1. Capacity By Rebecca Last 0703174, Claire Pither 0808157, Kathryn Pittar 0812803

2. What is Capacity? Capacity is the amount of liquid a container can hold when full. (Mooney, Briggs, Fletcher, Hansen, McCullouch, 2002. Mooney, Ferrie, Fox, Hansen, and Wrathmell, 2002 and Haylock, 2005) “Volume is the amount of three dimensional space an object occupies.” (Mooney, Ferrie, Fox, Hansen and Wrathmell, 2002: p145) National Curriculum: KS1 Ma3 4a, c KS2 Ma3 4a,c (DfEE, 1999)

3. How capacity differs from volume “Volume is the amount of 3-D space which is occupied by an object. Capacity can be defined as a measure for the space with which a 3-D container can be filled.” (Dudgeon, 2006: p117) Internal volume can be referred to as capacity. (Dickson, Brown and Gibson, 1984)

4. Theory “Volume is the amount of three dimensional space something occupies and we normally measure this in cubic units. Capacity on the other hand refers to the actual container and describes how much liquid volume it can hold when full.” Measured ml or l. (Mooney, Ferrie, Fox, Hansen and Wrathmell, 2002: p67)

5. A possible issue when teaching “A litre jug will hold one litre of water when it is full (usually nearly to the top). However if the jug is half full, how should this be referred to? we could say that the amount of water was half a litre or, more precisely, that the volume of water was half a litre. It would be incorrect to say capacity.”(Suggate, Davis and Goulding, 2006: p177)

6. Vocabulary Full Empty Half full Holds more/less Millilitres (ml) Litres (l)

7. Key Points in the Learning Journey “Pre-measuring: comparing two or more objects and be able to order three or more objects.” “Using arbitrary units” For example non standard units such as cups, marbles and sand. “Using standard units” Progressing to the use of decimals. “At Key Stages 1 and 2 capacity is studied but not volume.” (Mooney, Briggs, Fletcher and McCullouch, 2002: p55) Volume is introduced in ks3 (Blair and Hughes, 2001: p49)

8. EYFS Shape, Space and Measures – involves talking about shapes and quantities, developing appropriate vocabulary, children use their knowledge to develop ideas and to solve mathematical problems. (DCSF, 2007; p. 1)

9. PNS KS1 Reception: Use language such as more or less. By the end of KS1 children should be able to: Understand and use vocabulary to estimate and compare two quantities. Measure using suitable uniformed non standard or standard units and measuring instruments. Choose and use standard units (DfES, 2006)

10. Key Principles Piaget identifies two fundamental operations upon which the measurement process is dependent. These are conservation and transitivity. (Dickson, Brown, Gibson, 1990: 83) Transitivity Conservation Comparison (ordering) (Suggate et al. 2001) (Open University, 1982) Using units to measure

11. Misconception KS1 “My container has greater capacity because it is the tallest!” “My container has greater capacity because it is the widest” (Dudgeon, 2006) “It appears there is more water in the second container. The children believe that the amount of water must have changed.” (p.118)

12. PNS KS2 Continue from KS1 but also: know the relationship between litres and millilitres. Yr 4- Yr6 children should be able to: choose and use standard metric units and their abbreviations when estimating, measuring and recording capacity. Use decimal notations and be able to convert between units e.g. 2.75 litres to 2750ml To Yr 7: use decimals to three places. (DfES, 2006)

13. Misconception KS2 “My container has a capacity of 1 litre” “My container is larger as it has a capacity of 1.5kg ”

14. Bibliography DCSF, (2007) The Early years foundation Stage, Problem Solving, Reasoning and Numeracy London: DCSF Mooney, C. Ferrie, L. Fox, S. Hansen, A. and Wrathmell, R. (2002) Primary Mathematics Knowledge and Understanding achieving QTS Exeter 3 rd edition: Learning Matters Ltd Suggate, J. Davis, A. and Goulding, M. (2001) Mathematical knowledge for primary teachers London: Fulton Suggate, J. Davis, A. And Goulding, M. (2006) Mathematical knowledge for primary teachers London: Fulton Mooney, C. Briggs, M. Fletcher, M. And McCullouch, J. (2002) Primary Mathematics Teaching Theory and Practice achieving QTS 2 nd Edition Exeter: Learning Matters Ltd Haylock, D. (2005) Mathematics Explained for Primary Teachers London: Paul Chapman Publishing Ltd Blair, H. And Hughes, P. (2001) Primary Mathematics Curriculum Guide London: David Fulton Dudgeon, J. (2006) Measures in Hansen, A. (2006) Children’s Errors in Mathematics Understanding Common Misconceptions in Primary Schools Exeter: Learning Matters Ltd DfES (2006) Primary National Strategy Norwich: DfES DfEE (1999) The National Curriculum London: DfEE Dickson, L. Brown, M. and Gibson, O. (1984) Children Learning Mathematics A Teacher’s Guide to Recent Research London: Cassell Educational Ltd Dickson, L. Brown, M. And Gibson, O. (1990) Children Learning Mathematics London: Cassell Education Ltd