an area of 9 squares. Draw four diagrams to show how 12 matchsticks can be used to enclose areas of 8, 7, 6, and 5 squares.

Class 07 Pencil Puzzles

 Pencil Puzzles

Can you draw these figures without lifting your pencil off the paper? You are not allowed to retrace any lines but you can cross over lines

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Pencil Puzzles - solution

Can you draw these figures without lifting your pencil off the paper? You are not allowed to retrace any lines but you can cross over lines

Solution:

Figure 1: yes. Start any vertex and complete it at other end. (All even vertices)

Figure 2: yes, Start at any even vertices and complete it at other end. ( All even vertices)

Figure 3: yes, Start at any even vertices  and complete it at other end. (All even vertices)

Figure 4: yes, Start at any odd vertex (3) and complete it at other end. (it has exactly 2 odd vertices)

Can you draw these figures without lifting your pencil off the paper? You are not allowed to retrace any lines but you can cross over lines

Solution:

Figure 5: no, It has more than 2 odd vertices.

Figure 6: yes, Start at any even vertices and complete it at other end. ( All even vertices)

Figure 7: yes, Start at any even vertices (4) and complete it at other end. (All even vertices)

Figure 8: no, It has more than 2 odd vertices.

Class 07 Grid Game

 Grid Game 

A game for 2 players.

Materials Required: 

A4 x 4 grid.

8 counters, 4 of one colour for one player, 4 of another colour for the other player.

Method: 

The counters are placed on the grid as shown.

The players take it in turn to move their counters. 

At each turn, only one counter may be moved horizontally or vertically, one square at a time. 

They may not be moved diagonally.

The winner is the first player to position 3 of his or her counters beside each other, either horizontally, vertically or diagonally.