Maths to share - CPD for your school
Measure - mass
It is common with most areas of measure (length, capacity, mass) to find less progression in skills across key stages than there might be in other more frequently taught areas of the curriculum, such as calculation. Teachers often find it difficult to know where to ‘pitch’ their teaching, and so revert back to early skills and build up again. There can also be a reluctance to allow pupils to ‘play’ with measures and so practical activities are limited.
Before the session, ask teachers (anonymously) to write down and bring one ‘concern’, ‘anxiety’, or ‘area for development’ relating to the teaching of mass. Collect these together and group them if appropriate. Hold an open discussion around the points raised, and allow colleagues time to provide advice and support each other. All too often, pockets of good practice exist in schools, but are confined to individual classrooms.
This might be an appropriate point to ensure that all teachers are comfortable with the difference between ‘mass’ and ‘weight’. ‘Mass’ is the amount of matter or substance and can be measured in grams, where ‘weight’ is the amount of pull something exerts and is properly measured in Newtons. In space, a spaceship is weightless because there is no gravity, but its mass is the same as when it was on earth. We should continue to use ‘weight’ as this is the phrase children will be most familiar with, although they need to understand to what the term ‘mass’ refers.
It would be helpful to familiarise yourself and the staff with the units of mass and how they relate to other standard measures. You could take some information from this Wikipedia entry.
The article A Little Bit of History in issue 11 of the Primary Magazine focused on the history of weight, and is an interesting read. Encourage all teachers to do so – there are some interesting points to share with the children too!
Display the following question and allow colleagues time to consider how they might work towards an answer:
| Would you rather have a column of £1 coins as tall as you,
or a collection of 5p pieces as heavy as you?
Share the outcomes of their discussions. What key points do they include in their arguments? Ask them to consider the mathematical skills, equipment or key facts they would need to use to reach a solution. Did they use any estimation skills? For those wanting to calculate a solution, it may be helpful to know that the thickness of a £1 coin is 3.15mm, and a 5p coin weighs just 3.25g!
‘Open’ questions such as these, which require a great deal of exploration and application of skills, can be extremely useful in the classroom. Other ‘open’ questions might include:
- if you lined up counters for 1km, how much would they weigh?
- my dad says that together, he and I weigh nearly half as much as an elephant. Can he be correct?
- how much sugar does the staff get through in a week? (With this they will need to talk about the fact that they are translating a measure of volume (number of spoonfuls) into a measure of weight (grams and kilograms)).
Encourage the children to invent their own questions for the class to investigate.
Next, ask colleagues to consider the progression in ‘weight’ skills needed to be taught throughout EY/FS, KS1 and KS2. Provide them each with a copy of the skills sheet. Allow time for them to work in pairs to cut them out and rearrange the statements into the order they would first be taught. They might be able to add year group labels to some. Spend some time discussing the results, and sharing teachers’ ideas.
The importance of providing pupils with opportunities to ‘play’ or explore, at all stages, when weighing should not be underestimated. Teachers TV hosts a wonderful Number Crew clip Roller Coaster II, based on a problem of allowing different animals to ride a roller coaster, depending on their weight. It clearly demonstrates the early concept of measuring mass using uniform non-standard units, in a fun, child-friendly way. ‘Fishy Scales’ is a wonderful book by Calvin Irons, available in several formats, including ‘Big Book’. This is another fantastic starting point for discussing the early notion of uniform non-standard units, and estimating measures. It has bright illustrations and follows the story of the sea creatures trying to weigh each other under the ocean floor.
Once pupils are secure with the basic language of mass (‘heavier’ or ‘lighter’), and then the notion of uniform non-standard units, they can be introduced to accepted standard units, ie. grams and kilograms. Focus colleagues’ attention on this statement: Being able to convert units of weight from metric (kg, g) to imperial (pounds, ounces) and vice-versa, from the skills sheet used earlier. How necessary do they feel this skill is for pupils at primary school level? Why? Discuss the fact that ingredient quantities for many recipes are now given in both metric and imperial, and that most adults still only know their weight in stones and pounds.
Now ask them to consider the following question:
|Will all of the children in your class together weigh more than one tonne?
As teachers, we often ask children questions of a similar style in the classroom, e.g. ‘Do you think this shoe weighs more than one kilogram?’ when, in fact, they have very little concept of what a kilogram actually is, or feels like. Do colleagues have similar feelings regarding a tonne? If necessary, inform them that 1 tonne is equivalent to 1 000kg. If they can imagine filling a box measuring 1m x 1m x 1m with water (at 4° Celsius), then it would weigh a tonne!
With any of the areas of measurement, teachers should plan to teach the main concepts through practical activities which include:
- use of vocabulary
- knowing the relationship between units
- suggesting suitable units
- recording estimates
- reading from scales
- using standard metric units
- suggesting suitable tools.
There should be planned opportunities for problem solving, many good examples of which can be found on the internet. The NRICH site hosts a good selection of problems involving mass, at all levels. Children can submit their own answers too, and read those of other children around the country. Simple comparison problems can be used from a very young age, and can provide a useful insight into a pupils’ understanding. Examples could include:
|Five bricks balance a spoon. Three bricks balance a ruler. How many bricks will balance the ruler and the spoon together?
|These cubes balance these marbles... these marbles also balance the book. What can you tell me about the cubes and the marbles?
Above all, the most important aspect of teaching and learning measures is to allow time to experiment with ‘real life’ objects and situations. Worksheets asking young children to match objects to their weights, including items such as eggs and articulated lorries weighing approximately 50g and 44 tonnes respectively, are not ‘real life’ for most children!