Al Qamar Academy, Chennai, Grade 3
Small Science – Class 3
Chapter 9 – How many, How much?
How many, How much?
One day in class Aneesa Aunty read us the story of Mini and Apu making rotis. It was funny how they forgot to measure how much of what they put in, and eneded up making dosas instead of rotis. After this Aneesa Aunty asked us to bring one recipe each from home.
Then she talked about numbers — how numbers are a language and tell a story. She asked us to go hunt for numbers everywhere. At first we didn’t understand what she wanted us to do. How can we find numbers just anywhere? She insisted we look everywhere. So off we went. Khadijah found a lot of numbers where children were doing maths — big numbers too. Aadhil found two numbers on someone’s chappal: ‘Ben 10’ and ‘7’. The first we recognised as a comic book hero who magically turns into 10 different ‘alien creatures’; ‘7’ was the size of the chappals. Sarah found numbers on a clock. Ayaan just quietly sat at his desk – he didn’t go anywhere. He found lots of numbers in the textbook itself — the page numbers, the unit and chapter numbers, the activity and exercise numbers. Hafsa found dates on a picture card about an artist. Aunty told us that these dates were when he was born and when he died. Really, numbers do tell stories.
Then Aunty gave us each a small matchbox and asked us to find numbers on it, without opening it. We actually found quite a few — the price, the pin code where it was made, the phone number of the company that made the matchboxes and finally, the number of matchsticks in the box. A little puzzle printed on the back of the box also had numbers. Numbers really are everywhere.
Next we wrote and brought recipes to class. At first we thought aunty wanted us to make the dish and bring it. But she explained she only wanted a recipe, which said how much of each ingredient was needed and how to make the dish. Sarah brought a dosai recipe. Dakshin had an easy recipe for making laddoos. Abdul Malik’s recipe sounded delicious — banana pancakes. Aunty asked us to show with our hands how much of each ingredient we had to put in. Sarah lifted up one finger to show 1 egg. 2 cupped hands were for maida. A small fist size was the amount of sugar.
The recipe needed ½ cup of water and ½ cup of milk. Jayashree Aunty asked us if ½ cup of water and ½ cup of milk will together make 1 cup, more than 1 cup or less than 1 cup. Hmm! Aneesa Aunty asked us to vote — Some voted for less than 1 cup, some said more than 1 cup. Nobody voted for exactly one cup. Aunty brought 3 tumblers. They all had markings on the side to show how much liquid they could hold. She asked if we had seen milk packets — we all had seen half litre packets. Two of the tumblers could each hold 500 ml or half a litre of water. The third one had a mark for 1000 ml or 1 litre of water. Aunty filled up the smaller tumblers till the 500 ml mark — or that is what we thought. Then she poured all the water into the big tumbler. Guess what — the water came up below the 1 litre mark.
This caused a lot of excitement. Those of us who had voted for ‘less than a litre’ were triumphant at having been proven right. Khadijah insisted that milk and water mix so well, together they must add up to less than 1 litre. Aneesa and Jayashree Aunty looked perplexed and confused. They promised we would do the activity another time after checking out if the tumblers were okay.
We also did another activity — we lifted up our lunch baskets to see whose basket is the heaviest. Maryam, Asad, Aadhil, Dakshin, Khadijah and Saleem brought their baskets. We broke up into teams and took turns holding the baskets in each hand. We found that Asad, Dakshin and Aadhil’s baskets were the heaviest in the class. Then Aunty asked us to rank the three — which was the heaviest, which was next and which was the lightest. We all lifted the baskets two at a time, one in each hand; some of us also switched the baskets to the other hands to check if our feeling was right. We agreed that Asad’s was the heaviest basket of all. Aadhil said that was because he brings three tiffins for himself and his mother’s tiffin also in the same basket. There was a lot of competition among the boys to prove whose lunch basket was heaviest.
In the next class we re-did the experiment of pouring 500 ml of water. Aunty brought two beakers. She showed us the line which had 500 ml written next to it. She poured water into them until the water line was exactly up to the 500 ml mark. This time we all checked it carefully, looking from one side and not from the top, and noting the water level in the middle of the tumbler, not near the sides where it was slightly curving up.
Aunty also had an empty beaker with a 1000 ml line on it. She again asked us if she poured both the beakers into the larger one, would the amount be less than, equal to or more than the 1000 ml mark. This time too we had different guesses. Then she carefully poured the water from both the beakers into the large beaker. Guess what — the water came up EXACTLY to the 1000 ml line! Aneesa Aunty looked pleased.
Aunty talked to us about how it is very important to be careful and precise when doing a science activity. Otherwise our results will be wrong.
We also made balances today using a pencil, scale and two matchbox drawers. It was really difficult to make the scale balance on the pencil. We used double sided tape to stick the pencil on the table and the drawers on the scale. Two teams decided to attach the pencil sticking out over the edge of the table. Sometimes one drawer was lighter than the other so the pencil kept swinging up. We had to keep re-adjusting the scale and the pencil. Finally Khadijah’s team got the scale to balance correctly. They added one matchstick into the left drawer. It went down very very slightly. Then they put a matchstick in the other drawer. Next they added three matchsticks into one side. It went down. Aunty asked us why that side went down. We thought about it and then said, “because it’s heavier!” We used sundal (chickpeas) as another weight. We had to put 19 matchsticks before they balanced. Aadhil’s team put a pencil sharpener in one box. They kept counting and counting till they used 64 matchsticks to make it balance. Sarah’s team tried to weigh a one rupee coin. That one took many many matchsticks — we think it was 70.
In the next class we played with water. First Aunty divided us into two teams. Each team got a mini bucket, a small coffee tumbler and a bigger plastic cup. We went to the tap and filled the small tumbler. Before pouring it into the bucket, Aunty asked us to guess how many tumblers would fill the bucket. Khadijah guessed about 18. Most of us thought it would be lesser number of tumblers. Khadijah’s guess turned out to be very close. We needed 17 and a half tumblers to fill the bucket. Then Aunty asked us if we would need more than 17 and a half or fewer plastic cups of water to fill the bucket. We had to think over this question. Hafsa guessed that we would need less cupfuls, and she was right. We only needed 5 cups to fill the whole bucket.
Then Aunty gave each team 5 containers — a bowl, a coffee tumbler, a glass bottle, a water bottle and a mini bucket. First she asked us to arrange them from the tallest to the shortest. We drew pictures of these in our workbook. Then she filled another coffee tumbler with water. She told us she would pour a tumbler of water into each container. But before that we would have to guess where the water level would be. Asad guessed the level for the heart shaped bucket. He thought the water would be at a very low level — and he was quite close. He explained that the bucket was very wide. Some of our guesses were not right, maybe because the tumbler was broad on top and narrow at the bottom. But as the first container got filled our estimation got better.
Then we counted how many tumblers we needed to fill each container. It was a surprise again — because the bucket which was quite short, held more water than the tall glass bottle.
We were puzzled yet again by a question in the workbook where we had to guess how many mugs of sand would be needed to fill a bucket which took 12 mugs of water. We also had to guess the number of mugs if the sand was level, or if it was heaped in the mugs. Rasmi Aunty made us do the exercise in the playground. First we filled a bucket with 12 glasses of water and marked the level. Then we filled it with sand. The bucket only needed 11 glasses of sand to fill to the same level. Perhaps we had slightly heaped the sand in the glasses, or we had spilt some of the water in the glasses. Water was impossible to heap in the glass, and very easy to spill. Now we could guess that if we heaped the sand more, we’d need even fewer glasses of sand.
In the next class Aneesa Aunty made us sing nasheeds and clap along. It was quite difficult — maybe because Hafsa sang a very slow nasheed. But we all joined in and enjoyed singing.
Then Aunty made us sit in a circle. We had to pass the duster to each other in the circle. Abdul Malik was elected as the timer. He had to count ‘Tick Tick One, Tick Tick Two’… It took us 8 Tick Ticks to pass the duster around. Khadijah then recited a tongue twister while we counted ‘Tick Tick…’. It took 8 Tick Ticks. Aunty read a poem from the Small Science Book while we counted. Then Dakshin wrote a sentence and we counted.
Finally we went to the stairs. One person had to climb till the top while another one counted ‘Tick Tick…’ to see how many seconds we took to climb up. Most of us took only 5 Tick Ticks, some took more. Aadhil was very quick and reached up at 4 Tick Ticks only.
It was a lot of fun.
- This chapter was full of surprises for the students and for us, the teachers. We know from the studies of Jean Piaget (1896-1980), that children at this age are actively developing their quantitive notions: of number, weight, volume, length, time, etc.. We as teachers must provide them the right kind of experiences and the scaffolding that they need to develop these notions.
Piaget’s experiments suggest to us that children’s qualitative experiences of such attributes gradually develop into quantitative measures through the intermediate steps of comparison, seriation and use of a referent.*1 Chapter 9 of ‘Small Science Class 3’ aims to stimulate and support such ‘qualitative to quantitative’ transitions for number, weight, volume, time and temperature, while Chapter 10 focuses on ‘length’. Quantification is seen as a way of experiencing the world and communicating one’s observations, for the most part using everyday, non-standard units.
- Although the activities in these chapters are simple to carry out, we are continually surprised how much of a challenge they are when it comes to thinking through while doing them, especially when students’ intuitive notions differ from adult ‘commonsense’ ideas. Collaborative activities and spirited discussions on contradictory notions added to students’ engagement in the classroom.
For example, students’ conviction that two half cups of water may add up to less (or more) than one cup was difficult for us to counter, and it did not help that in the experiment of adding the water we probably made an error in checking the meniscus. Repeating of the activity was preceded by much anticipation and students were at least a little surprised at the outcome.
- The activity of making and testing a balance took a long time –- it’s better to reserve 2 full periods for it. Also it is important to let the children get the balance right after a lot of trial and error. Teachers shouldn’t take over this activity, however tempting it is to get on with the task. Children also kept forgetting to count the matchsticks when they were trying to balance other objects or they forgot how many they had put despite counting. I made them repeat the experiment, which they did without much complaining.
- The activity of filling the bucket needs to be done before the children understand the question. Initially I posed the question by just showing the mugs to the children. But they couldn’t state clearly that we would need fewer bigger mugs to fill the bucket. However when we started the activity, they immediately piped up with the correct answer. This difficulty is typical of problems involving proportional reasoning, which can often be addressed easily through concrete experiences.
- The activity with 5 containers and the exercise question about filling a bucket with water or sand are also not intuitive for most children and need to be done physically for them to understand. As a small school, we were able to have all the children do the exercises to see what happens.
- Students are getting better at reading the questions and recording in the workbook.
- Most students drew the water containers reasonably – but not exactly. They tried to mark the levels but weren’t very accurate. We felt this was perfectly natural at this age.*2
- Students knew their birth date and how old they were but only a few could accurately count how many months old they were.
- Some students wanted us to tell them when the school starts and ends but when we refused to ‘give answers’, they supplied the answer themselves. I think they weren’t confident of their answers and needed reassurance.
- Most students could easily arrange the times from the longest to the shortest. However most got stuck on the mango flowering and fruiting part. Some actually wrote it takes longer than a year. Others ignored it.
- As they have been doing a lot of gardening, students easily wrote the germination events accurately.
- The cold / hot questions were also easy.
- At first students ignored the ‘Ask and Find out’ questions on their own weight / milkman / dates of birth and temperature during fever. I assigned this as a home activity. One of the teachers brought her kitchen measuring jars – very typical in Tamil Nadu which are used to measure volumes of solids –- like rice and dhal — both in shops and at home. The children experienced how rice was measured.
- The ‘Figure it out’ questions are HARD! The first one got interesting answers which bore no relation to the question but may have been due to manipulating numbers: like “1 & ½”.
- Two students who attempted the Orange / Mosambi juice question intuitively got it right — “Same”. I’m not sure if that’s because “Same” was an easy answer — but it confirmed the comment in the Teacher’s book that the question may be easy for children who answer it intuitively but difficult for adults who try to reason it out logically.
Visitor from HBCSE
*1 Pande, P. & Ramadas, J. (2013). Students’ measurement experiences and responses to length comparison, seriation and proportioning tasks. In G. Nagarjuna, A. Jamakhandi, & S. Ebie (Eds.), Proceedings of epiSTEME-5 (pp. 145–151). Mumbai: HBCSE, TIFR.
*2 See the note on ‘drawing from observation’ in From inquiry to learning – 2. Also see the articles on this subject by Dr. Karen Haydock — who incidentally made the illustrations for Small Science Class 4.