Class 08 Activity – Visualizing Solid Shapes

Objective:

 To verify Euler's formula for different polyhedral : Prism, Pyramid and Octahedron.

Materials Required: 

Chart papers, pencil, a pair of scissors, tape, scale, gum etc.

Procedure:1. 

Draw/ prepare the following nets (as shown in the figures 1 (a), 2 (a), 3 (a), 8 (a) on chart paper.

2. Cut out these nets.

3. Fold the above nets along the line and join them by gum or tape.

4. Obtain the different models of Right Prisms and Right Pyramids.

Fig. 1 (a), shows the net of a Right Triangular Prism.

Bases are congruent equilateral triangles and the lateral faces are congruent rectangles.

Fig. 2 (a), shows the net of a Right Rectangular Prism. The base and top of one prism are congruent squares and the lateral faces are congruent rectangles.

Fig. 3 (a), shows the net of a Right Pentagonal Prism.

Bases are congruent regular pentagons and the lateral faces are congruent rectangles [Breadth of rectangle = side of regular pentagon]

Fig. 4 (a), shows the net of a Right Hexagonal Prism.

The bases are congruent hexagon and the lateral faces are congruent rectangles [breadth of rectangle = side of regular hexagon]

Fig. 5 (a), shows the net of a Triangular Pyramid. 

Base is an equilateral triangle and the lateral faces are conguent isosceles triangle with base equal to the side of the equilateral triangle.

Fig. 6 (a), shows the nets of a Rectangular Pyramid.

The base is a square and the lateral faces are congruent isosceles triangles with base equal to the side of square.

Fig. 7 (a), shows the net of a Pentagonal Pyramid.

The base is a regular pentagon and the lateral faces are congruent isosceles triangles with base equal to the side of the pentagon.

Observations:

Draw the following observation table and complete with the help of the models of polyhedra obtained. 

Fig. 8 (a), show the net of a Hexagonal Pyramid. 

The base is a regular hexagon and the lateral faces are congruent isosceles triangles with base equal to the side of hexagon.

Conclusion:

Students will find that in each case of the relation F-E + V has value 2.Hence, the Euler's formula F + V-E = 2 is verified.

2. In a prism the number of faces = n + 2, number of edges = 3n, number of vertices = 2n.

3. In a pyramid, the number of faces = n + 1, number of edges = 2n, number of vertices = n +1.

Class 08 Activity – Comparing Quantities

 Class 08 Activity – Comparing Quantities

Objective: 

To compare the interests earned on Saving Bank Accounts applying simple interest and compound interest methods, respectively.

Materials Required: Paper, pencil, envelopes and play money.

Procedure: 

Divide the students into four groups. 

Give each group an envelope with Rs 100 play money in it, as the initial deposit money. 

Each group will have the same depositing pattern, however, two groups will have simple interest account and the other two will have compound interest account.

 Students will calculate the interests over five deposit cycles.

 The rate of interest for the four groups can be taken as below: 

Group I: Simple interest of 20 % per cycle 

Group II: Compound interest of 20 % per cycle

Group III: Simple interest of 40 % per cycle 

Group  IV: Compound interest of 40 % per cycle

After every cycle, each group will receive its next deposit and its interest.

The simple interest groups will keep aside the interests received after each cycle. They will add the initial deposit and the total balance obtained after fifth cycle to get the gross total amount. 

While the compound interest groups will deposit the total amount received in the next cycle and therefore, will get the gross total automatically after the fifth cycle. 

Now each group will fill the following tables. 

Group I (Simple Interest of 20 %)

Group II (Compund Interest of 20 %)

Group III (Simple Interest of 40 %)

Group IV (Compound Interest of 40 %)

After the completion of five cycles, the pair of group with 20 % rate of interest will fill the table given below to compare the gross amount earned by the rate of simple interest and rate of compound interest. 

Similarly, the pair of group with 40% rate of interest will fill the table given below.

Now based on the above table, ask the students the type of Saving Bank Accounts they should be opening

 Class 08 Activity – Comparing Quantities

Objective:

 To find out prices of different items after discount and tax. 

Materials Required: 

Rate list of different stores, paper money and pencil.

Procedure: 

Divide the class into four groups. Give each group rate list of different stores. 

Remember that there must be some items in every rate list that has discount. 

Give paper money of Rs 500 to each group. 

They have to purchase 5-10 items present on the list with the help of this money. 

They are free to choose items from the rate list of any store. 

They are free to choose items from the rate list of any store. 

They should be recording their purchases in the table below. 

The group that will buy maximum number of items with minimum amount of money will be the winner.

 Class 08 Activity – Understanding Quadrilaterals

Objective:

 To make the following by paper folding and cutting.(a) Kite (b) Rhombus

Materials Required:

 White sheets of paper, a pair of scissors, glue stick, geometry box, etc.

Procedure: 

(a) To make a kite

1. Take a white sheet of paper and fold it once from the middle as shown below.

2. Draw two line segments AB and BC of different lengths as shown.

3. Cut along the line a segments AB and BC and unfold the cut –out . Draw a dotted line along the  fold and mark the two other vertices as C and D.

(b) To make a rhombus

Take a sheet of paper and fold it from the middle as shown below. 

2. Draw two line segments AB and BC such that AB = BC as shown.

3. Cut along the line segments AB and BC and and unfold the cut out. Draw a dotted line along the fold and mark the two other vertices as C and D.

Observations:

On measuring the sides AB, BC, CD and DA in figure 3, we find that AB = AD and BC = DC.

Hence, ABCD in figure 3 is a kite.

2. On measuring the sides AB, BC, CD and AD in figure, we find that AB = BC = CD = AD.

Hence, ABCD  in figure 6 is a rhombus.