Capacity and Volume Some activities for the Primary years

Transcription

1 Capacity and Volume Some activities for the Primary years Doreen Drews 1

2 Capacity Capacity:- The amount that a container can hold. The inside space is therefore measured. The standard measure used is litres. A useful starting point for group/class activities is to focus on containers. A collection of containers would make a useful display and could form the basis for discussions and practical tasks. Think about providing: a) containers which belong to the same shape family but with different capacities, b) containers which have approximately the same capacity and are similar shapes, c) containers which have approximately the same capacity but are all different shapes, d) containers which have different shapes and different capacities. (It might prove useful to make up four collections, as described above, to enable children to focus on specific aspects of containers, their shapes, and capacities.) Other materials which will prove useful junk materials, strong plastic containers, marbles, beads, bricks, small cubes, pasta, sand, rice, peas, water, measuring jugs, bowls, large trays, scoops, clixilpolydron and card. Throughout activities, aim to develop children s estimation and ordering skills. Using Clixi/Polydron 1. Using up to 10 pieces for each, make two different containers with lids 2.. Guess which holds more. Use two different methods to find out. 2. Make a container, with a lid, to keep one of these toys in. Try to make a snug fit. 2

3 3. Make a container which is a different shape, but which will have approximately the same capacity as this bottle or tub. 4. Can you make two different containers that will each have a capacity of approximately 500 cubic centimetres? 3

4 Using Junk materials 1. Estimate first, then put the bottles in order by capacity. 2. Use another method to put the boxes in order by capacity. Do any hold the same amount? 3. Can you make another container which looks a different shape but which has approximately the same capacity as this tub? 4. Five of these containers have approximately the same capacity. One container has - a different capacity. Which one is the odd one out? 4

5 Which holds the most? My guess holds most holds least We found out holds most holds least This is how we found out the order of our containers. 5

6 Which is the odd one out? Draw the six containers and put a ring around the odd one out. This is how I found out which container was the odd one out: 6

7 Using paper and card 1. Using 2cm squared paper, make an open box which has a capacity of 12 multilink cubes. How many different shaped boxes could you make which would each have a capacity of 12 multilink cubes? Compare the size of a centicube (1cm cube) to a multilink cube (2cm cube). How many centicubes could your 12 box hold? 2. Using a sheet of A4 card construct an open box. (You may use scissors, glue or sellotape to help.) Can you make the box which holds the most? 3. Design and construct a container (which must close in some way) to hold one of the objects in front of you. The object should fit snugly inside your box. Try to make your container as unusual, and attractive, as possible. 7

8 Which holds the most? Materials: Identical pieces of card. Sellotape Making: Take one sheet of card and make a container Sellotape it so there is not overlap. (Do you want a base or a lid?) * How many other kinds of containers can you make? (Remember, use only one sheet of card for each) Predicting: * Order your containers according to which holds the most. Testing: Now test out your predictions by filling up each container with something that pours - - rice, macaroni or dried peas are ideal. Weigh the contents. * Do they hold the same amount? 8

9 Developing the idea: Cut one sheet of card in half. Make two identical containers. Now take another sheet and make a large container the same shape. * which holds the most, the two small containers or the one large * What would happen if you halved the sheet this way? * What would happen if you divided the sheet up into four? EXPERIMENT * Design a container to hold a set amount, eg of rice, macaroni, etc. * Suppose your container had to be packed into a large cardboard box. Does this change your answer? * Which shapes hold the same amount? 9

10 Design and Construction Take a sheet of paper, e.g. 84 x 59 cm Decide what item your bag will hold bag will hold. Think about: - seams - handles - strength - folding for storage Design a carrier bag for a specific object. Contact a manufacturer - for information - for a market Make one - note the faults Test for strength Redesign Make them for sale - cost of paper - labour -- best value for money Compare bags for: size volume strength 10

11 Volume Volume: The measurement of the space occupied by a solid object. The standard measure used is cubic centimetres/metres. a) Children need many, varied, activities to develop an understanding of conserving volume. Plasticine. multilink and centicubes are useful materials for this purpose. b) Activities should not focus exclusively on the construction, or observation, of cuboids as children could make mental links that volume is only concerned with the measurement of cuboids. c) When appropriate, children need time to investigate the relationships between capacity and volume in order to make sense of displacement activities. d) For some children, links can be made between formulas for area of plane shapes and formulas for volumes of prisms. 11

12 Using Multilink 1. Building Cuboids you can to the size of your box. Record your multilink cuboid on the paper of your choice. Using the same amount of multilink build a different cuboid. Record this cuboid on the paper of your Choose a cuboid box from the collection. Using multilink, build a cuboid as near as choice. Experiment to find out how many different cuboids you can make, using the same amount of multilink each time. What is different about all your cuboids? What is the same about all your cuboids? 2. Build yourself a collection of 4 cuboids. Each cuboid should use a different amount of cubes. Which cuboid has the greatest volume? Which cuboid has the least volume? 3. Multilink Animals Make an animal using no more than 10 Multilirik cubes. Make a different animal with the same volume. Compare the animals. Make an animal with twice the volume of the first. Make an animal which is an enlargement of the first, but twice every length. Is it twice the original volume? What is the volume of each animal in cubic cm.? 12

13 4. Multilink Cuboids Using 24 Multilink cubes each time, make as many different solid cuboids as possible. Record and name the cuboids on paper of your choice. Choose one of the cuboids as your original and build three more solid cuboids by. halving 1 dimension of your original, halving 2 dimensions of your original and, halving three dimensions of your original. Compare the volumes of the four solids. What would the volume of each be in cubic centimetres? 13

14 Using Card or Paper 1. Halving Dimensions Choose a cuboid box from the selection available. Using card or paper of your choice, make... a) a box which has halved one dimension of the original; b) a box which has halved two dimensions of the original and c) a box which has halved three dimensions of the original. What has happened to the volume of each box in comparison to the original box? 2. Twice/Half the Size Choose a box from the selection. Using card or paper of your choice, make a box which is either twice the size, or half the size of the original. Compare the capacities and volumes of the two boxes. 14

15 Developing relationships between capacity and volume The link between volume and capacity can be demonstrated by water displacement of irregular objects. Such work will only be meaningful to children if they have had opportunity to investigate the relationship between 1 litre of water and 1000 cubes (cm). An open plastic cube measuring 10cm x 10cm x 10cm may be filled with centimetre cubes and the capacity/volume recorded as 1000 cm 3 (The identical size cube can be constructed adjacent to the plastic cube to show that the capacity and volume are the same except for the amount of plastic.) If the centimetre cubes are removed, the children can measure the capacity of the plastic cube using a graduated litre measure. The discovery that 1 litre of water has the same volume (capacity) as 1000 cm 3 is a very important one. Through further experimentation the children could also discover a relationship between water, cm 3 and grammes. 1 litre of water has the volume of 1000 cm 3 and the mass of 1 kilogram. Oranges How much of an orange is juice? Estimate the volume of an orange and its juice. Now measure each. Show the volume of each in centicubes. How many oranges like this would you need for 1 litre of juice? 15

16 Exploring the volume of Poleidoblocs Poleidobloc blue cube red cube red cuboid green cuboid yellow cuboid blue cuboid red triangular prism Volume (in blue cubes).one (blue cube) Make a building which has a volume of 24 blue cubes List all the blocs you used. Now make a building which has half the volume. DDIRJB/