Maths Activities

# Maths Activities

## Maths Activities

The Hands-on-Activities play a vital role to understand any concepts of mathematics in play way manner. Here, I am going to provide some maths activities for the ready reference. Students and teachers can take ideas of maths activities from these activities while explaining the concepts in the class.

Activity 1

Look at the figure of laboratory thermometer shown alongside.
A laboratory thermometer shows temperature below 0° Celsius.
Place the thermometer inside the refrigerator for a few minutes on each shelf, and note the different temperatures.
You will see that the temperature shows anywhere between 0°C and 5°C.
Water converts to ice at 0°C. So, the temperature of the refrigerator should be kept at about 4°C.
At which shelf is it the coldest? Find out why is this so.
Place the thermometer inside the freezer for a few minutes. You will see that the temperature shows anywhere between –1°C and –15°C.
The refrigerator and freezer have temperature control knobs. Change the settings and note the temperature for each setting in the freezer.

Activity 2
Objective: To recognize the plane shapes with 3, 4, 5, 6, 7, and 8 sides.
Use rubber bands to make shapes with 3 sides, 4 sides, 5 sides, 6 sides, 7 sides and 8 sides on a geoboard.

How many angles does each shape have?
Identify each type of angle as acute, obtuse or right angles.

Activity 3

Objective: To find all the prime numbers and composite numbers between 1 and 100.
Consider the first 100 natural numbers.
1          2        3        4        5        6        7       8        9       10
11      12      13      14      15      16      17      18      19      20
21      22      23      24      25      26      27      28      29      30
31      32      33      34      35      36      37      38      39      40
41      42      43      44      45      46      47      48      49      50
51      52      53      54      55      56      57      58      59      60
61      62      63      64      65      66      67      68      69      70
71      72      73      74      75      76      77      78      79      80
81      82      83      84      85      86       87      88      89     90
91      92      93      94      95      96       97      98      99     100

1.      Cross out 1.
2.      Circle 2, and then cross out all the multiples of 2.
3.      Circle 3, the next number after 2 that is not crossed out. Then cross out all the multiples of 3.
4.      Circle 5, the next number after 3 that is not crossed out (4 has been crossed out). Then cross out all the multiples of 5.
5.      Continue doing this until you have visited all the numbers in the group.

Now, all the circled numbers are prime numbers and all the numbers (other than 1) which are crossed out are composite numbers.
Thus, prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the remaining numbers other than 1 are composite numbers.

Activity 4

Objective: To find the sufficient conditions needed to draw unique triangles.

You will need drinking straws and angle strips of different angle of pre-determine measures.
1.      Form a triangle using three pieces of drinking straws or pipe cleaners of lengths 5 cm, 7 cm, and 10 cm.
(ii)               What do you observe? Are all the triangles the same?
Try three different lengths of material (3 cm – 4 cm – 5 cm, 5cm – 5 cm – 5cm, and 7 cm – 7 cm – 5 cm) to see if the same conclusion holds true.
2.      Using the 5 cm and 7 cm pieces of straw and a 50° angle made from angle strips (or straws and pipe cleaners), form a triangle. The third side can be any length necessary to complete the triangle. Experiment by placing the 50° angle in different locations so that it is the angle between the two given sides and then as the angle opposite one of the given sides.
(i)                 Sketch and label the triangles that you have formed.
(ii)               Compare your triangles with those of your classmates for each case explored, and to state the conclusions.
(iii)             Where must the 50° angle be placed relative to the other known sides in order to produce triangles that are the same for you and your classmates?
Try three different combinations of lengths and angle measures of material to see if the same conclusion holds true.
3.      Using only the 7 cm straw and 2 angles of 50° and 60°, along with 2 other pieces of straw (cut to appropriate required lengths), explore possible ways of combining them to make a triangle.
(i)                 Sketch and label the triangles that you have formed.
(ii)               Compare your triangles with those of your classmates and observe how two angles and one side should be arranged such that triangles that are alike will always be produced.
Similarly, try three different combinations of lengths and angle measures of material to see if the same conclusion hold true.
4.      Explore using only 3 angles of 50°, 60°, and 70° to form triangles. Is it possible to form a unique triangle?
5.      Explore using three pieces of straws of lengths 3 cm, 4 cm, and 10 cm to form triangles. Also, try another different combination of lengths of material (3 cm –5 cm – 10 cm or 4 cm–5 cm–10 cm).
(i)                 Is it possible to form a unique triangle in each of the case?
(ii)               Find the sum of any two sides of each triangle in Task (5). Compare the sum of any two sides of a triangle with the length of the third side of the triangle.
(iii)             Refer to the lengths of sides of the triangles formed in Task (1). Find the sum of any two sides of each of those triangles in Task (1). What do you notice about the sum of any two sides of a triangle with the length of the third side of the triangle?

Activity 5

Objective: To recognize the relationship between nets and the solids formed from the nets.

1.      Copy the given nets on a sheet of paper.
2.      Cut each of them out along the solid lines.
3.      Fold each of them up along the dotted lines to form solids.

The solids formed from the above nets can be drawn as follows:

Activity 6

Objective: To compare between mean, median, and mode.

1.      Consider the data set A = {3, 3, 7, 8, 9}.
(a) Find its mean, median, and mode.
(b) If the number 54 is included in the set, find the new mean, median, and mode.
(c) Which measure in (a) is most affected by the addition of a large number?
(d) Which measure in (a) do you recognize to be the most appropriate representation of the center of the data set A? Explain your choice briefly.
2.      Consider the data set B = {1, 1, 3, 6} and C = {1, 1, 4, 10, 10, 10}.
(a)   Find the mean, median, and mode of data set B, data set C and the combined data set D of data sets B and C. Copy and complete the following table.

 Measure of Center Mean Median Mode Data set B Data set C Combined data set D

(b) Which measure of center involves all the data of a data set in its calculation?
(c) Suppose you are given only the numbers of items for sets B and C, and their individual measures of center. Which measure can you derive for the combined data set D from the given values?

Activity 7

Objective: To find the hexagonal numbers

A hexagonal number is a number that can be represented as a regular hexagon. The first few hexagonal numbers are 1, 6, 15, 28, ...

Find the generalized formula for hexagonal numbers.