Matching capacities
This task is about matching the capacities of everyday objects.
This resource can be used to provide evidence of students' understanding of capacity. In particular this resource assesses the ability to recognise the capacity of common containers using both litres and millilitres, which in turn underlies the ability to make meaning of measuring capacities. Giving a cumulative score for the number of parts of the question the student gets correct does not appear to give as useful an indication of a student's specific knowledge of capacity as looking at responses to the different containers.
Y6 (10/2010) | ||
a) |
1 litre Reasonable response (2 litres) |
easy very easy |
b) |
250 millilitres Reasonable response (50 mls) |
moderate easy |
c) |
10 litres* Reasonable response (4 litres) |
difficult easy |
d) |
50 litres Reasonable response (10 litres) |
difficult moderate |
e) | 5 millilitres | easy |
f) |
2 litres Reasonable response (1 litre or 4 litres) |
difficult easy |
a) - f) |
All 6 correct 4 or more correct 2 or more correct |
very difficult difficult easy |
Based on a representative sample of 201 Y6 students.
NOTE:
A reasonable response is the closest alternative from the list (in a proportional sense) that is in the same units as the correct answer.
* The bucket is approximately 10 litres (actually 9+ litres)
This resource is about assessing students' sense of capacity by asking about the size of everyday containers that are measured in either litres or millilitres. It is about students' knowledge and experience rather than being something they can solve. Sense of size is important knowledge in measurement, especially with regard to estimation. The items selected for this resource were everyday items that were intended to be accessible for students and teachers.
Prior knowledge
- Students need to know about litres and millilitres as measures of capacity.
- This resource relies upon students having experienced capacity maths problems and explored the size of different vessels for capacity. It is about their knowing based on experiencing and exploring capacity. They need benchmarks of containers that are measured in litres as well as in millilitres. Often these experiences are outside of school.
- Understanding the nature of estimation, especially for large capacities, is also helpful for this measurement resource.
Common response | Likely misconception | |
a) & f) |
2 litres (milk bottle) and 1 litre (ice cream container) |
Confuses 1 and 2 litres |
c) & d) |
Both bucket and rubbish tin incorrect, and the other four correct |
Lack of experience with large containers |
a) b) c) d) e) f) |
2 litres (milk bottle) 50 millilitres or 1 litre (glass) 4 litres or 50 litres (bucket) 10 litres or 500 litres (rubbish tin) 50 millilitres (teaspoon) 1 litre or 4 litres (ice cream container) |
Uses estimation to get close to the answer |
Confuses 1 and 2 litres
Some students correctly identified the milk bottle and the ice cream container as having 1 and 2 litre capacities, but thought that the milk bottle was 2 litres. This may be that the student has had little experience of 1 litre bottles, and sees all milk bottles as 2 litres. The exercise could be repeated using the real objects rather than pictures of them. Comparing an actual 1-litre and a 2-litre milk bottle may help the student see that the picture is of the former.
Lack of experience with large containers
These students probably have a sense of the size of 1 litre in smaller containers but not in larger containers, especially much larger ones. They need to estimate and investigate using water (or sand) how many litres go into other larger containers. They could use actual containers to build up from 1 litre to a 10-litre bucket, and then to a 40-litre bin. These larger capacities can then be used as benchmarks for estimating (or measuring) even larger volumes.
Uses estimation to get close to the answer
These students need to work further with a range of containers to refine their spatial awareness with capacity to higher levels of accuracy. They need to know the capacity of the containers they are exploring using whole litre measurement as well as millilitres. Relating 1 litre to the 1000s place value (or to the bottom half of a 2 litre milk bottle) is a useful way of visualising how large 1 litre is.
Students can also relate the ones place value block to 1 millilitre. They could use this to estimate the number of unit blocks in containers that are less than 1 litre, and that 1000 millilitres make up 1 litre. After this students should start to develop a sense of being able to estimate containers' capacity. They could follow these steps:
- Explore capacity by filling actual containers.
- Compare real objects. For example, they could estimate how many 1-litre milk bottles (or 1000's place value blocks) to fill a bucket; or about how many unit blocks it would take to fill a small bottle (up to 100mL).
- Checking capacities using a measuring jug, especially for small containers.
This helps them develop a wider experience of capacity, and a wider set of benchmarks for further estimation.