Mathematics at Home: Practical Activities for Parents and Children

Mathematics at home Practical activities for parents and children John Davis

THE QUESTIONS PUBLISHING COMPANY LTD BIRMINGHAM 2001

The Questions Publishing Company Ltd 27 Frederick Street, Birmingham Bl 3HH ©John Davis 2001 Text and activity pages in this publication may be photocopied for use by the purchaser or in the purchasing institution only. Otherwise, all rights reserved and text may not be reprinted or reproduced or utilised in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. First published in 2001 ISBN: 1 84190 046 X Cover design by Lisa Martin Illustrations by Devinder Sonsana

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Contents Introduction

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Numbers and the number system Teachers 9 notes * Number spotter * Brick builder <* Car prices «$> Door to door <$> Equal shares «$> Washing line «$> Hundred up «$> Positive and negative

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Calculations Teachers 9 notes * All change * Shopping bills * Tables bingo <* In the family <* Double cross <* Loose change <* Calculator skills * Check it out

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Solving problems Teachers 9 notes * Body measures *> Floor show *> All the way round <* Time out <* Make a date <* Keeping watch * Cool down * Right angle

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Handling data Teachers' notes * Tasty fruits * Take a letter * Mealtimes * On the cards * Happy birthday * Quick conversion * Shoe sizes * What's the chance?

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Measures, shape and space Teachers' notes * Take a guess * Magic V * Full up * Roundabout * Perfect fit * Food packaging * Mirror shapes <* Take it in turns

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Introduction Why homework? Much can be achieved if the school and the home work positively together to develop the child's understanding of mathematics, so parents have a great deal to offer if they are keen and enthusiastic about helping children with their homework. It is easy to identify the possible reasons for this. Helping your child with their homework: • demonstrates your own interest in what they are doing and the progress they are making; • sends a clear message to them that you are fully aware that their schoolwork is important; • can give you the opportunity to show and apply your own knowledge, expertise and enthusiasm; • will give you the chance to work cooperatively with your child on an enjoyable activity; • updates you and keeps you in touch with the changes that have taken place in primary school maths teaching; • illustrates that the home environment has different and distinct opportunities and potential for learning in mathematics.

Parents, carers and homework An activity done at home gives the parent or carer an opportunity to work in a familiar setting on a one-to-one basis with the child a situation that is rarely possible in school. Some tasks are best done little and often, although it may be possible to spread problem solving and investigation work over a longer period of time. Always choose a time when the child is not involved in something else and when they have the setting and energy levels to concentrate fully on what they have to do. Remember that sometimes maths questions will produce answers that are either right or wrong. But with many problem-solving tasks and investigations, solutions may be variable and open ended, with a range of acceptable possibilities. This is where the importance of discussion comes in. Encourage children to put forward their own views about how to find the answer. Find out what they know already and consider the way in which they explain things. Always listen carefully to what they have to say. Teach them to be flexible 1

MATHS AT HOME and open-minded. Resist the temptation to step in straight away and tell them what to do or to insist that only one particular approach should be used. There are usually many different ways to find a maths solution. Sometimes it is possible to work mentally. Then there is the use of approximations and rounding off. Some children prefer to work through jottings or paper and pencil methods, while on occasions a calculator will help. Often a combination of several of these approaches is needed. The child will benefit more from these activities if they are fun, enjoyable and interesting. Keep them practical and 'hands-on' wherever possible. Through the activity, encourage the child, boost confidence, promote self-esteem and praise success. It is vital that children appreciate as early as possible that mathematics is a key life skill that they cannot manage without. During almost every situation in a normal day, maths will be encountered in some form or another. One of the main purposes of these home-based activities is to highlight this fact and to show that whatever we are doing - travelling, shopping, decorating, cooking, even playing - will require the ability to know and apply mathematical understanding.

Using the pupil sheets: a note for teachers The tasks in this book are not just to provide homework as such, but to exploit the tremendous potential for maths learning that is found in the home environment. Through the activities it is hoped to set up a three-way dialogue involving the child, the parent/carer and the teacher. Before children start on the activities it might be best to send home a general letter to help explain a number of important points. These would include the following: • the worksheets are supporting, consolidating and extending the work children have been doing in school and are crossreferenced to the teaching programmes in the National Numeracy Strategy framework; • the chance to involve parental/carer support will help to encourage the child's thinking, planning and motivation; • the tasks are intended to be largely practical in nature and will entail a range of different methods of recording; • the activities will usually require equipment, apparatus and other resources, but that these are easy to find and make available at home;

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MATHS AT HOME • teachers would welcome feedback on the activities especially if they are of a problem-solving or investigative nature with a variety of solutions. It should be stressed when activities are set up that essential home safety rules will apply at all times, that parent/carers will be kept informed about what their child has been asked to carry out and that sometimes close supervision may be needed. On the occasions where special safety advice is required, this is given in the teachers' notes.

Working through the tasks: page layout The headings used on the photocopiable pupil pages are as follows:

Title: Child's name: Date activity set: Write here the date on which the task was sent home. Date for returning this sheet to school: To give the child and the parent/carer some indication of when you are expecting the sheet to be returned to school. To the parent or adult carer: This short section explains the main objectives of the activity. It also lists what equipment or resources are needed and gives practical suggestions for carrying out the task. What to do: This paragraph explains the activity. It has been written so that both the parent/carer and the child are able to read the instructions. What to talk about: This is a chance for the child and the parent/ carer to discuss what they have found out while working on the activity. It is important to remember that with some tasks, strategies will often vary and that some solutions are open-ended and may produce outcomes different from those found by someone else. What to record: This need not always be in written form and the parent/carer might occasionally want to act as a scribe for the child. 'Recording' should relate as much as possible to the 'real life' situation involved and could involve drawing pictures, making charts or graphs or producing other diagrams. Sometimes the findings might be better recorded by using a tape or a disk. 3

MATHS AT HOME

Comment from parent/carer: This is the opportunity for feedback. Was the task set too easy or too difficult for the child? Did it link well with work that had been carried out in school? Was there difficulty with some aspects of the task that might require consolidation or revision in school? Did the home environment provide a suitable setting for working on the task? Was it obvious what skills the child had to use? Did the parent/carer appreciate the purpose of the task and were the objectives achieved? Has it improved communications and/or helped to establish a dialogue between the home and the school?

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1 Numbers and the number system Teachers' notes Number spotter Through this activity children will be able to practise important elements of place value and notation. They start with three-digit numbers and can then proceed to four-digit, five-digit and six-digit numbers as their confidence increases. They will be able to write chosen numbers in both digits and also in words. The task also involves the ordering of numbers where they have to be placed in size, starting with the smallest. Children should be encouraged to say the numbers out loud each time as they are writing them. Learning outcome (Year 5): Read and write whole numbers in figures and words and know what each digit represents.

Brick builder Sequence and pattern are vital elements in the process of understanding how numbers work. From the list of numbers given in each row, the child should be able to find the sequence rule that is being used, and from this predict what number or numbers will come next. In some investigations, being able to predict answers often saves unnecessary calculations being carried out. Knowing how number sequences work will help children to learn other topics in maths including multiplication tables. Once the child understands a sequence or pattern involving a single-step process, two-step processes can also be introduced. Learning outcome (Year 5): Recognise and extend number sequences formed by countingfrom any number in steps of constant size.

Car prices The ability to round off numbers quickly, especially to the nearest 10 or the nearest 100, often enables calculations to be done easily and approximate answers to be found quickly. It needs to be emphasised that the rule has been established that if numbers come at exactly the halfway point, 5 for 10 and 50 for 100, they are rounded up. Stress that the tasks given put the rounding-off and approximation skills into everyday situations where they are 5

often useful, e.g. car prices, house sales and holiday costs. Some preparation work on where these sections are to be found in local newspapers would be useful before the activity is sent home. Learning outcome (Year 5): Use the vocabulary of estimation and approximation. Round any integer up to 10,000 to the nearest 10 or 100.

Door to door Both odd and even numbers have something in common in that they are also groups of alternate numbers. Discuss the meaning of this word with the child and also the meaning of the word consecutive as it is applied to numbers. The task involves establishing rules for the adding and subtracting of odd and even numbers, but there is more potential here, and some children might go on to explore what rules apply when odd and even numbers are multiplied and divided. Learning outcome (Year 5): Make general statements about odd/even numbers, including the outcome of sums and differences.

Equal shares Make it clear when the activity is being discussed that the child understands a fraction is part of a whole one. Point out that there are no set questions for this task and that children will have to make up their own fraction facts once the items have been cut into parts. Take the opportunity to work on other key aspects of vocabulary like 'denominator' and 'numerator' and any equivalent fractions that might occur. Food items are used for this activity and may well be handled. They should be disposed of once they have been finished with. Learning outcome (Year 5): Use fraction notation.

Washing line This is a totally practical activity that will not require any written recording. Children should show the answers as they peg them up on the washing line and also get used to saying the decimal numbers out loud using the correct place value. The decimal point and two digit cards will allow tenths and hundredths to be shown first. Some may be able to add another digit card to permit an examination of thousandths as well. Learning outcome (Year 5): Use decimal notation for tenths and hundredths. 6

Hundred up The main purpose here is to help children improve their understanding of the concept of percentage. Later it will improve their initial calculations involving percentages if they memorise important links between percentages and fractions. They should know, for example, that l/z = 50%, 1/4 - 25%, 3/4 - 75%, V& -20% and yio - 10%. Doubling 10% will give 20% and halving 10% will yield 5%. Discuss as many practical life situations as possible where knowledge of percentages will be important. Learning outcome (Year 5): Begin to understand percentages as the number of parts in every 100.

Positive and negative A good deal of reinforcement is needed here as many children find it difficult to understand that there is a whole number line below zero where negative or minus numbers are found. Initially, the child will need to work with a number line like the one provided on the worksheet so that they can use a pencil to move physically along the line when counting up or down. Discuss the use of such a number line on thermometers, where positive numbers show temperatures above freezing and minus numbers temperatures below. Looking at temperature recordings in newspapers can be helpful here. Learning outcome (Year 5): Order a set of positive and negative numbers.

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MATHS AT HOME

Number spotter Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Encourage your child to say the numbers as they are written. When they are confident with three digits, move on to four, five and six-digit numbers. Help with the spelling of key words when writing numbers, especially hundred and thousand, and the tens family like twenty, thirty, eighty and so on. Help with numbers that include the digit zero.

What to do:

To start with you will need the three digits that are found on a car registration number plate. It could be your own family car at home or one belonging to a neighbour. Use the numbers to make as many three-digit numbers as possible, e.g. 753 would make numbers like 375 and 537. Arrange the numbers in order of size, smallest first. How many different ones can you make? Write the number in words as well as figures and also split them to show the value of each digit. For example, 753 would be 700 + 50 + 3. Take one digit from another car registration plate and use it with the original three to make four-digit numbers. How many different numbers can you make now? Repeat the same process. If you are ready to continue, take a fifth digit to make five-digit numbers and then a sixth for six-digit numbers. Again count up the different numbers you have been able to make.

What to talk about:

Our number system is called the denary system - it means based on families of ten. Discuss how the value of digits in our number system depends on their position and not just their size.

What to record:

On the back of the sheet write down the lists of numbers that have been made. What is the biggest number you have made in all the lists? What is the smallest number?

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Brick builder Child's name: Date activity set: Date for returning to school:

To the parent/carer:

The figures written on each row of bricks illustrate two of the key elements involved in the study of numbers - pattern and sequence. Ask your child to explain what rule is used each time before going on to complete the sequence. When they make up their own sequences, start with simple one-step patterns. What to do: On each row of bricks shown in the drawing there is a different number sequence. Sometimes the numbers get bigger, sometimes they get smaller. Complete each of the five sequences on the sheet and write at the end of each row what number rule has been used, e.g. +5, -10, +20 and so on.

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2. 73 103

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4. 9118 8118 5.

6542

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What to talk about:

Use this sequence work to revise sequence patterns found in the times tables, e.g. 5, 10, 15, 20; 3, 6, 9, 12. Look at rules that give practice going up or down in tens, hundreds and thousands. Investigate sequences that combine two steps, e.g. 10, 12, 17, 19, 24 (+2+5).

What to record:

Using a ruler to keep the lines straight, draw rows of bricks on the back of the sheet and make up your own one-step then two-step sequences. Ask a friend to explain what rules have been used.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Car prices Child's name: Date activity set: Date for returning to school:

To the parent/carer

Explain to your child that there are many times when it is useful to round off large numbers in order to find out an approximate cost of something quickly and easily. Remind them that when rounding off to the nearest 10, if the number ends in 5 or more we round up. When rounding off to the nearest 100, if the number ends in 50 or more then again we round up. Have copies of local newspapers ready. Some holiday brochures may also be needed.

What to do:

These numbers have been taken from an advert for car sales in a local newspaper. Round each of the ten amounts off to first the nearest 10 and then the nearest 100. For example, £3222 would be £3220 to the nearest 10 and £3200 to the nearest 100. 1. £1993; 2. £4696; 3. £4892; 4. £5879; 5. £5996; 6. £6211; 7. £8772; 8. £3444; 9. £10495; 10. £11723. Find car sale prices in your own local newspaper at home and round off the amounts to the nearest 10 and then the nearest 100. What was the most expensive car you found? What was the cheapest?

What to talk about:

Also find in the newspaper some lists of house prices with five- and six-digit numbers. Do the same with these. Which figures are used most often? If you have a holiday brochure, practise rounding off some of the costs. Does it help you to work out the approximate cost of a holiday for your family if you round off the figures first? How close was your approximation?

What to record:

Record the answers to the 10 questions above on the back of the worksheet. Also write down your examples using house prices and/or holiday costs, so that they can be discussed back in school.

Comment from parent/carer:

This pace may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Door to door Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Odd and even numbers are commonly used in most systems of street numbering where there are buildings on both sides of the road. Ensure your child understands that ALL odd numbers have 1f 3, 5, 7 or 9 as the smallest digit and ALL even numbers have 0, 2, 4, 6,or 8 as the smallest digit.

What to do:

Start with your own front door number and the numbers of the houses or buildings on either side of you. If you don't have house numbers, use those of a relative, friend or neighbour. Are they on the even or the odd side of the road? Write down the numbers of three houses or buildings that are on the opposite side of the road. Are these numbers odd or even? Continue the series of three even numbers that you have collected so that you both increase and decrease them for at least ten more numbers. Do the same with the list of three odd numbers that you have collected. Try to establish certain rules for adding odd and even numbers. Solve these puzzles. Even + even = ?, odd + odd = ?, even + odd = ? and odd + even = ?

What to talk about:

Both odd and even numbers are also known as 'alternate' numbers -they occur every other one in the number line. Talk about the meaning of the word 'consecutive' in terms of numbers. This means that every number is included and no gaps are left between them. Move on to establish rules for subtracting odd and even numbers. Using numbers already collected, or choosing others, find the answers to these puzzles: even even = ?, odd - odd = ?, even - odd = ? and odd - even = ?

What to record:

Lists of odd and even numbers that have been collected, and addition and subtraction sums to help suggest and establish rules, should be written neatly on the back of the worksheet ready for checking and discussing.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution. 11

MATHS AT HOME

Equal shares Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Discuss with your child what he/she understands by the word 'fraction' before they start. A fraction is a part of a whole one. Explain that a half means one equal part out of two, a quarter means one equal part out of four, three-quarters means three equal parts out of four and so on. Your child will need a small food item, e.g. a small round cake, a round biscuit, an apple or an orange. Cut these items into four equal parts to start them off. The items are likely to be handled so it is better they are not eaten afterwards. Reward with fresh items. Later you will need to cut another similar item into eight equal parts. Centimetre squared paper and coloured pencils may be needed later.

What to do:

Using the four equal quarters that you have been given, make up at least 10 different addition and subtraction fraction facts. Here are three to get you going: 1

/2 + 1/2 = 1, 1/4 + 1/2 = 3/4 and 1 - 3/4 = 1/4.

Ask your helper for the other item cut into eight equal parts this time. Each of these parts is one eighth. This time try to find at least 20 different addition and subtraction fraction facts. These will help you to get started: 1/4 + 1/4 = 1/2, 1 - 3/8 = 5/8/ 1/2 + 1/8 = 5/8.

What to talk about:

What addition and subtraction fraction statements have you found? For example: How many halves make a whole one? How many quarters make a whole one? How many quarters make a half? How many eighths make a half? How many eighths make a quarter?

What to record:

Although the addition and subtraction fraction facts should be written down quickly at the start, you may just want to record neatly by showing your choices in coloured diagram form. Draw some simple shapes on the squared paper so that the different fractions can be shown accurately.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing; institution

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MATHS AT HOME

Washing line Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Your child will begin to appreciate the value of decimal fractions and how to arrange decimal fractions in order of size by using this practical activity. Provide an old piece of washing line, string, twine, ribbon or even wool at least one metre long, pieces of plain paper or thin cardboard A4 size and some pegs.

What to do:

Start with the piece of line, the pegs and three pieces of card. With a crayon or felt-tip pen, label one of the pieces of card with a large decimal point and put any two single digits on the other pieces.

The key rules are that all three cards have to be used each time but that they cannot be used more than once in the same question. Set yourself some questions and show the answers by pegging them up on the line. If, for example, the digits 3 and 7 and the point are used, problems might include: What is the highest number that can be made? (73.) What is the smallest number? (.37) What number is closest to one? (.73) Then make another single digit card and use it with the other three to make up more decimal number problems.

What to talk about:

While you are pegging up the decimal numbers, say your solutions out loud. It will help understanding if 7.3 is not said as seven point three but as seven and three-tenths, and 3.17 not as three point one seven but as three and one tenth and seven hundredths.

What to record:

There is no need to write the decimal numbers down on paper for this activity. Your helper can check the solutions by looking at the way you arrange the cards on the washing line and how you say the decimal numbers.

Comment from parent/carer:

This pag^e may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Hundred up Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Establish first of all that your child understands that percentage is a way of expressing an amount as part of 100 or out of 100. Provide some clothes items that contain clear labels for your child to have a look at. Later, squared paper will be needed, and a set of coloured pencils to show percentage amounts.

What to do: Look carefully at the clothes labels and find where the percentage sign (%) is shown. If an article is made from just one kind of fabric it will be labelled 100%. A fleece jacket could be 100% cotton, or a jumper 100% wool. If an item is made from a mixture of different fabrics it could be labelled 55% cotton and 45% polyester, or 66% cotton and 34% nylon. Notice that the two numbers add up to make 100. On the squared paper make squares and rectangles containing 100 small squares. For example, try a 10 by 10 square and a 25 by 4 rectangle. Use coloured pencils to show percentages that total 100. You could try 70% red and 30% yellow, or 48% blue and 52% white. If 43% is coloured green and 29% yellow, how much would you have to colour orange?

What to talk about:

Talk about situations where the word percentage has been adopted into the language, like 'not one hundred per cent fit' and 'fifty-fifty'. Discuss other occasions where percentages are often used like extra tax, e.g. VAT, test results, building society interest, shop sale bargains and holiday savings.

What to record:

Draw pictures of the clothes labels on the back of the sheet and clearly label the percentages that are shown. Use the squared paper and the coloured pencils to draw a range of different percentage diagrams all adding up to 100.

Comment from parent/carer:

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This pace may be photocopied for use only within the purchasing institution.

MATHS AT HOME

Positive and negative Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Integers or whole numbers can come in positive or negative form. This task will help your child to understand that there is a number line of whole numbers that goes down below zero into negative numbers and is in no way connected with either ordinary fractions or decimals. If you have a thermometer in the home, make it available as it will probably show numbers both above positive (+) and below negative (-) zero. If not, use the integer number line.

What to do: I

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Use the integer number line to help you to solve these problems: 1. Start at -4 and jump six spaces in a positive direction. Where do you land? 2. Start at +5 and jump eight spaces in a negative direction. Where do you land? 3. Moving in a positive direction, complete this number sequence: -9, -6, -3, ?, ? 4. Moving in a negative direction, complete this number sequence: +10, +4, -2, ?, ? Now make up some of your own questions like these: Positive and negative numbers are used on a Celsius thermometer scale to show temperatures above and below freezing point (zero degrees C). Use a thermometer to help you work out these problems. Find the rise or fall in temperature between these readings: 1. -2°C and +5°C; 2. 0°C and +9°C;

3. +4°C and -3°C; 4. -6°C and +1°C.

Make up some of your own temperature changes.

What to talk about:

Discuss what time of the year negative or minus temperatures might be expected in this country. Newspapers usually carry details of recorded temperatures locally, nationally and internationally. Find and discuss some.

What to record:

Use this activity as a purely oral exercise. Once you have discussed what the task is about, work out the answers and your opinions, then talk about your findings with your parent or helper.

Comment from parent/carer:

This page may be photocopied for use only -within the purchasing institution.

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2 Calculations Teachers' notes All change The commutative law - that numbers produce the same total despite the order in which they are added - is one way of making calculations easier to do. Show how the law also applies to multiplication but does not apply to subtraction and division. Some discussion might also take place about the associative law. This involves regrouping numbers during addition. For example, 35 + 17 + 42 can be added as 35 + (17 + 42) =35 + 59-94 or (35 + 17) + 42 = 52 + 42 = 94. Learning outcome (Year 5): Rapid recall of addition and subtraction facts.

Shopping bills To make the task more meaningful it is better to use a recent shopping bill of items that have been bought for the family. It is important that the correct procedure is used and that a calculator is not involved this time. Despite this being a very formal method, take the opportunity to talk about how rounding off and estimating cost helps to keep a 'running' total during the shopping process. Learning outcome (Year 5): Extend written methods to column addition/ subtraction.

Tables bingo It is recommended that children learn their times tables in this order: 2x, 5x, lOx (Year 3) ; 3x and 4x (Year 4). By Year 5 they should also know their 6x, 7x, 8x and 9x plus the related division facts. Vary the level of difficulty depending on the ability of the child and also the way in which the questions are phrased. Some children may understand 20 divided by 5 but may not follow a question like 'how many threes are there in 24?' Some equipment will need to be prepared ready for the game, especially the complete 100 squares and some blank pieces of card. Learning outcome (Year 5): Know by heart all the multiplication facts up to 10 x 10. 17

In the family The fact that each trio of numbers can be used to make two multiplication and two division facts should help the child to appreciate the close relationship between these two processes. Once the numbers have been established, they can be put into the correct places without any time-consuming calculations taking place. It is also an important opportunity to reinforce the fact that the inverse operation can be used to check answers while working with these two rules. Learning outcome (Year 5): Understand the principles of the arithmetic laws as they apply to multiplication.

Double cross The benefit of this activity is that it gives the child the chance to use dartboard type skills without the possible dangers of playing the actual game. It needs to be stressed that the type of dartboard being used for the task is different from the normal kind. The one shown on the worksheet has an outer ring for doubling numbers and an inner ring for halving numbers. An actual dartboard has an outer ring for doubling and an inner ring for trebling, as well as the inner and outer bull. Stress that if a normal dartboard is used, it should be used for number purposes only for this task, and that no actual darts need be thrown. Learning outcome (Year 5): Use doubling and halving, starting from known facts.

Loose change Although involving some money work practice, the main purpose here is to improve the child's understanding of the term 'factor'. It is, however, restricted to factors at present that can be shown through the use of coins. For example, 4 is a factor of 20 but cannot be represented by a single coin. For those who are ready, the term 'prime number' might also be discussed. A prime number is one that only has factors of 1 and itself. Emphasise that hands should always be washed thoroughly after coins have been handled. Learning outcome (Year 5): Use factors.

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Calculator skills There has been a lot of debate recently about the extent to which calculators should be used during Key Stage 2. While they should not replace other methods, there are some occasions - doing investigations, using very large numbers and dealing with difficult calculations, for example - when they are very useful. This task will give the child the chance to practise some of these calculator skills. For discussion: Would the calculations have been possible without the calculator? What methods could have been used? Learning outcome (Year 5): Develop calculator skills and use a calculator effectively.

Check it out The ability to use rapid, effective and accurate methods for checking calculations is extremely important. The opportunity should be taken here to examine as many different methods as possible, particularly in relation to other worksheets that have been carried out before in the Calculations section. The most important four methods at this stage would be: 1. Using the inverse operation; 2. Estimating and approximating; 3. Changing the order of the numbers involved; 4. Using an equivalent calculation. Learning outcome (Year 5): Checking results of calculations.

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MATHS AT HOME

All change Child's name: Date activity set: Date for returning to school:

To the parent/carer:

The main aim of this activity is to stress to the child that when adding a series of numbers, the order in which they are rearranged does not affect the total. So if 12 + 29 + 6 = 47, then 6 + 29 + 12 = 47 and 29 + 6 + 12 = 47. The same rule, though, does not apply to subtraction, e.g. 46 - 28 = 18 but 28 - 46 does not give the same answer. Sometimes it makes addition easier to purposely change the order of numbers when adding, e.g. 32 + 36 + 18 = 86 might be quicker as 32 + 18 + 36 as the first two numbers now total a round number, in this case 50.

What to do:

You are going to use some front door numbers again, but this time they will be used to help you with your adding. Choose two two-digit door numbers from houses close to where you live, say, 21 and 25. Add them up. Now change the order so they become 25 and 21. Add them up again. What do you notice?

Now choose three two-digit numbers and add them up. Change the order and add them again. Repeat this process several times. What do you notice about each answer? Find some front door numbers that have three digits in them, e.g. 235 and 241. Add them up. Change the order and add again. What happens? Repeat the process with three three-digit numbers. Does the same thing continue to happen?

What to talk about:

The mathematical name for this process is the 'commutative law for addition'. This law does not apply to subtraction, e.g. 19 - 8 = 11 but 8-19 does not produce the same answer. It does, however, apply to multiplication. If 6 x 3 = 18 then 3 x 6 = 1 8 and if 5 x 2 x 4 = 40 then 4 x 2 x 5 , 2 x 5 x 4 , and so on, will also equal 40.

What to record:

Write the door numbers and their totals on the back of the worksheet so that answers can be compared. Try an alternative method of recording the answers for example, recording missing numbers in questions like this: 43 + 29 = ? + 43 = ?

Comment from parent/carer:

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This pace may be photocopied for use only within the purchasing institution.

MATHS AT HOME

Shopping bills Child's name:

Date activity set: Date for returning to school:

To the parent/carer:

In order to carry out this activity, your child will need a recent shopping bill with details of food items that have been bought. A selection of items should be included so that the child has plenty to choose from. The purpose is to enable the child to use pencil and paper methods for adding and subtracting money amounts. Do not allow a calculator to be used this time.

What to do:

Choose two amounts from the shopping bill and write them down horizontally (side by side) as in question 1 below. Then write them down in columns or vertically to make them easier to add up. See question 2. Remember the numbers must go into the correct columns, and the decimal points, which mark off pounds from pence, must line up under each other. Label with the £ sign to show it is a money calculation. Choose other amounts from the bill and use the same method to carry out some subtraction calculations. See questions 3 and 4. 1. £2.59 + £1.94^

2. £2.59 +1.94

3. £3.69-£1.75 ^

4. £3.69 -1.75

What to talk about:

Revise work done earlier on rounding off, estimation and approximation. It might be useful while shopping to add up amounts or keep totals to have a quick idea of how much has been spent before arriving at the checkout.

What to record:

Attach the shopping bill that has been used to the back of the worksheet so it can be referred to later. Write down the shopping addition and subtraction examples, showing clearly how the switch was made from horizontal to vertical methods of writing. Make a list of the important rules that you had to follow.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Tables bingo Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Help your child to construct this game of bingo that will test their knowledge of the multiplication tables up as far as 10 x 10, as well as the related division facts. You will need to make a 100 square like the one shown in the diagram, 20 questions made up from the tables and some small blank pieces of cardboard that can be used for covering up the numbers. Think about different ways of asking the questions, e.g. What are 7 fives? 6 times 3? What is the product of 8 and 4? 20 divided by 4? How many threes in 27? 7 2 3 4 5 6 7 8 9 10 77 72 13 14 15 16 17 18 19 20 27 22 > continue to 100

What to do:

You will be asked 20 multiplication and division questions about the multiplication tables. They will be read out in different ways using key words. Listen carefully so you know what operation to do. When you have worked out the answer, find the correct number on the 100 square and cover it with a piece of cardboard. The winner is the one with all 20 correct squares covered when the questions are completed. When you have finished this, start a second game with 20 different questions. Take it in turns to be the caller.

What to talk about:

Discuss the different words that have been used in the questions for multiplying and dividing like 'times', 'product' and 'divided by'. Multiplication and division are inverse operations, and this rule can be used to check answers, e.g. if 5 x 7 = 35 then 3 5 - 7 = 5 and 35 - 5 = 7.

What to record:

The 20 questions may have to be written down each time, otherwise the same questions may be repeated. They will also be needed for checking at the end. Apart from this, everything else can be done orally.

Comment from parent/carer:

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MATHS AT HOME

In the family Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Your child will need to cut out the strips of paper containing the three numbers that are given below. These will be used to make multiplication and division facts. They will also need a separate piece of paper on which they can stick the strip of paper and write down their answers.

What to do:

Look carefully at the numbers inside the boxes. The three numbers will help you to make multiplication and division facts. Each set of three numbers should make four facts, e.g. if you chose 20, 4 and 5, you could write 4 x 5 = 20, 5 x 4 = 20, 20 + 5 = 4 and 20 + 4 = 5. Cut out the number strips and stick them onto another piece of paper. Underneath them write down the four facts each time. When you have completed the ones on the sheet, can you think of your own group of three numbers that could be used in the same way?

What to talk about:

Make sure the facts you have written contain two for multiplication and two for division. What do you understand now by the term inverse operation? Did you need to do any actual calculating to work out the number facts? How can the information you have collected be used to check the answers to questions?

What to record:

As previously mentioned, the strips containing the three numbers should be cut out and stuck onto a separate piece of paper. The multiplication and division facts should be written down underneath each strip. Spare space can be used for recording your own groups of three.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Double cross Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Dartboards are a good way of helping children to calculate numbers quickly in their head. This task uses a dartboard with a difference as it does not need any darts to be thrown. It is used purely to encourage mental thinking involving doubling and halving numbers up to 50. If an actual dartboard or a picture or diagram of one is available, it can be used for follow-up work.

What to do:

The diagram below shows a special kind of dartboard. It only has eight sections and does not need darts to be thrown at it. Double all eight numbers in the large outer ring and write down your answers.You might find it easier to partition the numbers, e.g. double 29 is double 20 then double 9, i.e. 40 + 18 = 58. Halve the eight numbers in the smaller inner ring and again write down your answers. You could partition, e.g. half of 48 is half of 40 and half of 8, i.e. 20 + 4 = 24. If you have a real dartboard, use it to make up your own doubling and halving questions.

What to talk about:

Which method of doubling and halving did you use to find the answers? Talk about ways in which doubling and halving can help with other calculations, e.g. multiplying numbers by 4 is doubling and doubling again; multiplying numbers by 20 is multiplying by 10 and then doubling. If an ordinary dartboard is being used later, talk about the different method of scoring.

What to record:

Write down the answers on the worksheet in the empty spaces on the dartboard drawing. Other answers can be written down on the back of the sheet.

Comment from parent/carer:

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MATHS AT HOME

Loose change Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Collect a selection of loose change to help your child to carry out this activity. They should have available at least one each of the coins, i.e. 1p, 2p, 5p, 10p, 20p, 50p, £1 and £2. Don't forget to encourage them to return it afterwards. As well as reinforcing the child's understanding of the coins used in our money system, it will also help to introduce the meaning of the word 'factor'. A factor of a number is any number, including 1 and itself, that divides into it exactly.

What to do:

• Put a 1 p coin in front of you. Now find coins whose value will divide into it exactly with nothing left over. Write down what these coins are and how many you would need to make 1 p. (The only coin that goes into it is the 1 p and you would need only one of them to make up the amount.) • Do the same with the 5p coin. (This time the 1 p coin and the 5p coin will divide into it exactly. You would need 5 of the 1 p coin to make up its value or 1 of the 5p coin.) • Now do the same with the 10p coin. The coins that would divide into it would be the 1p, 2p, 5p, and 10p, but how many of each coin would be needed? • Repeat the same process with the 20p, 50p, £1 and £2 coins. Each time, write down which coins will divide into them exactly and how many would be needed to make up its value.

What to talk about:

What do you understand by the word 'factor'? Remember to restrict its usage to the coins being used at this stage. For example 4 is a factor of 20 but since there is no 4p coin available it cannot be used. Also, 25 is a factor of 50 but again there is not a single coin available to represent this amount. Talk about fractions as well, e.g. 5p is half of 10p and 20p is a fifth of £1.

What to record:

If a large number of coins are available, they could be stacked to make up the amounts, e.g. a pile of five 10p coins to make 50p. If not, the solutions should be written down on the reverse of the worksheet for checking.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Calculator skills Child's name: Date activity set: Date for returning to school:

To the parent/carer:

There are several advantages to using a calculator. One is that it allows quick calculations to take place, especially when the numbers involved are awkward or difficult. Another is that it enables children to find answers quickly even when the numbers are very big. Items that will be needed, in addition to the calculator, include a sliced loaf of bread or packet of biscuits, a large book, a ball of thin string or twine and a ruler.

What to do:

• Take a large sliced loaf first. Count the number of slices inside. Measure the whole length of the loaf to the nearest centimetre. Use your calculator to work out the thickness of each single slice to two decimal places. The answer will be length of loaf -H number of slices. • Try the same activity with a packet of biscuits. Again, count up the number of biscuits in the packet, measure the length of the packet and then divide. • Now try a large book. Remember one sheet of paper is usually two pages. From the middle section count out 100 sheets of printed paper. Measure the width of these sheets, this time to the nearest millimetre. Find the thickness of a single sheet of paper like this: width of 100 sheets +• 100. • Take the ball of thin string and, starting at zero, wind it around a ruler carefully and tightly for 100 turns. Record how far along the ruler it reaches. To find the thickness of the string carry out this calculation: Length of 100 turns of string shown on ruler + 100. For example, if the string reached as far as 5.4cm, the thickness of the string would be 5.4cm + 100 = 0.05 cm.

What to talk about:

Discuss ways in which the calculator might be used to work out calculations involving very big numbers. For example, going from the last birthday, how many days have you been alive so far?

What to record:

Avoid putting the questions or the answers down on paper. Use the calculator to work out each stage of the process and discuss this with your helper as you go. Talk about how difficult the task might have been without the calculator.

Comment from parent/carer:

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MATHS AT HOME

Check it out Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Through this activity your child should be able to reinforce and strengthen understanding of the relationship between addition and subtraction. It will also help to revise the ability to use the inverse operation to check the answers to calculations. It will be necessary to refer to a previous task entitled 'Shopping bills', where the child practised formal written methods of addition and subtraction. A shopping bill and the calculator will also be needed.

What to do:

Take some of the amounts that were added up on 'Shopping bills', and check the answers by using subtraction. For example, if £1.49 + £3.05 = £4.54 then £4.54 £3.05 = £1.49 and £4.54 - £1.49 = £3.05. This is called 'using the inverse operation'. Use a calculator to double-check the answers. Take some of the amounts that were subtracted during the same task and check the answers by adding. For example, if £4.99 - £2.74 = £2.25 then £2.25 + £2.74 = £4.99. Again, you are using the inverse operation to make sure the answer is correct. Double-check with the calculator.

What to talk about:

The inverse operation can also be used to check the answers to multiplication and division problems. If 12 x 7 = 84 then 84 -7 = 12 and 84 -H 12 = 7. Also, if 100 -r 25 = 4 then 25 x 4 = 100 and 4 x 25 = 100. Check the work done on the sheet called 'In the family' in connection with this. Also discuss other ways of checking calculations. For example, changing the order of numbers when adding or multiplying. See 'All change'. Doing an equivalent calculation, e.g. 35 x 4 = 140, could be done as double 35 (70) then double again (140). See 'Double cross'.

What to record:

Show clearly on the back of the worksheet the three methods that you have used to check the answers to your questions. Show examples of the inverse operation, changing the order of numbers and using an equivalent calculation.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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3 Solving problems Teachers' notes Body measures The children will be used to measuring-length work associated with rulers and tape measures etc, but this task gives them the chance to use one of the earliest systems developed by man. Measurements of this kind are usually referred to as non-standard units. Pieces of string or long strips of paper may prove to be useful during the measuring process. Historical note: the Egyptian system was used some five thousand years ago, and Henry I reigned in England between 1100 and 1135. Learning outcome (Year 5): Suggest suitable units and measuring equipment to measure length.

Floor show Many children find the difference between area and perimeter confusing in what the words mean, how they should be calculated and what units should be used to record them. Much practical 'handson' work should be done to improve an understanding of the two concepts. Stress the use of the formula length x width as a quick way of calculating area. It is important with this activity that the quality, appearance and toughness of the floor covering will need to be considered in addition to the cost. Distances should be measured where the floor space is clear. Any furniture moving should be done with permission and supervision. Learning outcome (Year 5): Understand area measured in square units.

All the way round Give advice on what kind of measuring devices should be used for this, especially that tape measures are more flexible than items like metre sticks. Safety advice given in the previous activity would also apply here. Discuss with the child, either before or after the task has been carried out, quick ways of working out the perimeter. Suggest they try side x 4 for a square and length x 2 added to width x 2 for a rectangle. Learning outcome (Year 5): Understand, measure and calculate perimeters of rectangles. 29

Time out Children need to get used to reading as many different clock faces as possible and should also be able to record the same time in various ways, e.g. 7.40 can be said as forty minutes past seven or twenty minutes to 8. Give reminders that clocks are delicate instruments and should be handled carefully. Permission should be obtained before any are moved, especially those on shelves and fixed on walls. The 24-hour system is believed to have been originated by the military so they could be more precise about when orders should be carried out. Remind children that in this system p.m. times are added to 12.00 and not 10.00. So 4.00 p.m. becomes 16.00 hours. Learning outcome (Year 5): Use units of time.

Make a date Point out that it will be much easier to use a large display calendar that shows all the months together, rather than using something like a diary of dates where pages need to be turned frequently. Knowing a number of key facts will be important in carrying out this task. Children will need to know the number of days in a week and how many days there are in each month. The old rhyme 'Thirty days has September, April, June and November' is still a good way of remembering them. Reinforce the fact that there are 365 days in a year but 366 in each leap year. Also that a leap year occurs every four years and that the date is always divisible by four. The next ones will be 2004, 2008, 2012 and so on. Learning outcome (Year 5): Use the calendar.

Keeping watch Give the children plenty of practice in working out how long events last by building up how time is passing in easy steps. Remind them they are working in base 60 when times are added together. Some children may know a programme starts at 3.00 p.m. and ends at 4.30 p.m. but will find it difficult to comprehend what was showing at 3.45 p.m. Learning outcome (Year 5): Use timetables.

3C

Cool down This is not only a problem-solving task but will also help the children to remember the units that are used to measure capacity. Make sure they understand that 500 millilitres is half a litre, one litre is 1000ml and two litres is 2000ml. If they are using bottles from home, plastic containers must be used, not glass, and they should still be handled carefully. As well as working out the cost of each drink, there are other important factors to consider. Encourage thought about the wider issues. It may be cheaper per 100ml to buy a two-litre bottle, but is that entire amount wanted and is it worth spending that amount of money? Learning outcome (Year 5): Use all four operations to solve simple word problems based on 'real life\ money and measures.

Right angle All the right angles chosen should be viewed from ground level. Widen the discussion to point out that right angles are in many ways the 'cornerstone' of construction. Why does this angle make such a good join? Are there possible alternatives that could be used in its place? Using doors and the covers of books etc. to create turns, discuss angles that are less than right angles (acute angles) and angles that are between one right angle and two right angles (obtuse angles). Carry out simple movement tasks so that children can demonstrate a quarter of a turn, half a turn, three-quarters of a turn and a full turn or revolution. Learning outcome (Year 5): Make and investigate a general statement about familiar shapes by finding examples that satisfy it.

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MATHS AT HOME

Body measures Child's name: Date activity set: Date for returning to school:

To the parent/carer:

In this problem-solving section your child is going to use measurements that originated many centuries ago. The earliest forms of measurement used by human beings were based on themselves.

What to do:

Carry out some measurements of objects at home using the system started by the Egyptians - the digit, the cubit, the palm, the span and the stature (see box). List your findings.

During the reign of Henry I in England, measurements were based on the king's physique. From the nose to the tip of an outstretched arm was named a yard. His height was reckoned to be two yards. They measured the king's foot and found that one yard was equivalent to three feet. The foot was then divided into 12 inches and the hand four inches.

Egyptian measures

digit palm span cubit stature

width of first finger width across hand palm end of thumb to end of little finger elbow to end of closed fist fingertip to fingertip (outstretched arms)

Check these measurements on yourself and a helper. Measure from the nose to the tip of an outstretched hand. Do three of your feet make this distance? Is your height twice the yard measurement? Does the length of the foot measure three times the palm of the hand? Is the length from fingertip to fingertip on outstretched arms, the stature, the same as a person's height?

What to talk about:

Which of the body measures did you find easiest to work with? How reliable do you think this form of measurement was? Does the fact that people are different sizes cause problems?

What to record:

Draw diagrams of different kinds of body measures you have used on the back of the sheet to help you remember their names. List the measurements made of the objects and also the comparisons you made between you and your helper.

Comment from parent/carer:

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MATHS AT HOME

Floor show Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Your child is going to work out the area of their bedroom or another small room at home. The easiest way is to measure the length of the room, measure the width of the room and then multiply the two distances together. They will need a tape measure to find the length and width. Rounding off the distances to the nearest centimetre may be necessary to make the numbers easier to work with.

What to do:

You are going to find out how much it will cost to put new floor covering in your bedroom or another small room at home. First you will need to measure the length and the width of the room so you can multiply Carpet shop them together to find the area in square metres. Price per square metre Do this with a tape measure and round off the measurements to the nearest centimetre. You will Topqualitycarpet £11.99 need help if you have to move any furniture. Budget price carpet £4.99 Inside the box you will see the prices of some floor coverings at the carpet shop. Work out how much the cost of floor covering for the room will be. Which type of floor covering would cost most money?

Vinyl floor covering

£4.95

Carpet tiles £2.75 each 4 for each square metre

Which one would be the cheapest? Which would you choose for your room?

What to talk about:

What do you understand by the word 'area'? Discuss the surface area of other items found inside the home. Which has the biggest area? Which has the smallest? Talk about the methods used to work out the cost of the floor covering. Which is the best value? Think about quality of carpet or vinyl as well as cost.

What to record:

Write down the measurements of the room on the back of the worksheet and show how you worked out the area. Write down what each of the floor coverings would cost and put them in order of size, from the cheapest to the most expensive.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution

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MATHS AT HOME

All the way round Child's name: Date activity set: Date for returning to school:

To the parent/carer:

It will be important that your child realises that while area is the amount of surface in a shape, the perimeter is the distance around the outside of the shape. Again some kind of measuring device will be needed, with a tape measure being easier to handle and more flexible than a ruler. For this task, straight-sided objects like door frames, window frames, square and rectangular tables and work surfaces are the best things to use.

What to do:

You are going to measure the perimeter or the distance around the outside of some large, straight-sided objects that you can find at home. Measure items like door frames, window frames, tables, desks, cupboards, picture frames, small mats or rugs and kitchen work surfaces, but avoid things that are hard to reach unless an adult will help you.

Round off your measurements to the nearest centimetre to make them easier to work with. One way to find the perimeter of an object is to measure all four sides and then add them all together. But can you find an easier or quicker way in which to do the calculation?

What to talk about:

As a result of working on this activity and the last, 'Floor show', can you explain the difference between area and perimeter, how they are calculated and what kind of units they are recorded in? Think of examples when it would be necessary to work out perimeter calculations at home in order to solve a problem. Talking about such things as putting up wall friezes or borders and fencing gardens might get you started.

What to record:

A list of the objects used and their perimeter measurements should be written on the back of the worksheet for comparison and discussion in school. Also make a brief note of any quick methods, perhaps in formula form, that were used to work out the answers.

Comment from parent/carer:

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MATHS AT HOME

Time out Child's name: Date activity set: Date for returning to school:

To the parent/carer:

It will help your child if all the different types of clocks used in the house could be examined during this activity. This would include analogue clocks - traditional ones with hands and numerals - and those that show a digital read-out in numbers only. Something to draw around, like a large coin or a button, will speed up the process of drawing clock faces during recording.

What to do:

On the back of the sheet make a list of ten different things that you do during the day. For example, the time you get up, the time you go to school and the time you have lunch. Remember to include whether it is a.m. time or p.m. time. Do more if you have the space. You are now going to show how the same time can be written in a number of different ways. Alongside each one, write the time that this event happens, how it would be shown on an analogue clock and what the digital read-out would be. Then show how this time would be written as a 24-hour clock time. Here is an example.

What to talk about:

Talk about the different ways of writing the same time for the events and check that they are correct. Make a tour of all the different clocks in the house. Decide whether they are analogue or digital and whether they use the a.m./p.m. system or are 24-hour clocks. Which clocks in the house do you consider to be most important? Say why. Would it be possible to manage at home without any clocks?

What to record:

On the back of the worksheet, record the different times chosen in the style shown in the example. Say any other ways of giving the times.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Make a date Child's name: Date activity set: Date for returning to school:

To the parent/carer:

This task looks at time over a longer period, that is months and years. To do this activity, your child will need a calendar, preferably for this year, although one from the previous year or the next year could be used. The large poster display version would be desirable, as it will save a lot of page turning. School dates for the year will be needed for the last two questions.

What to do:

Answer these questions from the calendar: How many days are there in April and May? How many days are there in June, July and August? Which is the shortest month of the year? What day will Christmas Day fall on during the year? When is Bonfire Night? How many Tuesdays are there in January? How many Fridays are there in July? On what day does your birthday fall this year? Here are some more difficult challenges: Is this year a leap year? Were you born during a leap year? Work out your exact age in years, months and days. How many weeks are there until Christmas? How many weeks do you spend in school this year? How many days do you spend in school this term? _

What to talk about:

Discuss why calendars are important, especially for organisational purposes. Talk about diaries. Why do some people keep them? Give definitions of key time words, not just month and year, but also decade, century and millennium.

What to record:

Write the answers on the worksheet in the space following each question.

Comment from parent/carer:

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MATHS AT HOME

Keeping watch Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Your child will need a current or recent copy of a newspaper or magazine, showing the listings of television programmes on each of the channels they usually watch. It will be vital to remember that, when adding up times to find out how long programmes last, they will be working in base 60 (60 seconds to the minute and 60 minutes to the hour) and not base 10 as they usually do.

What to do:

Make a list of a selection of programmes that you have already watched or intend to watch this week. You will need to record the name of the programme, what channel is showing it, what time it starts, what time it ends and how long it lasts. Fill in the chart below with your answers. Programme

Channel

Time starts

Time finishes

Time taken

What to talk about:

Discuss your favourite programmes and why you like watching them. What programmes do other members of the family prefer? Talk about what is called the 'nine o'clock watershed'. Is it really necessary? Give the reasons for and against.

What to record:

Fill in the chart given on the worksheet.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Cool down Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Is it cheaper in the long run to buy items in large quantities? Your child will need to work with the quantities and prices provided on the worksheet first, where a calculator may help. They should be able to do some of their own research later. Provide labelled plastic drinks bottles and details of how much each of them cost.

What to do:

In the table below is the capacity of bottles containing three types of drink orange, lemonade and water. Prices are also given. By dividing, find out which bottle of each drink provides the best value for money. Work out how much 100ml of each drink would cost by dividing the cost of the 500ml bottle by 5, the 11 bottle by 10 and the 2I bottle by 20. Round off each answer to the nearest penny. The first one is done for you. Drink Orange

Lemonade

Water

Capacity 500ml 11 21 500ml 11 21 500ml 11 21

Price 69p £1.15 £1.29 29p 39p 55p 39p 59p 75p

Cost per 100ml 13.8= 14p

Carry out the same research using plastic drink bottles that you have at home.

What to talk about:

Was it cheaper to buy the largest amount? Was this always the case? Discuss other factors in the buying process. Was the largest quantity actually needed? What would happen if it was not used up straight away? Would the higher cost of the large amounts prevent people from buying it?

What to record:

As well as filling in the chart, list on the back of the worksheet some advice for people who are thinking of buying refreshments like this. Also give details of your own research.

Comment from parent/carer:

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MATHS AT HOME

Right angle Child's name: Date activity set: Date for returning to school:

To parent/carer:

The main purpose of this activity is to help your child identify the main type of angle used in construction at home - the right angle. Help them find as many different examples as possible. Details are given about how to make a simple device for checking right angles if this is necessary.

What to do:

Figure 1

Make a simple right angle measurer that can be used to test out any you are not sure of. You will need a piece of stiff paper or thin card about A4 size. Fold the paper or card in the way shown in Figure 2.

Figure 2

Look around carefully at home, inside and outside, and try to spot as many different right angles as possible. Right angles are equal to 90 degrees and some examples are shown in Figure 1.

List, on the back of the worksheet, all the examples of right angles you can see.

What to talk about:

Talk about the variety of right angles you have found. How many different ways have they been used? Why are right angles so important in construction? What important properties do they have? How many right angles make a straight line? How many right angles make a complete turn?

What to record:

On the back of the worksheet, note all the different right angles you have found. A labelled diagram will be fine. Say which ones were inside and which outside.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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4 Handling data Teachers' notes Tasty fruits This is the first in a series of activities about handling data. It is important that children have had experience of all these tasks in class before they are sent home. In this case, each symbol on the pictogram will represent one item, but children should also be aware that, when dealing with larger numbers, symbols could stand for two items, five items, ten items and so on. Supplies of squared paper may need to be given out if it is not available at home. Learning outcome (Year 5): Solve a problem by representing and interpreting data in pictograms.

Take a letter The tallying system is used this time. Again, ensure children understand how this system works by going through examples of its use in class. Stress that it is particularly useful when counting larger numbers where the bundles of five make it easier to add up recorded amounts. The words 'consonant' and Vowel' form an important part of the task and should be discussed before it is sent home. Learning outcome (Year 5): Solve a problem by representing and interpreting data in tally charts.

Mealtimes Several important items need to be revised with children before this task is sent home. Point out that, when showing the times, they will need to make decisions about how many minutes each square will represent. It will depend on the length of times they choose to use and the size of the graph paper provided. Also remind them that graphs of all kinds need to be fully labelled. They should provide a title, label both axes carefully and also indicate what scale is being used. When it is complete it will need to be interrogated for information. Learning outcome (Year 5): Solve a problem by representing and interpreting data in bar charts. 41

On the cards Most junior-aged children should be familiar with Venn diagrams that use two rings, but this task moves up a stage and uses three different criteria. Make sure the children have a set of playing cards they can use at home. If not, show them a pack in class and point out that the main activity uses the numbers 1 to 13 inclusive, with the picture cards having the following value. The Ace is 1, the Jack 11, the Queen 12 and the King 13. As background information, Venn diagrams are named after John Venn, a Cambridge mathematician, who used them to help simplify relationships between groups of numbers. Learning outcome (Year 5): Solve a problem by representing and interpreting data in tables (Venn diagrams).

Happy birthday This moves a stage further still than the previous activity. Some children may be unfamiliar with Carroll diagrams and will need plenty of practice. Introduce boxes that show just two sets of information first and extend to four boxes when children become more skilled. Lewis Carroll (1832-1898) - better known as a writer of children's books including Alice in Wonderland— is said to have originated this form of diagram. He taught mathematics at Oxford University. Learning outcome (Year 5): Solve a problem by representing and interpreting data in tables (Carroll diagrams).

Quick conversion Many adults still talk in terms of distance measured in miles and speed in miles per hour. In this activity, children work on converting kilometres into miles, but miles could be changed into kilometres just as easily. There are approximately 1.61 kilometres to the mile and one kilometre is equal to 0.62 miles. The graph must start at zero because no distance has been travelled at this point. The graph is a straight line because the distances increase at the same amount each time. This is known as 'constant proportion'. Emphasise that the points should be located accurately and connected with a ruler. Learning outcome (Year 5): Solve a problem by representing and interpreting data in tables (conversion graph).

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Shoe sizes Only adult shoe sizes are being used in this activity because of the confusion that might be caused by the fact that small children's sizes also use two-digit numbers like 12 and 13. It is important that children understand what operation or operations are needed in order to find the meaning of the words listed. The questions at the end of the sheet should lead to a general discussion about the rapid growth of children's feet and therefore the need to change shoes often. Learning outcome (Year 5): Find the mode and range of a set of data. Begin to find the median and the mean of a set of data.

What's the chance? Take the opportunity to talk about probability in everyday situations when setting up this activity. If a ball is thrown into the air, for example, it is certain it will come back down and, while we know for sure that the sun will rise tomorrow, we cannot be certain whether it will be sunny, cloudy or rainy. Sometimes findings are placed on a probability scale where impossible is shown as 0 and certain is registered as 1. All other probabilities lie somewhere between these two points. When the coin is tossed it is equally likely to come down heads or tails. This is what is known as an even chance. Learning outcome (Year 5): Discuss the chance or likelihood of particular events. It should be stressed to children when they are carrying out some of these information gathering, recording and interpreting activities that, under supervision, they should question only relatives, neighbours and friends who are known personally to them. On no account should they talk to strangers in the street or collect details by knocking on doors.

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MATHS AT HOME

Tasty fruits Child's name: Date activity set: Date for returning to school:

To the parent/carer:

This is the first of the data-handling tasks that your child will be doing. They will be making and using a pictogram - a type of chart or graph that shows information using diagrams or drawings. On this occasion, because of the small numbers involved, each symbol will represent one unit. Squared paper will be needed, and some pictures of fruits for the child to look at may also be useful.

What to do:

You are going to make a pictogram - a kind of graph or chart where pictures are used to show information. In this pictogram, one picture will represent one item. Make a survey of the members of your family to find out what kinds of fruit they eat during a typical week. You may want to ask some of your relatives and friends as well. Draw a careful picture of each fruit you record on the pictogram. Stick a piece of squared paper on to the back of the worksheet where you can draw your pictogram. Remember to draw a pair of axes on the squared paper. Label the axes, give the pictogram a title and show how many items each symbol stands for. Make up at least five questions that can be answered by looking at the pictogram. Here are some examples: How many fruits are shown? Which was the most popular fruit? Which was the least popular fruit?

What to talk about:

What were the main findings of the pictogram? Did you find this type of graph easy to read? Why? Discuss the importance of eating plenty of fruit in our diet. What is the recommended daily intake of food items like this?

What to record:

The fully labelled pictogram drawn on squared paper should be fixed to the back of the worksheet. Also write down the questions that were used to interpret the pictogram and the result of the findings.

Comment from parent/carer:

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This page may be photocopied for use only within the purchasing; institution.

MATHS AT HOME

Take a letter Child's name: Date activity set: Date for returning to school:

To the parent/carer:

This activity involves the use of tally charts. The tallying system is a quick and reliable way that your child can use to collect information for data-handling activities. For this task they will need a book from home or a suitable newspaper or magazine.

What to do:

You are going to use a tally chart to make a letter survey from some words in a book, newspaper or magazine. Choose a short paragraph of writing and count up exactly 100 words. On the back of the worksheet make a list of the letters of the alphabet. Using the tally chart system, record every time each letter occurs. (See the example.) Remember tallying involves bundles of five. Four items are recorded by short vertical strokes while the fifth mark consists of a diagonal line across them.

Make up at least five questions about the tally chart and then write down the answers. Here are some ideas to start you off: Do vowels score more highly than consonants? Which letter has the highest total? Which letter has the lowest total? Are there any letters that do not score at all? Which are they?

What to talk about:

Are consonants used more frequently than vowels in writing, or is the reverse true? Which vowel is used most often? Which is the most common consonant? Choose a further 100 words from another piece of writing. Does it give the same kind of results? Compare your findings with 100 words of your own writing.

What to record:

List the results of the tally chart surveys and your most important findings on the back of the worksheet. Try to do surveys from at least three different passages.

Comment from parent/carer:

I This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Mealtimes Child's name: Date activity set: Date for returning to school:

To the parent/carer:

This is another method of collecting and recording data or information that your child will be familiar with from work carried out in class. This type of chart is called a bar chart, but is sometimes known as a block graph or column graph because of its method of construction. Before they start you will need to discuss with them the time taken to cook certain meals at home, as these will be recorded on the graph.

What to do:

You are going to make a bar graph of cooking times. Your helper will provide you with the times it takes to cook certain items of food, e.g. beans on toast, fish, chicken, stew and sponge cake. You will need at least five items. Squared paper will be provided for drawing the graph. Draw the two axes to help you organise your graph and label them. Then decide what each square will represent. It could be two minutes, five minutes or ten minutes, etc. You will have to decide based on the times you are given.

Once the graph has been made, labelled and given a title, interrogate it to find out what information it shows. For example, which item takes the longest to cook? Which takes the shortest? Compare the times taken by the different items.

What to talk about:

Discuss your favourite foods and how they are cooked. Talk about nutrition and a balanced diet and why it is important, especially for growing children. Find out the meaning of key food words such as 'protein', 'vitamin' and 'carbohydrate'. Split the meals into sections such as snacks, main courses and desserts. Why do some items take longer to cook than others?

What to record:

The bar chart and its findings should be recorded on the graph paper. This can be fixed on the back of the worksheet or pinned to it. Colour in the columns on the bar chart so that they are easy to see and interpret.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution. I

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MATHS AT HOME

On the cards

jih

Child's name: Date activity set: Date for returning to school:

To the parent/carer:

In this method of showing data, rings are used instead of axes. This version is called a Venn diagram. To generate the numbers that are going to be placed inside the Venn diagram, your child will need to have a set of playing cards. Something circular to draw around will speed up the diagrams. What to do: To start with, you are going to use the numbers on a set of playing cards. Choose one of the suits. Cards 2 to 10 will count at their face value. The Ace will count as 1, the Jack as 11, the Queen as 12 and the King as 13. Now place the numbers 1-13 inclusive inside the correct section of the three rings shown in the box.The rings should contain the multiples of 2, 3 and 4. If the number meets two of the criteria, show it in two rings. If it meets three criteria, show it in all three. If it does not fit any, write it at the side. Now choose ten of the same cards at random and see if you can use a Venn diagram to sort them in a different way.

What to talk about: Make another Venn diagram using three rings like the one in the box. Label them 'rainy', 'cloudy' and 'sunny'. Talk about weather conditions in the last week. Place each day in the correct ring or rings. Why might some of the days appear in two or even all three of the rings?

What to record:

Using something large to draw round, record all the Venn diagrams that are produced, either on the back of the worksheet or on another piece of paper. Make sure all the rings are labelled carefully.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Happy birthday Child's name: Date activity set: Date for returning to school:

To the parent/carer:

The focus for this activity changes to another kind of diagram used to collect and show data. This type is called a Carroll diagram. It consists of a box structure, not a series of circles. The boxes are arranged so that they are able to show four different kinds of information at the same time.

What to do:

An example of a Carroll diagram is shown in the box on the right. It has four sections and each one has a separate title. Take the birthday months of the members of your family, but also include some relatives and friends as well and sort them into the correct sections. Use the information to answer these two questions: Are more females than males born in the first half of the year? Are more males than females born in the second half of the year? What other information does the Carroll diagram tell you?

Male

Female

First half of year Jan-Jun

Second half of year Jul-Dec

What to talk about:

Are both Venn and Carroll diagrams a better way of showing data than bar graphs and tally charts? Explain your answer. What advantages might the diagrams have? What is the most difficult part about drawing them? Lewis Carroll first used Carroll diagrams. As well as being a clever mathematician, what else is he famous for?

What to record:

The task involving sorting out the birthday months could be done using the boxes given on the worksheet. Draw your own larger version on the back if you think this is necessary. Try to make some Carroll diagrams of your own based on items found at home, e.g. furniture, types of food and favourite colours.

Comment from parent/carer:

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MATHS AT HOME

Quick conversion Child's name: Date activity set: Date for returning to school:

To the parent/carer:

One of the most useful features of a graph is that it can be used to investigate relationships. This graph will show the relationship between two measurements of distance - miles and kilometres. Your child will need squared paper, a sharp pencil and a ruler in order to make this graph, which will require both care and accuracy.

What to do:

You are going to make a special type of graph called a conversion graph. It will turn kilometres into miles. One kilometre is equal to 0.62 miles. The information you need to draw the graph is given in the box. The distances have been rounded off to the nearest whole number. Draw the graph on squared paper. The points lie along a straight line that starts at zero. The first two points have been marked for you. 80

1

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(> <>

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Kilometres

What to talk about:

Explain why you think the graph is a straight line. Using atlases, maps or road signs, find the distance the family travels when they go on a long journey from home. Use the graph to change miles into kilometres or kilometres into miles.

What to record:

Complete the graph on the squared paper provided and write conversions of the journeys made on the back of the worksheet.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Shoe sizes Child's name: Date activity set: Date for returning to school:

To the parent/carer:

When interpreting some kinds of data, a number of key mathematical words are used. These include range, median, mode and mean. The meanings of these words is explained to your child as they work through the questions below. Help them to collect the shoe sizes they require from ten adults. A calculator may be useful for some of the calculations, especially if any half sizes have been included.

What to do:

You are going to find out the meaning of some important words used in handling data. First you will need to collect details about the shoe sizes of ten adults. Use members of your family first and then try relatives, friends or neighbours.Write the sizes down in a list and then use the statistics to help you understand the meanings of these words: Range: The range is the difference between the highest and lowest size. Find the answer by subtracting the smaller from the larger. Mode: This is the item in the list that occurs most. It will be the most popular size, if there is one. Median: The median is the middle point of all the sizes you have collected. Mean: The mean is the average value. You add up all the shoe sizes you have and divide by the number there are of them (ten).

What to talk about:

Discuss the way in which the shoe sizes of children and adults are organised. How often do the children in your family need to change the size of their shoes? Why do adults usually stay with the same size? Why do companies who run shoe shops need to know which sizes are likely to sell best?

What to record:

List the shoes sizes used on the back of the worksheet. Show how the meaning of each word in the list was calculated by writing down the operation used as well as the answer. Draw round the outline of several shoes to show different sizes in the family. You will need a large piece of paper to do this.

Comment from parent/carer:

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MATHS AT HOME

What's the chance? Child's name: Date activity set: Date for returning to school:

To the parent/carer:

The chance of something happening is called 'probability' and its connection with the gathering of statistics is an important part of mathematics. To carry out this probability task, your child will need some sweets wrapped in coloured papers and a bag they cannot see through. Some coins and a die may be needed for follow-up activities.

What to do:

Place eight sweets into the bag. Five should be in red paper, two in blue paper and one in yellow.

If you pick a sweet from the bag without looking, then the chance of picking out a yellow one will be 1:8 or one-eighth. What will be the chances of picking out a red one or a blue one? Give the answers as a ratio and as a fraction. Suggest the number of times you will need to pull out a sweet in order to get as close as possible to this result. Have 10 goes, 20 goes, 30 goes, 50 goes, maybe even 100 goes. Remember to replace the sweet each time it is taken out. Is it true to say that the more goes you have, the closer you get to the actual ratio of 5:2:1 ?

What to talk about:

Try other probability tests that are easy to set up at home. Predict results before you start. Try an activity that has only two possible outcomes, like tossing a coin. Try 50 goes to see what happens. Or try a die showing the digits one to six. What are the chances of each of the numbers coming up now? Again test out your theory.

What to record:

It will be necessary to write down the results of the probability tests, but keep this as brief as possible. Discuss what you think might happen with your helper before tests are carried out, and then compare the ideas with your findings at the end to see whether you were correct.

Comment from parent/carer:

This pace may be photocopied for use only within the purchasing institution.

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5 Measures, shape and space Teachers' notes Take a guess Children are encouraged to become more competent at using different measuring devices, including a ruler, a metre stick and a tape measure. If these are riot available at home, perhaps the school will be able to provide them. Stress honesty in estimation, even if some are a long way out. Look at alternative ways of writing the same measurement. Go through examples. Point out the importance of sensible safety rules when measuring around the house. Learning outcomes (Year 5): Measure lines to the nearest millimetre. Suggest suitable units and measuring equipment to estimate or measure length.

Magic 'e9 On a technical note, this activity really involves mass and not weight. The amount of matter in an object is called its mass. Weight is a measure of the force that the Earth exerts on a body. We say the tin weighs 250 grams, but what we should really say to be more precise is that the tin weighs the same as a 250g mass. Great care will need to be taken over checking the readings on certain types of weighing scales. Some may measure in 100g or 50g and some even in 10g increments. Rounding off may be necessary in some cases. Point out that only clean packaging should be used once permission has been obtained, and mention the dangers of all types of glass containers. Learning outcomes (Year 5): Use read and write standard metric units including their abbreviations and relationships. Convert larger to smaller units, e.g. kg to g.

Full up If measuring cylinders are not available at home, it may be possible to convert either one-litre or two-litre plastic drinks bottles with divisions marked on the side using a felt-tip pen. Again on a safety note, using glass containers and lifting and carrying heavy quantities of water from one place to another must be avoided. Stress that 53

work should take place in areas where water will not cause any damage and that accurate results will only be obtained if spillage is prevented. The word 'capacity' here is taken to mean the amount a container holds. Volume is the amount of three-dimensional space taken up by an object. Learning outcomes (Year 5): Use read and write standard metric units including their abbreviations and relationships. Convert larger to smaller units e.g. I to ml.

Roundabout The activity will be enhanced if a wide range of different-sized round objects is used, e.g. a coin and a bicycle wheel. The greater the variation, the more relevant it becomes. Children may need some help with tapes or string when the circumference of large circles has to be found. When the circumference is divided by the diameter, the answer should work out at a little more than three each time, regardless of the size of the circle. This ratio is now known by the Greek letter pi (II) and for the purposes of calculation is reckoned to be equal to three and one seventh or 3.14. So the circumference of a circle is found by using this formula: circumference = diameter x3.14. Learning outcome (Year 5): Make shapes with increasing accuracy (2D). Explain a generalised relationship (formula) in words.

Perfect fit The word 'tessellation' comes from the Latin word tessera, the name the Romans gave to the small pieces of coloured stone used in the construction of mosaics. The 2D shapes involved need to be categorised into three families. There will be those that tessellate on their own, e.g. squares, those that tessellate with the help of other shapes, e.g. hexagons and those that will not tessellate under any circumstances, e.g. circles. Focus also on regular and irregular shapes, e.g. regular pentagons will not tessellate by themselves, while some irregular ones will. Learning outcome (Year 5): Make and investigate a general statement about familiar shapes by finding examples that satisfy it.

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Food packaging As pointed out on the worksheet, packaging should be clean, safe and undamaged. Again, stress the dangers of glass and sharp tin. Paper and cardboard containers will be best, as they can be cut apart easily to reveal the net of the shape. Compare the 3D shapes on the basis of faces, edges and corners. The use of gluing flaps will enable tidier models to be made, so they need to be included in the net stage. Learning outcome (Year 5): Make shapes with increasing accuracy (3D).

Mirror shapes Squared paper will need to be provided to help with devising these examples of mirror symmetry. If glass mirrors are being used at home to check patterns, they should be handled carefully and used under supervision. Other ways of making reflective symmetry are mentioned on the worksheet and should be tried out in class or at home. Learning outcome (Year 5): Complete symmetrical patterns with two lines of symmetry at right angles using squared paper.

Take it in turns Through their movements, both clockwise and anti-clockwise, children should realise that a quarter turn involves moving through one right angle of 90 degrees; a half turn, two right angles worth 180 degrees; a three-quarter turn, three right angles or 270 degrees; and a full turn, four right angles or 360 degrees. This information will help considerably with angle work later. Compasses may need to be issued to help children find directions at home. The position in which it is situated and the direction in which it faces is often an important factor when people are considering the purchase of property. Learning outcome (Year 5): Recognise positions and directions.

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MATHS AT HOME

Take a guess Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Three important aspects of length measurement are featured in this task. Your child will be able to practise estimation, work with several kinds of measuring device and learn to write the same length measurements in a number of different ways. They will need to use a 30cm ruler, a metre stick or strip and a measuring tape that can be used for longer distances than these.

What to do:

You are going to carry out some measurement tasks at home using a 30cm ruler, a metre stick or strip and a measuring tape. Choose objects suitable for the type of measuring device you are using, e.g. a book for the ruler, a shelf for the metre tape and the height of a door for the longer tape measure. Try to find ten of each. Before you measure each item, estimate how long you think it will be and write down your estimate. Don't cheat. When you measure it, try to go to the nearest millimetre. If not, round off to the nearest half centimetre. Finally write down the measurement in at least one other way, e.g. 3cm 6mm could be written as 36mm, 87cm could be written as 0.87m and 2m 15cm could be written as 215cm. Make a table like the one below on the back of the worksheet where you can record your answers.

What to talk about:

How close were your estimations? Were you better at estimating the shorter distances or the longer ones? Did your estimations improve with practice? Which measuring device was the easiest to use? Talk about the practical measuring activities that have to be carried out at home.

What to record:

Make a table like the one above to record your measurements. This should be done on the back of the worksheet or on a separate piece of paper. Remember to include the correct units on all your measurements.

Comment from parent/carer:

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MATHS AT HOME

Magic 'e' Child's name: Date activity set: Date for returning to school:

To the parent/carer:

The purpose of this task is to help your child recognise the importance of mass or weight labelling on packaging containing food items. They will need a selection of these items to look at, some including the use of the letter 'e' and some without it if possible. They will also need the use of some accurate kitchen scales. You may need to assist them with setting the scales and reading off the amounts.

What to do:

With permission, look carefully at some items of food packaging and find out how much they weigh. Some items may have a letter 'e' either before or after the weight and some may not. The letter 'e' stands for 'excluding' and means the weight of the food item inside the packaging but not including the weight of the tin, jar, carton, box or wrapping. Occasionally, the words 'gross' and 'net' are still used. Gross weight is the weight of a container and what it holds, while net weight is the weight of what is inside the container only. Using the kitchen scales, carefully weigh the items you have. By subtracting the 'e' weight from the weight that registers on the scales you should be able to work out just exactly how much the packaging weighs. Those containers that show no 'e' should weigh the exact amount.

What to talk about:

Talk about the types of packaging that have been used on the food items. Are they made from cardboard, metal, plastic or glass? Are any other materials used? Does the type of packaging suit the food item? Why do you think this kind of material has been chosen? Where would the food item have to be stored to keep it fresh?

What to record:

Use the back of the worksheet to record details of the food items and their weights. Show the operations you used to calculate the weight of the packaging. Which type of packaging was heaviest? Which was lightest?

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Full up Child's name: Date activity set: Date for returning to school:

To the parent/carer:

The metric units dealt with in this activity are millilitres and litres that are used for measuring capacity - the amount something holds. Your child should know that 1000ml = 1 litre and also the important fractions like how many millilitres there are in a half, a quarter, three-quarters and one tenth of a litre. A collection of containers of different sizes, a choice of measuring cylinders and a supply of water are needed. Encourage work in a large bowl or sink to prevent water spillage.

What to do:

• With permission, gather together a collection of different containers used at home. • Estimate how much water you think they will hold. Estimate to the nearest 10ml if you can. • Working over a large bowl or a sink and trying to avoid wasting or spilling any water, fill the containers to the top. • Check the capacity of each container by using a measuring cylinder. Make sure you can read the scale on the side of the measuring cylinder first and remember to use metric units instead of imperial. • Make a table like the one below for your estimates and measures. This time also work out the difference between the two to see how far out you were.

What to talk about:

How accurate were your estimates? Did the estimating improve with practice? Look at containers holding liquids at home. What is their capacity? Do some of them use the 'e' letter that you did some work on in the last activity? Do you remember what it means?

What to record:

Draw the table on the back of the worksheet and fill in information about as many containers as you can. Note details about the divisions used on the side of the measuring cylinders. Show how you calculated the difference between your estimation and measurement each time.

Comment from parent/carer:

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MATHS AT HOME

Roundabout Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Encourage your child to focus on all the 2D objects in the house first, although the main part of the activity will concentrate on circles. Ask them to make sketches of as many two-dimensional flat shapes that they can find. They should try to include squares, rectangles, triangles, circles, pentagons (five-sided), hexagons (six-sided) heptagons (seven-sided) and octagons (eight-sided). A ruler and a tape measure or string will be needed for work with the collection of circles.

What to do:

Make a collection of circular objects. These might include coins, tins, cups, plates, saucepans, clock faces and wheels on toys and bicycles.

Use a ruler or a tape measure to find Circumference the diameter and the circumference of each object. These two dimensions are shown inside the box. Each should be Diameter measured to the nearest millimetre. To measure the circumference of the objects, you may have to use a piece of cotton or thin string. Record your results in a table like the one below. In the last column you will need to divide the circumference by the diameter.

Look at the answers in the last column. What do you notice about your results? What is the ratio of the circumference to the diameter to the nearest whole number?

What to talk about: Go back to the other 2D shapes you have listed and talk about key words like regular and irregular sides, angles and vertices (corners).

What to record:

Make a table on the back of the worksheet like the one shown and record your results in the correct columns.

Comment from parent/carer:

I This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Perfect fit Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Homes usually have plenty of examples of tessellation - shapes that fit together without leaving any gaps in between. Your child will need to locate some examples of these first, but will also need to try out their own shapes to see if they tessellate. Thick paper or thin card, coloured pencils and scissors will be needed so your child can test out tessellation by making his/her own shapes.

What to do:

Find some examples of tessellation in your home. Think about brickwork, paving slabs, kitchen and bathroom tiles, carpet squares and patterns on floor coverings, curtains, wallpaper and furniture fabrics.

Make quick sketches of each tessellation on a piece of paper and note down what shape or shapes is used each time. Below are some 2D shapes. Make collections of your own shapes by drawing around them on thick paper or thin card and cutting them out. Then, with coloured pencils, draw round them to try to make your own tessellating patterns. Which shapes tessellate on their own? Which shapes need help to tessellate? Which shapes do not tessellate?

What to talk about:

Find some square tiles that tessellate. How many right angles are there where four squares meet? Find parallel lines in the square patterns. Look at different ways in which rectangular bricks are fitted together. Can you find out any of the names for these patterns? Locate where the right angles and parallel lines are.

What to record:

Most of the recording this time can be done through drawings and sketches. Use the shapes provided for making your own tessellation.

Comment from parent/carer:

This pace may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Food packaging Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Food packaging comes in a variety of shapes and sizes. Save some clean packaging for your child to examine, as it will help them to find out more about threedimensional (3D) shapes. Scissors will be needed to cut shapes apart to see how they are constructed, and sticky tape will help your child to put them back together again. Supplies of thin cardboard may also be required.

What to do:

• Collect as many safe, clean and undamaged items of food packaging as you can. • Find out which family of three-dimensional shapes they belong to. Look particularly for cubes, cuboids, cylinders, cones, prisms and pyramids. Count the number and shape of the faces, the edges and the vertices (corners). • Cut the shapes open carefully and spread them out so you can see how they have been put together. This is called the net of the shape. Use the sticky tape to carefully put them back together again. • Look around inside and outside your home to find other 3D shapes. You may find some different ones. • Thinking about the shapes you have seen and some of the nets you have examined, use pieces of thin cardboard to make up your own 3D shapes. Remember to use gluing flaps if you do not want the joins to show.

What to talk about:

Which is the most common type of 3D shape used in food packaging? Which is the rarest? Packaging creates a lot of rubbish. Is there any way it could be used again? Find out which food packaging items could be reused or recycled. Are there recycling facilities close to your home? What items do they take?

What to record:

Write down a list or make a quick sketch of the 3D shapes you have collected. Save the nets of the 3D containers you have cut open. Take the 3D models you have made into school to show your teacher. Remember any information you have found out about recycling so that you can use it in a class discussion.

Comment from parent/carer:

This page may be photocopied for use only within the purchasing institution.

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MATHS AT HOME

Mirror shapes Child's name: Date activity set: Date for returning to school:

To the parent/carer:

There are several kinds of symmetry. One of the easiest kinds to recognise is called reflective or mirror symmetry, because the shape formed on one side of the lines of symmetry is identical to that formed on the other side. After trying out a simple example on the worksheet, your child is asked to devise and draw their own symmetrical patterns. They will need squared paper, coloured pencils and a mirror.

What to do:

Make a symmetrical pattern using the squares on the worksheet. Colour in the coded squares. The colours being used are r = red, b = blue, y = yellow and g = green.

r

b

b

r

g

r

r

y

g

r

r

y

r

b

b

r

Repeat the same coloured pattern on the other side of the lines. When you have done this you will have completed a piece of reflective or mirror symmetry. Check the pattern is correct by putting a mirror along the lines. Draw straight lines at right angles on your own piece of squared paper and devise your own patterns with reflective or mirror symmetry.

What to talk about:

Look for examples of reflective or mirror symmetry. They are often found in wallpaper designs, in carpeting, on tile patterns and in textiles used for making curtains and furniture covers. Ask your teacher about other ways of making reflective symmetry, like blot painting or cutting folded sheets of coloured paper.

What to record:

Using coloured pencils, complete the example of reflective symmetry on the worksheet and then devise your own and draw them on squared paper.

Comment from parent/carer:

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This pnge may be photocopied for use only within the purchasing institution

MATHS AT HOME

Take it in turns Child's name: Date activity set: Date for returning to school:

To the parent/carer:

Movement and direction are the main features of this activity. It will provide the opportunity to look at movement in terms of right angles, the difference between clockwise and anticlockwise movement and the eight points of the compass. It may be necessary to check locations on a direction compass if you are not sure in which directions the front and back of the home are pointing.

What to do:

You are going to use your body to make certain turns inside a room at home.

Stand facing one of the points in the room. Make a quarter turn clockwise. How many right angles is this? What are you facing now? Go back to where you started. Now make a half turn clockwise. How many right angles have you turned through this time? What are you facing now? Going back to the starting position again, do the same for three-quarters of a turn and a full turn clockwise and answer the same questions. Repeat the process but this time move anti-clockwise. Remember to return to the start position for each go and answer the same questions. Ask an adult to tell you the compass direction that your home faces in. From this you should be able to work out where each of the four main compass points are in relation to the building. Mark the points in between to make it eight points altogether. Draw a sketch plan of the building showing the compass points on it.

What to talk about:

Make sure you understand what the words clockwise and anti-clockwise mean and also quarter of a turn, half a turn, three-quarters of a turn and a full turn or revolution. Discuss compass points in relation to the building. Are there advantages to buildings facing in a certain direction? What are they?

What to record:

The turns, the number of right angles involved and the different locations in the room can be recorded orally. Talk through the solutions with a helper, remembering there will be a separate set of answers for both clockwise and anticlockwise. Draw the sketch plan of the building on the back of the worksheet. Mark the main four compass directions and all eight compass points if possible.

Comment from parent/carer:

I This page may be photocopied for use only within the purchasing institution.

!

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MATHS AT HOME

Glossary Alternate numbers: numbers that come every other one in the number line with a one-number gap in between, e.g. 35, 37, 39, 41

(odd) and 242, 240, 238, 236 (even). Analogue clock: a clock face in which hands - one for the hour and one for the minute - are used to show the time. Angle: the amount of turn between two lines. An acute angle is less than 90 degrees, a right angle is exactly 90 degrees and an obtuse angle is between 90 and 180 degrees. Area: the amount of surface in a shape, measured in square units. The quick way to find the area of a square or rectangle is to multiply the length by the width. Associative law: this states that numbers can be regrouped in both addition and multiplication problems in order to make calculations easier. For example 16 + 17 + 4 can be added as (16 + 17) + 4 or 16 + (17 + 4) and 8 x 2 x 5 can be multiplied as (8 x 2) x 5 or 8 x (2 x 5). Axes: lines, usually one horizontal and one vertical, which are used as a framework for drawing graphs and positioning coordinates. Bar chart: a type of graph or chart in which information is shown in solid blocks or columns. Capacity: the amount a container holds. Carroll diagram: a method of sorting information by using boxes. The boxes are labelled according to the column and the row. They are named after Lewis Carroll. Celsius: scale for measuring temperature, with 0 degrees freezing point and 100 degrees boiling point. It is named after Anders Celsius, a Swedish scientist. Circumference: the name for the perimeter or the distance around the outside of a circle. Clockwise: following the same direction and course taken by the hands around the face of a clock. The opposite direction is called anti-clo ckwise. Commutative law: this states that groups of numbers can be added or multiplied in any order and still produce the same solution, e.g. 5 + 3 + 6 and 6 + 3 + 5-14; 4 x 2 x 5 and 5 x 4 x 2 - 40. Consecutive numbers: numbers that come in their exact number line order, e.g. 34, 35, 36 or 107, 106, 105, 104. Consonant: all the letters of the alphabet that are not vowels. Constant proportion: a sequence of numbers that increases or decreases by the same amount each time, e.g. 3, 8, 13, 18, 23 (+5);

41, 35, 29, 23 (-6). Conversion graph: a graph that can be used to change one set of units into another, e.g. kilometres into miles and vice versa. 65

MATHS AT HOME Decimals: another method of expressing a common fraction, using tenths, hundredths and thousandths with a decimal point between the whole numbers and the fractions, e.g. 7.325 is seven whole ones, three tenths, two hundredths and five thousandths. Denery: the base ten number system on which our counting operates. Diameter: a straight line that cuts a circle exactly in half. It starts and ends on the circumference and must go through the centre. It is twice the radius of the circle. Difference: a comparison between two numbers that is usually found by subtracting the smaller from the larger, e.g. the difference between 8 and 20 is 12. Digit: the single symbol for a number, e.g. 7. The ten digits in our number system are 0, 1,2, 3, 4, 5, 6, 7, 8 and 9. A two-digit number would be 47, three-digit 129 and so on. Digital clock: a clock without hands in which the time is shown only in numbers, e.g. two-thirty would be shown as 2.30. Doubling: multiplying a number by two, e.g. double 45 = 90. Equivalent calculation: checking a calculation by using a different number operation, e.g. 27 + 29 - double 27 + 2 or 67 x 3 - 67 + 67 + 67. Estimate or approximate: to make a careful and reasoned guess of a measurement or calculation before finding the exact answer. Even chance: when there is exactly an even or fifty-fifty chance of an event happening. Even number: any number that can be divided by two. Factor: a number that goes into another number exactly without leaving any remainder, e.g. the factors of 12 are 1, 2, 3, 4, 6 and 12. Formula: a general rule that is followed in order to obtain a certain result in a calculation, e.g. area of rectangle = length x width. Fraction: a part of a whole number or amount. In the fraction 3/4 the 4 shows the fraction family and is called the denominator and the 3 shows the number of parts there are and is called the numerator. An equivalent fraction is where the same value is expressed in a different form, e.g. l/% = 5/io = 0.5. Gross weight: the weight of a container and what it holds. Halving: dividing a number by two, e.g. half of 72 = 36. Horizontal: a line that is parallel to the horizon - the line at which the earth and sky appear to meet. Integer: another name for any whole number. Inverse operation: the process of checking calculations by using the opposite number operation, e.g. 5 + 3 = 8, so 8 - 3 = 5; 10-4 = 6, so 4 + 6 - 10; 2 x 7 = 14, so 14 + 7 = 2; and 24 4- 3 = 8, so 8 x 3 - 24. Mass: the amount of matter in an object. Weight is the measure of the force that the earth exerts on a body. We say the tin weighs 300g, but what we should really say is that the tin weighs the same as a 300g mass. 66

MATHS AT HOME Mean: an average found by dividing the total of a set of values by the number of items. Median: the middle value when a set is put in order from smallest

to largest. Mirror or reflective symmetry: where the shape formed on one

side of a line or lines of symmetry is identical to that formed on the other side. Mode: the most popular or frequent value in a set. Net weight: the weight of what is inside a container only. Non-standard units: where ordinary objects are used for measuring purposes because the children know them. Examples might be handspans for length, postcards for area and cupfuls for volume. Number sequence: a group of numbers that follows a set pattern, e.g. 3, 8, 13, 18 increases in fives while 42, 36, 30, 24 decreases by six each time. Odd number: any number that is not an even number. Ordering: placing numbers in order of size. This can start with the smallest number or the largest number. Parallel lines: lines that remain the same distance apart all the way along their length. Partitioning: splitting numbers into various parts in order to make calculations easier, e.g. 75 + 39 could be added as 70 + 30 = 100 and 5 + 9 = 14, or 37 x 5 could split into 30 x 5 + 7 x 5. Perimeter: the distance around the outside or the edge of a shape. Percentage: another way of expressing a fraction using the parts out of a hundred, e.g. 15% is 15 parts of 100. Pi: the Greek letter (IT) used to represent the ratio between the diameter and the circumference of a circle. For calculation purposes it is reckoned as three and one seventh or 3.14. Pictogram: a form of chart or graph that shows information by using diagrams or drawings. Place value or notation: the position or column in which a digit is written that conveys its value, e.g. in 247 the 2 is worth 200, the 4 is worth 40 and the 7 is worth 7. Positive and negative numbers: positive numbers are greater than zero in the direction of increase, while negative numbers are less than zero in the direction of decrease. Prime number: a number that only has factors of 1 and itself, e.g. 13 is a prime number. Probability: the likelihood of an event happening. Product: the answer to a multiplication calculation, e.g. the product

of 4 and 3 is 12. Range: the difference between the highest and lowest values in a set of numbers. Ratio: a method of showing a comparison between amounts, e.g. 1:3 means one part in three. 67

MATHS AT HOME Revolution: a complete turn through four right angles or 360 degrees. Rounding off: taking numbers to the nearest round number in order to make them easier to use in calculation, e.g. 28 becomes 30,172 becomes 170, 5794 becomes 6000, 9.8 becomes 10 and 5.37 becomes 5.4. Sum or total: the answer to a calculation problem in which numbers are added together. Tallying: a system of recording numbers during a data handling activity. Items are counted in groups or bundles of five, made up of four down strokes with a diagonal line through them. Tessellation: fitting a shape or shapes together so that there are no spaces left between them. Thermometer: an instrument used for measuring temperature. They are usually marked with both positive and negative numbers to show temperatures both above and below freezing point. 3D: a three-dimensional solid shape. Times: an alternative name for the multiplication process, e.g. 8 times 2 is 8x2-16. 2D: a two-dimensional flat shape. Trebling: multiplying any numbers by three, e.g. treble 10 = 30. Venn diagram: a diagram that uses loops or circles to simplify the relationship between two or more sets of information. They are named after John Venn. Vertical: a line that is at right angles to the horizontal. Sometimes the word perpendicular or upright is used. Vowel: in the alphabet, the letters a, e, i, o and u. Volume: the amount of three-dimensional space taken up by an object.

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