Mass and capacity without a worksheet

Mass and capacity

without a worksheet

Mass and Capacity Activities Developed by the

West Sussex Leading Mathematics Teachers

The following activities have been tried and tested by the

West Sussex Leading Mathematics Teachers.

They are designed to be investigative, open ended and

easily differentiated.

These areas were chosen to enhance the teaching of MA

3 and to move away from worksheet based activities.

These activities have been devised to provide good MA1

and MA3 assessment opportunities. The Assessing Pupil

Progress documents have been used and referenced in

the document.

Mass Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: MASS

TITLE OF ACTIVITY

Penguin Post

This could also be related to Christmas presents or birthday presents OBJECTIVES (from Framework)

Compare non standard units

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) Use developing mathematical ideas to solve practical problems Use language such as heavier and lighter to compare quantities DESCRIPTION OF ACTIVITY

Freedom and Play

Bucket scales available. Objects, parcels, food stuffs e.g. apples, rice

Read story Penguin Post. The adult penguins leave the baby penguin in charge of the post office. Wrap parcels decide are they light or heavy?

Sort into sacks light /heavy.

Vocabulary: light heavy same lighter heavier Resources

Parcels weighing scales Plenary

Weigh the parcels using weighing scales SUPPORT AND EXTENSION OPPORTUNITIES Make your own parcels to add to the sacks

Mass Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: MASS

TITLE OF ACTIVITY

Heavier or lighter

OBJECTIVES (from Framework)

Year 1 – estimate, measure, weigh and compare objects, choosing and using suitable non-standard or standard units

MA1 Describe ways of solving puzzles and problems

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) Using and Applying Level 1 and 2

Ma3 level 1 extension level 2 DESCRIPTION OF ACTIVITY Introduction

Discussion around the terms heavier and lighter.

Which object do you think is the heaviest? How can you find out? Why do you think it is the heaviest?

Send children to find a heavy object and a light object in the classroom – does it always relate to size? Join with a partner. Put the 4 objects in order, estimating using hands. Vocabulary: heaviest, lightest, equal, balance

Activity

Children to have a group of objects on the table. E.g. fruit, toy cars, pebbles (choose items linked to topic) work in mixed groups with the more able the only ability group working together.

Key Question – which is the heaviest? Which is the lightest? How can you find out? Make a guess before you start.

Resources

Children to be given balancing scales and the objects to order

Teacher to try and ensure that the largest item is not necessarily the heaviest. Also try to get a range of items eg fruit.

Mini plenary

How did you find the heaviest/lightest? Which did you think it would be? Why? Is the actual answer the same as you thought? Children to go back to their objects and try to put them in order

Plenary

How did you order the objects? Did you find it more difficult than you thought? Did you agree? Share the different ways the children ordered the objects. SUPPORT AND EXTENSION OPPORTUNITIES

Support – mixed ability peer support

Mass Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: MASS TITLE OF ACTIVITY

Is the biggest box the heaviest?

OBJECTIVES (from Framework)

To be able to estimate and compare weights. To read a scale to the nearest labelled division. To begin to use everyday non-standard and standard units to measure mass. To know which measuring tools to use to find how much an object weighs.

(APP Level 2 measures guidelines)

Discuss their workings using mathematical language. Explain why an answer is correct? Use apparatus to represent and clarify a problem.

(APP Level 2 MA1 Guidelines)

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) During the lesson there are opportunities to assess the above DESCRIPTION OF ACTIVITY

NB: This activity would be better if completed in small groups throughout the day/week due to the number of resources needed. The lesson is planned bearing this in mind. RESOURCES:

5 boxes of different sizes (to include a long and tall box and a very small box). Boxes to be labelled A-E. Each box to contain a bag of sand weighing different amounts that the children will be able to read on a scale.

ENSURE THE SMALLEST BOX WEIGHS THE MOST. REMEMBER TO INCLUDE THE WEIGHT OF THE BOX AND THE BAG OF SAND WHEN CREATING YOUR DIFFERENT WEIGHTS. Selection of weights and measuring scales and weights.

Introduction

Show the children one box. What can they tell you about the box? (Steer towards

language related to weight). Introduce a second box – do they think this box is lighter or heavier just by looking? Discuss the problems with just looking and the need to hold the box.

Main activity

Children to be introduced to the 5 boxes and the question ‘Is the biggest box the

heaviest? Why?’ Ask children to predict an order and record this. Allow children time to explore the question without any apparatus before introducing a range of measuring equipment for children to choose from. Children will need to prove their answer and record this in whatever way they choose.

Plenary

Children to present their findings to the teacher, discussing their choice of order at the beginning (prediction) and their final choice and the reasons behind their decisions. Introduce a final box and ask them where they would put it in relation to the other 5 boxes and why. Teacher to look for use of vocabulary, accurate reading of scales and explanations

SUPPORT AND EXTENSION OPPORTUNITIES

If this was carried out as a whole class activity the teacher or TA could support less able/extend more able. For less able children the weights of each box could be a whole

Mass Activities Developed by the

West Sussex Leading Mathematics Teachers

YEAR GROUP 4

FOCUS: MASS TITLE OF ACTIVITY

A filled mug will weigh the same whatever the contents. - Always true, sometimes true, never true.

OBJECTIVES (from Framework)

To know the meaning of kilogram and gram. Where appropriate use decimal notation. To be able to interpret scales.

To be able to read and record accurately.

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) To use non-standard and standard metric units of mass.

(APP Level 3+ measures guidelines)

Try different approaches and find ways of overcoming difficulties that arise. Discuss their mathematical work and begin to explain their thinking.

Understand a general statement by finding particular examples that match it. (APP Level 3+ MA1 Guidelines)

DESCRIPTION OF ACTIVITY Resources

One mug per group and a variety of items that can be used to fill the container e.g. sand, salt, marbles, clay, rice, multilink, counters. Range of scales for weighing.

Introduction

Discuss with the children the following terms:

Always true, sometimes true, never true. What do they mean and can they give an example for each? The pupils are shown a mug which is filled to the top (NOT

OVERFLOWING!) with sugar and the statement ‘a filled mug will weigh the same

whatever the content.Always true, sometimes true, never true.’ Discuss initial thoughts briefly and ask children to prove whatever response they choose.

Activity

Children to use the resources available to find an answer that matches the statement. They will fill the mug with one of the items e.g. rice and record the weight. They can choose whether they want to include the weight of the mug but they must be consistent. Children will need to devise their own ways of recording and generate evidence to

support their final decision. Plenary

Teacher to put the headings ‘Always, Sometimes, Never’ on the board and each group to put a tick under the heading they agree with. Do we all agree? Children to present their findings to support their decision and encourage them to use correct mathematical vocabulary. Discuss whether they think the investigation was carried out fairly. Were their results accurate? Could they have improved their investigation? (Science link).

Mass Activities Developed by the

West Sussex Leading Mathematics Teachers

SUPPORT AND EXTENSION OPPORTUNITIES

Changing the container, Changing the materials offered, The types of scales used

YEAR GROUP: 5

FOCUS: MASS

TITLE OF ACTIVITY

Clay weights

OBJECTIVES (from Framework)

Y5 – Read, choose, use and record standard metric units.

Interpret a reading that lies between 2 unnumbered divisions on a scale. MAI – Plan and pursue an enquiry, choosing appropriate strategies and explaining reasoning.

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) U & A L4

Reasoning and problem solving MA3 Measures L4

Bullet point 1 & 2

DESCRIPTION OF ACTIVITY Introduction

Teacher recapping facts about mass. Estimating the weight of objects and checking with weights and scales.

Differentiated questioning e.g. - Which object is heaviest/lightest?

- How many more packets of biscuits (for example) would you need to reach a kg? (Children using whiteboards to support)

Vocabulary:

Mass, weight, compare, strategy, method, scales, trail, improvement, persevere Activity

Working in ability groups (but can be mixed ability depending on your class)

Children had to read the CLAY WEIGHTS problem and discuss as a group. Once they felt they understood the problem, they had to work in pairs to solve it.

Children had a sheet to record jottings and thoughts (see suggestion below). They had to work out the weight of the balls before they could use the clay. Resources were selected by the children from a list of the following:

- Balancing scales, digital scales, analogue scales, clay, weights, spare paper, tissue paper.

Plenary

Children fed back whether or not they had solved it and then: - How they tackled the problem?

Mass Activities Developed by the

West Sussex Leading Mathematics Teachers

Clay Weights Problem

Make 3 clay balls

Make sure 1 ball is half the weight of another

Also ensure that the third ball of clay is the lightest and weighs between 60g and 100g The total weight of your 3 clay balls should be 500g

First work out what each ball will weigh! Record your workings out

Headings for Jottings sheet

Work out what your clay ball will need to weigh

Work out other ways you could have made the clay balls. What would they have measured?

What did you have to think about when solving this problem? - How did you eliminate particular measurements?

- What mistakes did you make? - What did/didn’t work?

- Why?

- How did you elicit the important information? - What did you find easy/tricky?

- Why? N.B.

This task can be adapted to suit Y4 and Y6 objectives and match the L3, L5 APP criteria. SUPPORT AND EXTENSION OPPORTUNITIES

Support

The question changed – Make 4 clay balls that equalled 100g in total

Can you do it so all the balls are not the same weight? Extension

Is this the only solution to the problem? How do you know?

Mass Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: MASS TITLE OF ACTIVITY

Fruity Fun

OBJECTIVES (from Framework)

Select and use metric units of measurement.

Convert between measurements using two decimal places. Read and interpret scales.

To be able to approximate different weights.

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress)

To be able to read and interpret scales on a range of measuring instruments, explaining what each labelled division represents.

To solve problems involving the conversion of units. Choose and use appropriate units and instruments. To make sensible estimates.

(APP Measuring Level 4/5)

Present information and results in a clear, organised way.

Identify and obtain necessary information to carry out a task and solve mathematical problems.

(APP MA1 Level 4/5)

DESCRIPTION OF ACTIVITY

NB This lesson would be a good assessment task after direct teaching of weights, conversion between grams and kilograms and ratio.

Resources

Variety of scales, variety of fruit, chopping boards, knives (NB: Ensure children are aware of safety issues)

Introduction

Teacher to use the mental starter to recap conversion between grams and kilograms. Introduce the children to the recipe for ideal fruit salad

E.g: For 4 people - 150g oranges, 250g apples, 140g bananas, 90g grapes, 60g strawberries

Explain to the children that they have to make the recipe for 10 people and that they have to write out the new recipe using grams and kilograms for each item of fruit. Once they have their new recipe they then have to make the fruit salad within their groups, weighing the fruit accurately!

Plenary

Class discussion to share the strategies they used to generate the new recipe. Did we all agree on the new amounts? What did they find difficult and how did they overcome it? Teacher to test the children’s ability to weigh accurately by weighing the bowl of fruit salad for each group (it should equal the total weight of all the fruit in the recipe for 10 people). Was anyone spot on?

SUPPORT AND EXTENSION OPPORTUNITIES

Mass Activities Developed by the

West Sussex Leading Mathematics Teachers

Capacity Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: CAPACITY

TITLE OF ACTIVITY

Full/Empty Jack – Full Jill - Empty

OBJECTIVES (from Framework)

- To understand the concept of full and empty

- AA to understand the concept of ½ in a practical context ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) - Self initiated play in water trays.

DESCRIPTION OF ACTIVITY Theme - “Water Week” Pirate topic

Could be related to Jack & Jill rhyme Introduction:

Bucket – empty bucket, pretend it has water in it. Accidentally trip, talk about pupils’ reactions. Use language full / empty.

Fill the bucket, how much is in the bucket? Is it full?

How could we fill it? Activity:

Children to find different ways to fill the bucket/containers.

(choose appropriate materials/objects from the classroom/outdoor environment) Objects available in water area:

Buckets, some buckets with holes, watering cans with different spouts, measuring cylinders, small containers (different sizes & shapes) e.g. teacups, squash bottles. L1 Objectives

Measure objects using direct comparison. Order the objects, which holds the most? Use the language of litres and ml.

SUPPORT AND EXTENSION OPPORTUNITIES

Extension:

Measuring cylinders of different capacity.

Which one holds the most?

Capacity Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: CAPACITY

TITLE OF ACTIVITY

Professor Plumber’s Problem

OBJECTIVES (from Framework)

- Answer a question by selecting and using suitable equipment, use these to solve the problem

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) - Through observation and listening to the pupil’s responses.

- Engage with practical mathematical activities involving measuring DESCRIPTION OF ACTIVITY

Water Tray  Incy Winsy Spider context Themed “Water Week”

Mr Plumber book

Pipes and attachments in the water tray.

Problem: How can we get the water to travel through the pipes? What equipment will we need?

Can we catch the water?

Selection of different sized water containers, watering cans, teaspoons and graded measuring cups. Watering cans with different spouts.

Present problem to small group of pupils. Children explore problems in groups. SUPPORT AND EXTENSION OPPORTUNITIES

Extension:

What shall we catch the water in?

Which container would not be suitable? Why? Support:

Capacity Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: CAPACITY

TITLE OF ACTIVITY

Fill your Buckets! (Seaside activity)

OBJECTIVES (from Framework)

To estimate, measure and compare standard and non-standard units ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) MA1 Using mathematics as an integral participant of maths activities Discuss their work and draw simple conclusions

MA3 Order objects using direct comparison DESCRIPTION OF ACTIVITY

Choose a container to hold water.

Competition- you need to walk along the line (masking tape on the floor) and fill your bucket (situated at the end of the line) without spilling water.

When the first bucket is full, stop the group and discuss why they won: share ideas Key Questions:

How can we make the race fairer? How can we fill it quicker?

How will we know it is fair? Record tally or number of times we filled the container Repeat the bucket challenge but this time they all use the same container so that children understand the need for using standard units.

When do we measure liquid?

What do we measure liquid with? Show jugs with scales on. Resources

A variety of containers of different sizes and scales e.g. cups, plastic glasses, teapots, plastic bottles, egg cups, plastic buckets (bucket and spade size)

Extension

How many of these will fit in this? (Litre containers)

Estimate and measure how many litres in the big buckets? How many buckets will be needed to fill the water tray? Find out and record.

Support

Capacity Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: CAPACITY

TITLE OF ACTIVITY

How to tame your dragon

OBJECTIVES (from Framework)

Y2 to compare measures using standard units and to be able to read scales in litres and millilitres

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) Level 2

Ma1 selecting the maths that they use and begin to represent their working in simple diagrams

Ma3 begin to use everyday standard and non standard units DESCRIPTION OF ACTIVITY

Prior to the lesson there will need to be a series of lessons on reading scales and using measuring equipment e.g. using different size containers like litre of orange, 330 ml coke can, teaspoon, 2 litre coke bottle. Also prerequisites needed are reading different scales and for more able children to know that 500ml is equal to half a litre.

Problem (FIRE and ICE Topic)

The dragon needs to be tamed in order to rescue the princess we need to make a potion with the capacity of 1 litre. (You must use a minimum of 2 different liquids.)

Key Questions:

Which liquids shall we use? How can we measure the liquids? How can we record/represent our recipe to show our mathematical thinking?

Key Vocabulary:

Capacity, scale, measure, more/less, standard/non-standard units, litre, half a litre and millilitre.

Resources:

A range of standard and non-standard equipment available.

Non Standard: Mugs, jugs with no scales, glasses, watering can and teapot. Standard: Measuring jugs, scaled cylinders of different widths and heights.

Different Liquids:

Water mixed with food colouring to create different colours, Washing up liquid, Milk, Squash

Ask the children to make a visual representation of their potion and include measures on the diagram.

SUPPORT AND EXTENSION OPPORTUNITIES

Can you use more than 2 different liquids? Can you record your measures in more than one way?

Further extension: Have a list of specific measurements with the liquids for example; you can only use 100ml of green water, 50ml of red water.

Support: Use containers that are ½ or ¼ of a litre and find out how many needed to make a litre.

Capacity Activities Developed by the

West Sussex Leading Mathematics Teachers

YEAR GROUP 3

FOCUS: CAPACITY

TITLE OF ACTIVITY –

What is capacity?

OBJECTIVES (from Framework)

Read, to the nearest division and half-division, scales that are numbered or partially numbered; use the information to measure to a suitable degree of accuracy.

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) Use non standard and standard units for capacity MA1

Read scales

DESCRIPTION OF ACTIVITY

Have a selection of objects on the table - standard and non standard e.g. jugs, litre bottle of orange, mug, teapot, can of coke, 2l bottle of coke, jugs with no scales

Key Questions What does capacity mean?

I need to find out about the capacity of these containers how can I find out? What skills do I need?

1. Begin to estimate the capacity by ordering the objects from the container that holds the smallest amount to the largest amount.

2. Find out the capacity- learn how to read scales. Colour the water to make reading the scales easier

3. Write labels for each container

4. Consolidate knowledge on iboard TES free resource, capacity, you have to estimate the capacity of the objects and then pour and check if your estimate is correct.

Extension

Use labels ½ L =500ML 250ML= ¼ l 1l=1000ML Support

Simplified scales on the jugs

Capacity Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: CAPACITY

TITLE OF ACTIVITY

Is tallest wettest?

OBJECTIVES (from Framework) Use standard metric units

Interpret intervals & division particularly numbered when estimating Report solutions to puzzles & problems

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress) - Use standard metric units

- Read simple scales

- Organise their work & check results DESCRIPTION OF ACTIVITY

Starter

IWB – Match image to the capacity - 2L bottle, 1L bottle, 500ml, 25ml, 5ml, 330ml can Discuss the order

Input

Estimate the amount in a selection of shampoo bottles. Put them in order of capacity. Find the actual capacity. Find out whether the tallest is the wettest.

i.e. does it contain the most liquid?

Children are then given the opportunity to present their results. Plenary

Write the actual answers on pieces of card. Move around to next table and match the card to the bottles.

Capacity Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: CAPACITY

TITLE OF ACTIVITY

Space Cocktails

OBJECTIVES (from Framework) APP L3 L4 Measures Assessment opportunities

Choose and use appropriate units and measurements Interpret and read scales with accuracy

Use standard units of capacity in a context

ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress)

Observe and record pupil responses – reasoning skills, why they were not going over a certain limit.

DESCRIPTION OF ACTIVITY Input prior to lesson

ITP measuring cylinders – reading scales and using standard units. Children had paper scales to read and interpret. Same to read and interpret. A mixture of scales necessary for differentiation.

Main lesson

Quick recap on ITP measuring cylinders. Selection of coloured squash in jugs.

Task: Make a space cocktail, record the amount of liquid for each part of the cocktail. Not allowed to go over 100ml.

Differentiation: Less able are only able to choose 2 coloured liquids. More able are able to choose up to 4 colours

Pairs checking the measurements.

Recording -> the colours they used, the amount and proving it did not exceed the limit of 100ml.

More able: not allowed to use multiples of 10. Key questions:

My cocktail measures no more than 100ml. I can use any of the flavours.

What flavours shall I use? When working with children. How do they know?

These activities could be adapted to meet Year 3, 4, 5 and 6 objectives. Objectives

- Choose and record standard metric units

- Measure capacity to a suitable degree of accuracy

- Interpret a reading that lies between two numbered divisions on a scale - Plan and pursue an enquiry

Capacity Activities Developed by the

West Sussex Leading Mathematics Teachers

FOCUS: CAPACITY

TITLE OF ACTIVITY

Posing Problems

OBJECTIVES (from Framework)

To be able to pose and answer questions (MA1 Problem Solving Level 4)

To choose and use appropriate units and instruments (MA3 Level 4 Measuring)

To be able to solve problems involving the conversion of units (MA3 Level 5 Measures) ASSESSMENT OPPORTUNITIES (from Assessing Pupil Progress)

Assessing Pupil Progress opportunities using the above references DESCRIPTION OF ACTIVITY

Introduction

Show the children the range of measuring equipment around the room

(equipment can be grouped so children stay working on the same table or it can be grouped so children have to move to find the resources they need. A carousel could be set up for children to move around).

Discuss what equipment they have and what the equipment can be used to measure. Activity

Ask the children to use the equipment to devise their own problem to solve. What questions can they generate?

Children then to solve their problem using the resources available to them and present findings.

Plenary

Share the questions the children generated. Which were engaging? Which questions encouraged us to work systematically? Which questions allowed us to meet our learning objectives?

Resources

Measuring cylinders, measuring jugs, bowls, cups, jugs, stop watches, sand, rice, water, sieves, thermometers etc.