Mathematical activities and exercises in primary science

Measurement is the subject of one of the four Units in Class 3 science. There are two chapters in this Unit: How many? How much? (dealing with quantity, weight volume, time and temperature) and How long? How high? How far? (dealing with length). The sequencing is inspired by Jean Piaget's experiments with children. The experiences are selected from natural contexts, using easily available equipment. In other parts of the Class 3 and Class 4 science books, there are exercises on counting, comparison, seriation and geometry. The measurement ideas introduced in Class 3 are applied later in different contexts. For example, a simple balance is constructed and used for comparing small weights. The same balance is used in Class 4 to estimate the amount of water lost by a flower drying up. Exercises under the title Figure it out call for a variety of quantitative and problem-solving skills.

We believe that if measurements are introduced at this early stage, through concrete experiences, then students would have time to learn the basic principles without getting lost in technicalities. Some features of these activities and exercises are listed below:

1. Quantifying in everyday activities: eg. Different kinds of plants and animals, parts of body, growth, techniques of finger counting, keeping score in games, measurement in recipes and such other procedures.

2. Prediction and estimation ("First make a guess, then do it and see") is a regular feature in all activities.

3. Informal techniques of comparison: more/less, large/small, heavy/light, tall/short, wide/narrow, warm/cool ...

4. Seriation: Ascending and descending order (eg. Find three things taller and three things shorter than you. Now arrange the names of all these things from tallest to shortest.)

5. Non-standard units are used in Class 3 (grains and matchsticks for weight, hand-spans for length, tick-tick numbers for counting time). Kilograms, litre, kilometer, time and temperature units arise gradually in everyday contexts. These are elaborated in Classes 4 and 5.

6. Picture graphs are introduced in Class 3 and developed into conventional graphs through Classes 4 and 5.

7. The calendar and the clock are used from Class 4 onwards. Phenomena are introduced on the scale of seconds, minutes, hours, days, months and years. Times of the day are correlated with daily activities.

8. Venn diagrams are introduced in Class 4 through concrete activities involving sorting slips of paper. In this case a task calling for multi-parameter thinking is guided by a series of age-appropriate concrete steps involving cutting and pasting or sorting. Such new approaches still need testing and refinement.

9. Decimal fractions are used from Class 5 onwards.

10. Geometrical ideas in 2-d and 3-d are used in construction activities. These include constructing with paper and other materials and drawing from observation. The idea of scale is introduced.

This is just a beginning. At present we are looking for opportunities to pilot test this curriculum in its English, Hindi and Marathi versions. Suggestions relating to both development and testing are welcome.