Teaching Capacity

Capacity versus Volume

What is the difference?

Capacity is how much something holds (if filled to the top). The units for capacity are usually L or ml.

Volume can be used to

· refer to capacity i.e. the amount of liquid a container actually holds (usually L and ml)

·        refer to the amount of space taken up by a solid object e.g. cube.

In this case the unit for volume is centimetre cubes (cm3).

Foundational concepts:

Conservation of Capacity: Piaget's famous example of conservation was performed using liquids poured into different shaped containers. Though the volume of liquid remains constant across the two containers, each container has a very different visual appearance, with one being tall and thin, while another was short and wide. Younger children were characteristically fooled by the appearance of the containers and tended to conclude that wider, shorter containers held less water than taller, thinner containers

Watch this video https://youtu.be/gnArvcWaH6I

Teaching Capacity

 

Identifying the attribute: What is ‘capacity’?

To develop the concept of an object taking up space, children need:

·        Practical experiences of filling and emptying containers with sand and water.

·        Pouring experiences with containers of similar shape but different capacity and vice versa.

·        To fill containers with objects and build structures with blocks.

·        The hear and use appropriate language relating to volume e.g. it’s full, it’s empty, there’s no space left, it can hold more

Step 1: Number-free Comparison

 

Language:

 

 

Resource materials:

Large and small cartons, boxes and a variety of containers, yoghurt cartons, egg cups, plastic cups, spoons, colanders, funnels

Filler: polystyrene chips, sand, rice, pasta, water, cubes

Relationship cards e.g. holds the same as

Free play:

Allow children to play/sort/build with various containers. This allows the children to become familiar with the various attributes of the containers.

 

Have containers in the sand/water bath for filling and pouring. Allow the children to play freely. Encourage more accurate pouring and filling as the children’s muscular control improves.

 

Does it fit? Selection of individual objects with their individual containers

pair of sunglasses into a glasses case, ring in a ring box, small object in a match box,

teddy in a shoe box… Remove and ask: Is there enough room?  Have a variety of other boxes and containers-What will fit into these?

 

Integration: Measuring Volume: Integrating Art and Maths

Watch it in you own time: http://www.youtube.com/watch?v=P-HQK1fejXM

 

Full/nearly full/empty

Model pouring and filling sand/rice referring to full, nearly full, empty, etc.

Pupils find matching sets of containers: two yoghurt cartons, two egg cups, two plastic cups.

Fill one, leave the other empty.

Create 2 sets: ‘full containers’, ‘empty containers’.

What do you notice about the full container? Empty container? (Heavy/Light)

Class demonstration: same containers – one full with dry sand and the other with wet sand.

Are they the same weight?

Use a balance to check.

 

‘Holds more than’

Choose one container (e.g. a mug) as your reference container.

Pupils guess whether a given container holds more than the mug.

They devise ways to test their estimate by pouring from one container to the other.

Encourage discussion and justification – how did you know that?

Encourage careful pouring and filling of the containers.

Have plenty of examples.

Find three containers that hold more than the mug.

Make a set and display on the maths table.

Change reference container.

 

‘Holds less than’

Same activity to introduce holds less than

Do not introduce both concepts at the same time as this may confuse children

Ensure that all understand more than before moving onto less than

Have a collection of sets of matching containers (4).

We want to pick out bottles that hold the same amount of water, so that all children will have the same amount to drink.

Children pick out the matching containers.

Non-identical containers. Have a collection of containers that hold about the same amount.

Teddy wants 2 containers that hold the same. How can we help teddy?

 

Children may need support to use the correct language: https://youtu.be/OvnBytBkBKY

Use an interesting context to justify the comparison: https://youtu.be/nWYxsKbdf78

Direct Comparison

What could the task be?

Which container holds: More? Less? The same as?

Remember you watched a clip of direct comparison:

 

Consider the teaching points for direct comparison:

 

 

Prediction is easier when the containers are similar shapes:

 

Watch a pupil estimating and comparing the capacity using direct comparison: HERE

 

Brainteaser for children!

·        Use 2 sheets of A4 card

·        Tape 1 sheet length ways to make a ‘tall’ cylinder

·        Tape the other sheet with short ends together making a ‘small’ a cylinder

·        Ask children to compare the capacity of the 2 cylinders (predict, estimate)

·        Place the ‘long’ inside the ‘small’ cylinder

·        Fill the ‘long’ cylinder with filler (rice/sand)

·        Lift the ‘long’ cylinder

·        Both hold the same amount- why?

 

Indirect Comparison

Which has more liquid? Comparing the volume

Watch this video to gain a sense of when indirect comparison:

 

Is there a different approach that could be taken to compare the volume?

 

Capacity sort

Collection of labeled containers

One marked as the ‘target’

Students’ task is to sort the collection into those that hold more than, less than, or about the same amount as the target container.

 

Recording sheet on which each container is listed and a place to circle “holds more”, “holds less”, and “holds about the same”.

Get children to estimate first and then to measure using rice (or other ‘fillers’).

Discuss results.

Then sort/order containers according to the results

 

Comparing and Ordering

The previous activities lead children to ordering containers according to capacity.

Start by comparing three containers and arrange in order of capacity. New language includes holds least/holds most. The language of comparison is still relevant.

Context: Goldilocks and the 3 bears- how much porridge will fit?!!!

Links with video: http://www.youtube.com/watch?v=P-HQK1fejXM   

 

 

Comparing and Ordering

Watch this video where a variety of different containers are ordered: http://earlymath.erikson.edu/seriating-objects-by-length-and-capacity-with-child-21/

How could you make the task more complex?

Step 2: Develop & Use Non-Standard Units

 

Why introduce non-standard units?

While comparing and ordering containers determines which holds more/less/same  and/or the most/least, it fails to answer the question 'How much does the container hold?'. 

 

Initially children (from seniors infants) use non-standard units to describe the capacity of containers i.e. the maximum amount they hold.  

 

Non-standard units are everyday items. 

Remember in the introduction session, you measured the capacity of your mug using an egg cup?

 

Note: When finding the capacity of a container (i.e. the maximum amount it holds), the non-standard units is generally  a 'vessel'.

Water (or any other 'filler') is NOT a non-standard unit.

This is a common confusion for student teachers.

 

Advantages of non-standard units

·        Everyday/accessible materials

·        This involves the children iterating (or repeating) the unit- refilling and pouring into the container to be measured.

·        Children work with numbers they are comfortable with.

 

General principles for using non-standard units for capacity

·        Precision should be modeled and promoted in measuring. While you are advised to use alternative language to that used in the clip below, setting of expectations and clear modelling is essential for pupils to work independently and gain the most from their experiences. Note also that the filler here (rice) works effectively in filling containers.

 

Practical Work

Lots of activities can be used

·        How many egg-cups of rice will fill the cup? How many jugs of rice will fill the bowl? How many cups of rice will fill the large container?

·        Compare and order capacity of containers using non-standard units

·        Encourage children to estimate as it involves the students in developing a sense of the size of the unit.

·        Discuss the appropriateness of units of measure: When measuring a bucket’s capacity, which is more apt – cup/spoon? Discuss reasons for choice. Watch:

·        Stations could be used.

 

REMEMBER: CONTEXT!!!!

 

VIDEO 1               VIDEO 2

 

It is important to model the activity, setting out the ground rules: https://youtu.be/3GPw1PT76Ns

 

Exploring Volume using Non-Standard Units

In addition to lots of filling activities using liquids, pupils can pack

containers with marbles and blocks build different objects with

blocks and count the number of blocks used

Steps 3 & 4: Develop need for and use a standard unit

 

Discovering the unreliability of non-standard units

Just like the other strands (length, weight, area), while non-standard units are a good first means of measuring more precisely, it is important to allow students to discover the potential for confusion when communicating using non-standard units.

e.g. if you're making a smoothie and the recipe says to use two glasses of milk, depending on the glass you use, then the smoothie may be too thick, too runny!!

 

Therefore, it is essential to discuss the need for using standard measures of capacity/volume. The motivation to move to step 3 should spur from experiences where the pupils get different answers when measuring an identical container using the same type of non-standard units. They realise that while they are all using cups, they are using different sized cups- with varying capacities. This allows them to appreciate that consistency in the units used allows for easier and more accurate communication.

 

Introduction of the Litre

The first standard unit to be introduced is the litre. This unit is used as a 'benchmark', where pupils estimate and check (by measuring) whether various everyday containers hold more than a litre, less than a litre or exactly a litre. 

 

 

Watch this lesson introduction: http://www.youtube.com/watch?v=RwacEo8jYmA

 

 

Developing a measurement ‘sense’

The standard units can be made meaningful by looking at the volumes of everyday objects. For example:

·        the litre milk carton,

·        the 2-litre bottles of soda

Pupils should be give the opportunity to estimate and measure to see if these items have volumes greater than, equal to, or less than 1L.

 

Video Introducing Standard Unit

 

 

 

Step 5: Establish need for smaller and larger units of measurement

Smaller unit of measurement:

Identifying containers as holding >/</= litre is limiting and in order to measure precisely, it is necessary to introduce a smaller unit of measurement. While initially 1/2 litre and 1/4 litre could act as smaller benchmarks to compare against, in order to measure volume more precisely the millilitre needs to be introduced. It is recommended to develop an understanding of the size of 10 millilitres. (1 millilitre is too small to be appreciated).

 

Importance of hands-on experiences

Children should be given a range of everyday containers and a range of standard measuring vessels to have the opportunity to estimate and measure more precisely.  They will need to become familiar with understanding the scales on these and what the intervals represent.  

 

Real- life Applications: Value for Money

·        If you had to buy 3L of Flora Sunflower Oil what way would be the best value to purchase it if 1L costs €2.40 and 2L costs €5.99?

·        What is the price per litre of each of the following:

o   500ml of 7-up at €1.35

o   2L of 7-up at €2.19?

·        What sized container of 7-up is the best value per litre?

 

Video using ml