Different sized capacities

Different sized capacities

Online interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about ordering capacities in litres and millilitres.

Question Change answer

Drag the following measures of capacity in order from smallest to largest.
 
  • 50L
  • 0.75L
  • 5ml
  • 1L
  • 1250ml
  • 250ml
  • 1.5L

Question

Which measure of capacity is larger? 0.5 litre or 50 millilitres?

    • 0.5 litres

    • 50 millilitres

    • They are the same

Explain why you chose this option.
Task administration: 
This task can be completed online (with some auto-marking).
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Key Competencies: 
Using language, symbols, and texts
Keywords: 
capacity, conversion of units, work samples
Description of task: 
Students order litre and millilitre capacities from smallest to largest, compare given capacities and explain how they know whether one is larger/smaller or the same.
Curriculum Links: 
This resource can be used to help to identify students' understanding of capacity for Measurement. In particular this resource assesses knowledge about how big the capacity is in both litres and millilitres, and making simple conversions between units with decimals. 
Key competencies
This resource involves describing why 0.5L is greater than 50mL. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

When ordering these capacities it is important to look at two things: 

  • the ordering of all the measures in relationship to the other measures; and 
  • the method or strategy that students used to order the measures. 

Bearing this in mind supports students with their next steps. 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.

 

Y8 (10/2010)

a)

5ml 
250ml 
0.75L 
1L 
1250ml 
1.5L 
50L

 
All 7 capacities in the correct order 

very easy 
easy 
difficult 
difficult 
difficult 
easy 
very easy

 
difficult
b) i)
    ii)		 0.5L is larger than 50ml 
Accept explanations that correctly describe or infer the relationship between litres and millilitres such as: 

  • 500ml is half a litre which is more then 50ml
  • 0.5L is 500ml and 50 ml is 0.05L
  • One half a litre is larger than one-twentieth
  • Other sufficient explanations.
 difficult
very difficult

Based on a representative sample of 191 Y8 students.

Teaching and learning: 

This assessment resource is about being able to order a range of capacities in millilitres and litres. It involves understanding the relationship between litres (the units) and millilitres (the sub-units) and working (or converting) between them. It also involves understanding or knowing the size (capacity) of the given measures.

Diagnostic and formative information: 
Generally, students could order the capacities in terms of ml and litres (i.e., they knew that ml were smaller than litres). Most students identified the two smallest (5ml and 250ml) and the largest (1.5L and 50L) measures of capacity. However, there were a number of misconceptions around the relationship between litres and millilitres: ordering all the millilitres capacities first and then the litre capacities; or using 100ml = 1L or 10ml = 1L. The capacities that students had most difficulty positioning were 0.75L, 1250ml, and 1L. These involved decimal values and were closer in size. 

For part a) students may order the millilitre capacities from smallest to largest and then the litre capacities, but not know how to work between millilitres and litres (some way off understanding the relationship between millilitres and litres). This is not comparable to a simple substitution or transposition error, but shows they understand the relationship between litres and millilitres.

For part b) a significant number of students thought that 50ml and 0.5 L were equal, which, amongst other misconceptions, suggests they thought that 1L = 100ml. Other students indicated that 0.5 L was [always] bigger because litres are bigger than ml (insufficient argument).

See Student work samples [pdf] for examples of the different student strategies.

  Common response Likely misconception
a)
b)  i)
     ii)
 		 5ml - 250ml - 1250ml - 0.75L - 1L - 1.5L - 50L 
0.5L > 50ml 
litres are larger than millilitres 
 		 Incorrect relationship between millilitres and litres (oversimplification: millilitres are smaller than litres) 
Students indicate that millilitres are always smaller than litres (this was a very common misconception). This is an over simplification of the relationship between millilitres and litres. It may also relate to not knowing how many millilitres in a litre (below).
a)
b)  i)
     ii)		 5ml - 0.75L - 1L - 1.5L - 250ml - 1250ml - 50L
50ml = 0.5L 
100ml is one litre so half is 50ml.		 Incorrect relationship between millilitres and litres (incorrect ratio of ml to L) Students indicate that they do not know how many millilitres in a litre, e.g., there are 100ml (or 10ml, or some other number) in a litre.
a) 0.75L - 1L - 1.5L - 50L - 5ml - 250ml - 1250ml Incorrect relationship between millilitres and litres (indicates that ml > L) 
Students indicated that millilitres were larger than litres. They may be confused with other measurement units that the suffix makes larger (e.g., km and kg)
a) 5ml - 250ml - 0.75L - 1250ml - 1L - 1.5L - 50L Do not convert 1250ml to litres and order correctly 
These students correctly ordered the other 6 capacities, but had difficulty converting 
1250ml to 1.25L.
Next steps: 

Incorrect relationship between millilitres and litres

Familiarity with millilitre and litre units 
Find out how familiar students are with units of measurement for capacity before asking them to put capacities in order. The resources: Throwing a party, How many litres?, Different capacities, and Using orange juice explore working out millilitres and litres with specific containers and could be used to develop students' understanding about how many millilitres make up 1 litre. Having students work by measuring capacity using scales (showing millilitres and litres) may help them to recognise the ratio relationship between the two units. 

Developing sense of size 
It may also help for students to develop a sense of the size of capacity measures. The resource Millilitres or litres? looks at whether millilitres or litres are the best measure for a range of everyday containers. They could also explore how many of one everyday container fit into another in the resources More or less than a litre and How many millilitres?. The resource How much to fill it? gets students to match up containers to their capacities. If students are uncomfortable using millilitres and litres, they may want to simply look at non-standard measures, e.g., how many jars fit into this container [Predicting capacity]. 

Converting millilitre to litres for decimal values:

Cannot convert 1250ml to litres and order correctly
Students who have difficulty converting whole numbers to the decimal fractions and vice versa for working with measurement units could explore the pattern of what happens when a number is multiplied or divided by ten (and powers of ten). They could also work with multiplying decimals to see that decimals work very similarly to whole numbers and ratios (which underlie scales). This may support their understanding of how to move between millilitres and litres. They may also need to explore actual measuring of capacity with measuring jugs and look at the scale to see both millilitres and litres together, for example, the resource How many millilitres? It would help to have a large container (e.g., 2 litres) with a scale of both units.