Measuring toy planes
Some children were measuring some toy planes.
They used the ruler under each plane to measure its length.
This resource can be used to provide evidence of students' understanding of measurement of length.
- Measuring from zero
- Accurate use of a ruler with whole number units
- Accurately identify and use the half measure
- Accurately identify and use the tenths suggests (working at curriculum level 3).
| Y7 (03/2010) | ||
| a) | 8.2 cm (plus or minus 2 mm) |
difficult |
| b) | 6.5 cm (plus or minus 2 mm) | difficult |
| c) | 8.5 cm (plus or minus 2 mm) | difficult |
This assessment resource involves being able to measure length of images of everyday objects. Specifically it involves two ideas:
- starting a measurement at zero (not 1); and
- identifying and recording the sub unit of measurement (in this case tenths).
A significant number of students read the scale correctly to get the tenths, but did not start measuring length at "0". For question a) this is particularly prevalent as the object aligns with "1" which is a common starting point for numbers. For question b) this error is more difficult to make as the measurement is likely to involve some form of counting. Therefore errors will relate to starting point, counting and dealing with parts of centimetre units.
| Common response | Likely misconception | |
|
a) |
9.1-9.4 cm |
Not starting to measure at zero |
|
a) |
9 cm |
Measuring to the nearest whole number and not starting to measure at zero |
Not starting to measure at zero
These students need to explore measuring physical objects and count up as they measure the units. For example, use 1cm cubes in a line and build a scale by marking each added new cube. This way the count of the first cube results in the first measure which supports students to recognise where zero might be and that measuring starts from zero. This is an important understanding in measurement.
Students need to find out that the units stack end to end on each other to accumulate (as with non-standard units) and that a measure is a combination of these "non-overlapping units". Students can then begin to explore what it means when the measure is halfway (or a portion) of their standard measure.
Measuring to the nearest whole number
For students who did not measure accurately to the nearest tenth, ask them how they could describe a measure if it is not a whole unit so they could let somebody else know how far along beyond the whole number the measure was. Have them explore other practical ways of measuring lengths that involve parts of a unit. They could also look at the relationship between kilometres, metres and centimetres and talk about the need to find smaller units to help measure the length/distance accurately, and how these smaller units relate to the larger units.
Students could also start by working out how many of the "sub units (millimetre)" there are in a centimetre, and explore partitioning of lengths (or number lines) into different numbers. An important concept in measurement is that it is the space that the measure takes up that is the measure not the mark itself (the space between the marks). This idea is also fundamental to the definition of partitioning (which underlies the construction of sub-units).
Correctly measured the lengths
For students who correctly measured the objects to the nearest tenth, they could be asked how many millimetres their answers would be. They could also look at the relationship between kilometres, metres, centimetres, and millimetres, and identify the best (most appropriate) measure for a range of lengths/distances. See Millimetre, centimetre, metre or kilometre? or Units of measurement.