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Learning area: Mathematics
Level: Years 5 and 6
Capacity sculpture
1 Nature of the assessment task
Students will build a structure or 'sculpture' from a number of junk objects (containers, boxes, tubes, etc). The structure will have a specified target capacity, and part of the assessment will focus upon the students' ability to construct a sculpture that will achieve that target. The task will involve measuring and recording the capacity of a wide variety of objects on a record sheet that will accompany the task.
The completed assessment task is expected to demonstrate the following qualities:
- evidence of accurate measuring in millilitres and litres using a range of appropriate measuring instruments
- understanding the relationship between millilitres and litres, and between millilitres and fractions of a litre
- ability to use problem solving strategies for measuring and solving the task with accuracy.
2 Links with State and Territory curriculum
3 Prior teaching and learning
For this task, students need to have an understanding of:
- the measures used for capacity, especially 1000 mL and 1 L
- the relationships between decimals of a litre and millilitres, and quantities containing whole and decimal fraction parts of litres – for example 1.25 L = 1 L and 250 mL, and also 1250 mL
- estimation of capacity in litres, millilitres and fractions of a litre
- the breaking down of whole litre quantities into fractional parts (eg 1 L into 600 mL and 400 mL, or 0.6 L and 0.4 L), the common fractional relationships such as half/500 mL, quarter/250 mL and the various other combinations of millilitres that make up 1 L (eg 900 mL and 100 mL; 250 mL and 750 mL).
In addition, students should be able to:
- read graduated scales of actual capacity-measuring instruments with a variety of labelled graduated intervals, and read real graduated capacity scales that use decimal fractions of a litre
- apply capacity measuring to solve a problem
- estimate the capacity of a range of common containers.
4 Teacher preparation
Student resources:
Other materials
Students will need access to a large collection of clean containers, boxes and tubes and measuring equipment. Teachers could encourage students to collect the following:
- clean plastic yoghurt pots, kitchen towel tubes, milk and juice cartons, small cardboard boxes, plastic drink bottles, medicine bottles. Even plastic straws and bottle caps can be collected – anything that can have its capacity measured.
Students will also need:
- a number of means of joining the objects: glue, thin wire, string, adhesive tape etc
- a range of containers to measure capacity: calibrated beakers, jugs, medicine spoons, medicine measuring cones
- water, as well as a range of dry materials to measure with – eg a jar of rice, beads, packing beads, lentils, small pasta items, salt, sand or anything that can be poured from containers into measuring items. If using food items, these should be kept in screw-top jars.
Teacher resources:
Teachers might find it helpful to examine an annotated worksample for the task. Further information about worksamples and how to use them can be found at this link.
5 Scaffolding: Preparing students for the task
The task suggested here is a practical one that asks students to apply theory to practice. Part of the teacher scaffolding is to promote discussion about solving problems involving these practical applications. It is recommended that in the preparation phase, plenty of opportunity is given for discussion and modelling by students. The discussion itself can provide valuable formative assessment opportunities by providing windows into students' thinking and understanding. Teachers should select from the following activities according to the prior experience of their students.
Throughout these scaffolding activities there will be informal opportunities to assess for learning, and opportunities to provide students with feedback on their progress.
Activity One
The scaffolding activities should focus on providing students with opportunities to practise using the measuring tools with both liquid (water) and dry (lentils, peas, salt, rice, beads, sand etc) materials.
- If students have only had experience of informal capacity measuring, set up a number of very simple measuring exercises using graduated measuring tools and containers, beginning with water as a measuring medium, and then using a dry measure. How much does a plastic cup contain? What is the capacity of a yoghurt pot? How much coffee does the teacher drink in one cupful at recess? Does a 325 mL soft drink can really contain 325 mL? There are many other options.
- Ask students to experiment with small measuring tools, such as a medicine spoon or 10 mL cup, to find out how many of each would be needed to fill a 50 mL cup while minimising spillage. This activity can be repeated several times if necessary with different sized measures. The resource Making 100 mL could be of use in this activity, although for students where this has been a part of earlier years' work this may not be necessary.
Activity Two
Students will also need to engage in practical scaffolding activities related to decimals of a litre and millilitres. Distribute copies of the Number line and ask students to order sequences of litre and millilitre quantities.
For example, put in order, smallest capacity first:
340 mL, 1 L 340 mL, 354 mL, 1.4 L
120 mL, 0.1 L, 1.1 L, 1200 mL
- Do you use millilitres or litres? Ask this question about measuring a series of containers – eg a teacup, a family-sized soft drink bottle, a bucket, a kitchen sink, a container of yoghurt, a saucepan. Make sure that estimation is used for each common container.
- Collect some 300 mL yoghurt or cream pots and ask the students to find out how many are needed to fill 1 L. Then pose the problem that after using the contents of three containers, the fourth one has some content left over. What size container would have been needed to make exactly 1 L?
- Model the equation:
300 mL + 300 mL + 300 mL + 100 mL = 1 L
also as:
0.3 L + 0.3 L + 0.3 L + 0.1 L = 1 L
(If necessary use the number line.) For a more advanced use of fractions, try using soft drink cans (usually 325 mL) where the decimal equation is:
0.325 mL + 0.325 mL + 0.325 mL + 0.025 mL = 1 L
Activity Three
Students will need to be prepared for the problem solving element.
Ask problem questions such as:
- 'Cough medicine comes in a 150 mL bottle. How many doses of 5 mL does that contain?'
'Kev runs a market stall that sells liquid detergent but only if you bring your own 2 L bottle. He has a drum of 140 L of detergent. How many sales can he make from that drum?'
A group/class oral discussion could be initiated by, 'A dripping tap wastes 500 mL every minute. Roughly how many litres of water will have leaked away in an hour? And, if it is not fixed, how many litres in one day (24 hours)?'
- Consider reading students the picture book Mr Archimedes' Bath by Pamela Allen, to encourage them to think about displacement as a problem solving tool.
- Make a small collection of objects that might be difficult to measure and have students discuss the problems they present, either as a class or in groups. Include objects such as a ball, a cardboard cone, a child's shoe, and containers that may not have the same capacity as printed on them (eg a milk carton). Ways of estimating as well as measuring should be discussed.
- Set up a problem of measuring an unusual shape and discuss ways of solving it with the available equipment. This exercise can involve small group discussions with a report back to the class. Don't do all of these or the problem solving element of the task will be compromised. Examples might be:
- a paper cone made by the teacher
- a triangular prism like a TOBLERONE™ packet
- a tennis ball
- a cardboard or plastic tube open at both ends
- a drink straw with a flexible top.
- Ask students to estimate the capacity of some of the containers in the classroom. Examples could be: a cup, a waste-paper bin, a spoon, a drink bottle from a student's lunch box. The estimating should indicate whether to use millilitres or litres, and the estimations should be checked if possible.
- Prepare the students for the problem solving element while at the same time working with decimals of a litre and millilitres. Use the resource Target measures. This depicts a target container at the top of each column and a set of smaller containers below. Each target container has a capacity that can be exactly filled with some of the containers. The task is to find the correct set. This task should be completed in small groups and the solutions discussed as a class while reminding students of the requirements of the task.
- The Target measures exercise can also be completed by writing a target on the class board and piling a number of containers, with their capacities named, on a table or the floor. Students are then challenged to get close to the given target using the containers available. Discussion might centre around how to cope with not having an exact solution. For example, if you need 250 mL to complete a target and you only have a 500 mL juice carton, try cutting the carton exactly in half.
6 The task
Explain the nature of the task to the students. Distribute the Task instructions: Capacity sculpture and Student rubric for capacity sculpture task to make sure that they understand how the task will be assessed.
- Students will work individually to produce a structure or 'sculpture' made of a number of different containers whose combined capacity measures exactly 4.35 L.
- Students may use any of the objects in the classroom set. To make the capacity of the sculpture fit the target they may (carefully) cut down the size of any object.
- Every container must be of a different capacity.
- The containers must be securely fixed together.
- Recording is part of the task. Recording must include:
- containers used
- estimation of capacity
- how they went about measuring
- problems that arose and how they were solved.
(In order that they provide evidence of an understanding of the relationship between litres and millilitres, and between millilitres and fractions of a litre, teachers might also insist that students show evidence of summing the total and converting.)
The Recording your sculpture worksheet should be used for this part of the task.
- Students could be encouraged to make their structures as attractive and original as possible, and teachers might consider allowing students to vote for the most attractive achievement.
7 Professional advice
Teachers could use the following diagnostic grid to record student performance on each of the expected qualities, thus obtaining a snapshot of those areas in which students will need further instruction. The teaching and learning activities that follow the grid are also related to each of the expected qualities and suggest some ways in which teachers could consolidate or extend performance. Click here for a sample diagnostic grid.
Teaching and learning activities
Evidence of accurate measuring in litres and millilitres using a range of appropriate measuring instruments
If students are performing at a low level on this aspect of the task, they need to work with measuring tasks that help them in the use of scales and in measuring with graduated containers.
Provide students with more opportunities to gain a concept of the size of millilitres by allowing them to measure with small graduated containers such as medicine spoons, medicine measuring cones etc. Further exposure to familiar containers such as spoons, soft drink cans, buckets and cups would be very valuable and help the students use these as personal referents when measuring. Personal referents will help the students to know that their measuring and interpretation of scales is reasonable.
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Students who are performing at a high level on this aspect of the task should be encouraged to explore the concepts of larger and smaller measures.
- Encourage them to investigate the language of capacity by finding the meanings of kilo (kilolitres), mega (megalitres) and giga (gigalitres) as well as micro (microlitres) and how they link with the units of millilitres and litres used in the task.
- This then leads to an investigation of how one measures very large and very small amounts. How does a water company measure the number of megalitres in a dam? How does the local council measure the number of kilolitres or megalitres in the local swimming pool?
- How is the water in our water supply dams related to the amounts of water we use daily? Most water meters read in kilolitres with fractions of a kilolitre. See the work suggestions relating to Water meters.
Teaching and learning activities
Understanding the relationship between millilitres and litres and between millilitres and fractions of a litre
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Students performing at a low level can practise with the Containers resource. This resource provides a number of pictures of containers that can either be slid around on screen or cut out to make up combinations of millilitres to add to the target capacities. More containers in the Word document can be made if required by using CTRL/select/drag or CTRL/D when a container is selected.
- Students could return to the Number line resource for help with relationships between fractions of litres and millilitres. It can be used to repeat the previous activity with 'containers', but this time they could be renamed using the number line as a guide.
- Students can continue practical measuring with 100, 250 and 500 mL flasks/jugs, common containers such as 300 mL and 600 mL milk cartons etc, to make combinations of millilitres that bridge 1000. The 1000 mL should then be related to the 1 L, and written results be expressed as 'x L y mL (eg 1 L 250 mL).
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Students who performed at a high level on this aspect of the task could undertake the suggested Water meters activity since it relates to higher level use of relationships through the decimal sections of the meter reading.
- Extend students' understanding of capacity relationships to megalitres and gigalitres, and discuss the place of these measuring units in the pantheon of metric measures (ie what the prefixes mega and giga mean in all metric measures).
- Provide students with opportunities to explore capacity relationships with cubic centimetres. This could move from areas where we interchange them automatically (eg engine capacities – cc for motorbikes and litres for cars), to areas where they are easily checkable (eg a 1000 block of centicubes or MAB 1000 block that fits snugly in a cubic 1000 mL container). Alternatively, find the number of millilitres of water that are displaced by submerging an MAB 1000 block.
Teaching and learning activities
Ability to use problem solving strategies for measuring and solving the task with accuracy
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If students have performed at a low level on this aspect of the task, provide a number of carefully scaffolded opportunities to develop problem solving strategies.
Students also need to have experience of brainstorming a variety of situations where non-standard, or creative, solutions need to be found to solve a problem. For example, these students may not have coped with the concept of measuring the capacity of an open tube, or of the need for a final 55 mL by working out how to cut an object at the correct position.
- Provide a number of odd-shaped objects and invite discussion about how they may be measured. A bent tube, a hollow toy and a shoe are a few examples that would provoke some innovative solutions.
- Discuss and demonstrate how a dry substance such as sand or rice can be measured in a measuring jug. (Some children have a fixed idea that a measuring jug is for liquids.)
- A number of small one- or two-step problems may be needed. For instance: I need 2 L but I only have a 200 mL container, or a 300 mL and an 800 mL container; or how can I get 1.5 L from bigger amount (eg 2.5 L of juice and an empty 500 mL container)?
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Students who perform at a high level on the solving of the problem should be able to tackle a number of extended problems relating to capacity.
- Students might investigate how many litres are needed to fill a swimming pool. This would also be a good way to introduce the need for kilolitres. How could we develop a set of strategies to solve this? Smaller versions of this task can be used for finding the capacities of other common containers around home that contain a large amount of water, such as baths, spas and paddling pools.
- Students might be asked to work out the number of litres of air in the classroom. (They could ignore some of the more difficult sub-problems such as identifying the capacity taken up by furniture, but include a good estimate of the space taken up by people.) As a straight capacity problem this may need to use sampling, which may need to be discussed after some thinking has taken place.
- A student might plan the amount of drinks needed for a large party. (This might involve a concept of average amounts children drink – something that could be determined by a survey.)
- What does it mean when we say that 15 mm of rain falls? How much rainwater might be captured in a rainwater tank from the roof of a building (eg a portable classroom) from a fall of 15 mm? What additional information do we need to find out?
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