Raising the Profile Whole school maths activities for primary schools
CONTENTS 1 Introduction 3 Activities 1. Show a hundred 6 2. Matchboxes 8 3. The answer is 6 10 4. Magic box 12 5. Crossword 14 6. What’s the question? 16 7. Which Wally? 18 8. Nature trail 20 9. Circle patterns 22 10. Show a half 24 11. Christmas maths 26 12. Magic squares 28 13. Dice and digits 30 14. Partners 34 15. Clown 36 16. Stars 38 17. What a space! 40 18. Pop ups 42 19. Tangram 44 20. Make a box 46 21. Rangoli patterns 48 22. Snail’s trails 50 23. Matchstick maths 52 24. Just a minute 54 References and resources 56
INTRODUCTION 3 WELCOME to what I hope is the first of many such primary resource books to come from the MA publications section. This one has been written partly in response to requests from colleagues and partly because I wanted to help, in some small way, to restore the fun that used to be evident in primary maths. I’ve chosen to call the book ‘Raising the Profile’ because that’s what I hope it will do – show children (and their families) and the wider school community that maths can be creative and thought provoking and something to talk about with enthusiasm. Recent UK initiatives have emphasised the open nature of mathematics and the importance of encouraging children to talk about their own strategies or ways of seeing mathematical solutions. The challenges in this book are, if you like, a logical extension of that but with the added freedom to explore, since there is no wrong way of meeting these challenges – only more or less inventive, or sophisticated, or careful. Open-ended activities carefully chosen can use the skills and knowledge that each child, whether young or old, has already mastered. To have the whole school community working and talking for a while about one mathematical topic has unexpected pay-offs, as older children explain to younger ones and parents share the common theme too. You may not choose to use the ideas in that way, but I do suggest that at sometime you give it a try – you may be surprised at the excitement maths can generate. In school I like to call the ideas ‘challenges’ but in order to avoid confusion with the M.A. Primary Mathematics Challenge competition, here I refer to them as activities. None of the ideas included here are mind-blowingly original but I hope that in gathering them together and presenting them in one place, you, as hard pressed teachers, maths coordinators or headteachers might be tempted to use them and ‘raise the profile’ of maths in your school.
INTRODUCTION 4 THE LAYOUT OF THE BOOK Each double page spread includes a photocopiable activity page and, on the facing page, ideas for introductions, alternative activities and extension suggestions for younger or older age groups, plus some examples of children’s work. At the lower edge of each sheet are brief guidance notes for parents or carers for home based projects. The activities are grouped according to content, and reference information about resources and the Word files on the accompanying CDrom are on each page. Providing them on disc allows you to adapt or improve them if you wish. There are also some other additional resources listed at the back of the book. IDEAS FOR USE Whole school assemblies Many of these activities were originally devised to be the focus of a monthly whole school assembly. Other curriculum areas had often been the focus of whole school gatherings, but maths was not really considered a suitable topic unless a visiting roadshow or perhaps a competition was involved. At each assembly I firstly fed back the results from the last activity. I chose children’s work from each class (or age group) and asked the children concerned to come to the front, at which point I talked about why I had chosen their work. Sometimes this was to do with an original response, or an extremely carefully produced answer, or perhaps something intentionally amusing. As a staff we were often surprised by the time, and energy, expended by children who perhaps did not particularly shine in the daily maths lesson. It was an opportunity for the younger children to see what the older pupils had done, and increased the understanding that there may be many possible responses to a problem. The children who were chosen were presented with a ‘maths challenge’ pencil and their work, together with a selection of other pupils’ work, was awarded a sticker and used in the display in the entrance hall of the school.
INTRODUCTION 5 In introducing the next challenge I tried to vary the content so that a number-based challenge would be followed by a shape and space or measure challenge, and so on. From the children I drew several examples of the sort of response I was expecting to get, leaving some unanswered questions to provide extra challenge for the older or more able children. Entry to the challenge was voluntary and we stressed the importance of just ‘having a go’. Some of the parents took this as on open invitation to submit their own responses too, and on occasions we had entries from non-teaching and kitchen staff, and governors, who duly received pencils and had their work displayed (if it reached an appropriate standard!). Maths clubs You may choose to use the activities in a maths club. Because the challenges are open-ended they lend themselves to co-operative work and the children often complete one challenge and then, having seen how others respond, choose to repeat the challenge because they have had a better idea. Choosing time Another possibility might be to have the sheets available as choosing time options in your classroom, as on-going activities for children who have finished their work. You might choose to link the challenge with the topic being studied in the daily maths lesson, or offer something totally different as light relief. Take home sheets It’s good to be able to send something home which is intended to be a fun, shared activity. Parents and carers often respond very positively to maths activities which they can’t get wrong…. Post Script You could raise the profile of maths in your school even higher! Why not send outstanding examples of children’s responses to Primary Mathematics for publication? Or suggest that the children make up their own challenges ……....and submit those for others to use? Lynne McClure
6 Show a hundred………………………A pattern, a picture, a sum, a model……..you choose. Name: Class: My title: Help for grown-ups: The solution may perhaps involve collecting 100 small objects such as buttons or pennies, drawing, making a 3-d model, or making up a very difficult sum. Your child may realise that there are many possible different arrangements for a hundred - encourage exploration! Date back to school:
7 Show a hundred Introductions For younger children a hundred is a very big number and they may need help in counting accurately. As an introduction you may wish to show a linear display such as 100 pieces of pasta threaded on a string, or a pattern illustrating an array of 10 x 10 items, or perhaps for older pupils a shape with an area of 100cm2, or a complicated calculation, the answer to which is 100. Extensions/alternatives You could: use for the 100th day of school, for a 100th anniversary or when 100 is in the news change the number to 1000 for older children. Or even a million ….. whilst the young ones are focusing on the magnitude of a hundred, the older ones could be encouraged to make a display of different ways of representing say, a hundred dots. Resources: Show a hundred 102 book and poster ATM
8 Matchboxes How many different items can you get inside a matchbox? Name Class: Here’s my list…. I fitted things into my matchbox Help for grown-ups: Finding very small items can be fascinating. If you have a magnifying glass you can have a lot of fun looking at the detail of natural items such as a human hair, the stamen of a flower, or a (dead) insect! Date back to school:
9 Matchboxes Introductions The idea behind this activity is to introduce, or remind, or reinforce, the idea of awe and wonder in maths. You could introduce the idea by asking the children what is the smallest thing they could hold in their hand. If you have a microscope which can be used in a whole school setting, you could illustrate the structure of a couple of prearranged items. The ‘power of ten’ website has a superb series of photographs starting with a view of earth from outer space and getting closer and more highly magnified up to the cell structure of an insect. Extensions/alternatives You could: make a display of photographs or pictures of magnified objects – perhaps with a quiz asking what they represent with older children, talk about estimating sensibly and calculate how many of something very small are in something of a reasonable size – how many grains of rice in a teaspoon for example talk about how we record very small measurements. How can we work out how thick a piece of paper is even though it is too thin to measure? Resources: Matchbox Website, powers of ten.
10 The answer is 6. … Your questions could use pictures, different kinds of sums, or even models. Name Class: 6 Help for grown-ups: Encourage your child to brainstorm as many different ways of making the number as possible before filling up the sheet. You may want to do this over several days, as more ideas will undoubtedly come to you both as you notice more instances of 6 around. Don’t be constrained by the space on the sheet – be creative!! Date back to school:
11 The answer is 6. Introductions How to introduce the number six? I’ve done this by bringing objects or pictures out of a ‘magic box’, and asking the children what it is that they all have in common. Six occurs in nature frequently so you may get some natural artefacts brought to school as examples if you include one or two in your collection. Or ask the early years children to come to the front and tell the ‘story of six’. You could start with six balloons, for example, and distribute them differently to illustrate the number bonds. Or play the clapping game – ask the whole group to count 1,2,3,4 etc. out loud and clap all the even numbers, up to about 30 or so. Even the little ones will be able to join in. Then ask the older children to clap the three times table. Then get both groups to clap together and ask what they notice. Hopefully some will volunteer that there are some numbers that everyone claps – and that these are the six times table. All these are good ways in to what makes a number special. Extensions/alternatives You could: challenge older children to use compasses to draw a hexagon inside a circle and look for patterns of six in repeats of different shapes challenge the children to make different arrangements of six shapes – hexagons or squares, or triangles use a digital camera to take photos of occurrences of six in nature, to make a display did you know six is the first perfect number? That’s because the sum of its factors is the number itself, 1 + 2 + 3 = 6. You could investigate factors and find the next perfect number, and the next… Resources: The answer is 6 Numbers fact figures and fiction
12 Magic box What’s your rule? Perhaps everything comes out twice as big …or half the size.. or upside down……or matching……….show some ins and outs for others to guess your rule. Name: Class: What goes in? What comes out? Guess my rule!!! (it’s on the back) Help for grown-ups: You could choose to make this either a number or shape activity. The magic box has to do the same to each number put in, so if the rule is add 2, then 5 becomes 7, 100 becomes 102 etc. If a shape is put in, it will be changed in some way – made wider, or twice as tall, or turned around………. Date back to school:
13 Magic box Introductions I often use a magic box as a way of attracting the children’s attention. In this case it’s being used as a function machine, and the objective is for the children to see that although different things come out, the rule stays the same. For the younger pupils you could bring out the partner – eg knife goes in, fork comes out, or a number goes in and is doubled (I like to use objects rather than numerals to make the point), or a subtle one is to put in a picture of a 2-d shape and bring out one which has one less side. Sneaky! Extensions/alternatives You could: read the story ‘Anno’s mysterious multiplying jar’ to emphasise the power of doubling make a display with the magic box and a different rule for ins and outs each day use the box backwards – what went in if ………came out? check out the primary strategy website and download the function machine interactive resource, and counter. Resources: Magic box Anno’s mysterious multiplying jar NNS counting machine, function machine
14 Crossword …… Make up your own crossword then write the clues. Name: Class: Clues Across Down 1. Help for grown-ups: You might want to start by listing mathematical words, and, if you have a Scrabble set, using the letters to help you to work out how to fit them together. Number the beginning letter of each word and work out the clues. Draw the empty crossword and clues on this side, and draw the solution on the back. Date back to school:
15 Crossword Introductions The intention in this activity is to focus more on the accuracy of the clues than the fitting of the words together. You could introduce the activity by displaying your own crossword and clues (for a short cut go to www.edhelper.com/crossword.htm where you can enter answers and clues and the crossword will be generated) and asking for answers from the children. Then put up a blank grid and go through the process of filling in intersecting words, and writing clues for them. Extensions/alternatives You could: make a display of crosswords to illustrate the rotational symmetry and suggest that older pupils create crosswords that use this element of design for older children restrict the content to a specific topic eg: shape change the crossword to a cross number play the Fourbidden card game – one team guesses the target word as the other describes it without using the four words on the card. Resources: Crossword Hangman, cross number and cross word websites R Fourbidden card game
16 What’s the question?…… What’s your favourite number? Write it in the sun and make up some interesting questions to write in the clouds. Help for grown-ups: What’s your child’s favourite number? You may wish to think about this for a few days before filling in the clouds. Date back to school: Name Class:
17 What’s the question?: Introductions The ultimate in the open ended question!! You could introduce this challenge by sharing your favourite number with the children, and perhaps asking some of your colleagues to share theirs too. A range of questions involving arithmetical calculation, shape, and general knowledge facts makes an interesting mix. The Richard Phillips book takes numbers up to a million and gives fascinating facts about each which can be used as a starter. Extensions/alternatives You could: ask a particular class or group of children to debate the merits or otherwise of choosing particular numbers have two different numbers which are connected in some way, such as 5 and 10 and use the results to start a huge version of this in a public place such as the entrance hall and encourage anyone and everyone to add their suggestions restrict the sort of questions for different year groups – year five and six aren’t allowed addition or subtraction, years four and three must include at least one fraction in their questions, etc. suggest that the favourite number could be other than a whole one. Resources: What’s the question Numbers fact figures and fiction 45 What is the 9th triangle number? What is the international dialling code for Denmark? 5 times the third square number Half of 90
18 Which Wally?........ How many different Wallys can you make? How do you know if you’ve got them all? Name Class: I made different Wallys Wally always wears one of his four hats. Draw them here: Sometimes he wears his scarf or bow tie. Draw them here: He always wears one of his two jackets: He’s only got one pair of trousers, so he always wears those: And he’s got two pairs of shoes to choose from Draw all the different outfits Wally could dress up in. Help for grown-ups: You could do this randomly or, with older children help them to work systematically. Use different colours to help. Date back to school:
19 Which Wally? Introductions This is a good activity to include some of the younger children. If you can have the clothes in a basket you can dress the children up to give an idea of the combinations that are possible. The sheet is a little sneaky in that it says that Wally SOMETIMES wears a scarf or bow tie – older pupils might realise that there is a no neckwear option too! Extensions/alternatives You could: support the younger children by giving a photocopy page of undressed Wallys (see disc) ask the children to make up their own questions like this and make a display of them with answers – older children will realise that there is a underlying similar structure to obtaining the complete solution set. In this example, there are 4x2x2x1x2=32 different Wallys, or 4x2x3x1x2 if you count no neckwear as an option look for activities that require systematic organisation of all combinations such as those on the ‘nrich’ website have an interactive display in the entrance hall where teddies can be dressed in a variety of different clothes. If you make some blank teddy cards on the disc, the them in all sorts of ways. I find that’s a good way to talk about the activity when everyone has had a go. Resources: Which Wally nrich children can record the outfits and you can then sort
20 Nature trail Do all flowers have the same number of petals? Do all ladybirds have the same number of spots? Do some numbers pop up in nature more often than others? Can you find an example of each number somewhere around you? Name: Class: 1 2 3 4 5 6 7 8 9 10 11 12 20 is also an interesting number because Help for grown-ups: Older children might just want to record their findings while younger ones may wish to draw their discoveries. Try to encourage them to find examples which are always true – for example, all spiders have eight legs. Date back to school:
21 Nature trail Introductions Some numbers do pop up in nature more often than others, notably Fibonacci numbers (1,2,3,5,8 etc). You could introduce the activity by bringing in a collection of flowers or pictures of insects or animals and counting the petals or legs or wings………did you know that all members of the rose family show five-fold symmetry in their fruits and flowers, whereas flowers with a three-fold symmetry are likely to be grown from bulbs? With younger children you could start with the numbers of body parts. Did you know that infants have 20 teeth whilst adults usually have 32? Extensions/alternatives You could: make a large display of the numbers to 20 and other exceptional ones, and encourage children to add to it by bringing photographs, their own drawings, or real objects make a display of body maths. You could include the numbers of bones, chromosomes, or the relationship between the lengths of different parts of the body such as those discovered by Leonardo da Vinci. Resources: Nature trail Thinkquest
22 Circle patterns………………....Number the points, then think of a rule and join up the points to make a pattern. Name: Class: My rule is: Help for grown-ups: Number the dots in order. Think of a rule, for example add two, and join them up in order, 1-3-5-7 to make a pattern. You might want to suggest continuing the numbering round the circle more than once, or your child may want to add extra dots and renumber them. Colouring will emphasise the pattern too. Date back to school: 1
23 Circle patterns Introductions This particular challenge links the visual with the numerical – a very powerful way of helping some children to make the connections in number patterns. A selection of pictures where the rule is to add a constant (add one, add two etc) produces a regular pattern with different numbers of points in a star and a different sized hole in the middle. Introducing the idea of multiplication emphasises the fact that the numbers get larger. If you have a circular perspex pinboard then you can model this on an OHP, otherwise prepare a transparency of the sheet and try a couple of different rules. Asking for predictions of the pattern and a justification for the prediction can produce some interesting explanations. Extensions/alternatives You could: use numbered children standing in a circle, and a ball of string passed between them according to a rule. If you hold the string up high in the air and then at the end lay the pattern on the floor, you will be surprised at the gasps of amazement! use the ‘nrich’ website to investigate star patterns for older children suggest that they investigate the different patterns in a systematic way, perhaps as a group. Resources: Circle patterns nrich website
24 Show a half Name: Class: My title: Help for grown-ups Younger children may well fill in the left or right hand side with a pattern. Older children may even subdivide the squares into smaller parts. Whichever, they need to cover in the equivalent of 50 squares. Date back to school:
25 Show a half Introductions The mesmeric Smile programme ‘Take Half’ has been updated and placed on the NNS website as a downloadable programme, ‘Take part’. It makes a wonderful introduction to the spatial idea of a half. Failing that, you could use an OHP and a transparency of the hundred grid to elicit ideas from the children. Some of course will take it literally…..see below. Extensions/alternatives You could: use a different fraction – perhaps a quarter – although to make it inclusive for the little ones you’ll need to make sure it’s not more difficult than that change the number of squares in the grid change the grid and make it a circular cake or pizza with lots of slices, or a subdivided triangle…or…(see below) choose to have no guidance as to shape – but you will need to do a very clear introduction in that case. Resources: Show a half
26 Christmas maths There were more presents each day. How many altogether? Show how you found out. Name: Class: I think there are presents altogether On the twelfth day of Christmas.. 12 pipers piping 11 drummers drumming 9 ladies dancing 5 gold rings 4 calling birds 3 French hens 2 turtle doves and a partridge in a pear tree Help for grown-ups: There are many different ways of working out the number of presents altogether. The obvious one is to write out each days’ total and add them all up – perhaps using a calculator. If your child is a little older, you could together look for different patterns and a quicker way to do the calculation. Date back to school: 10 lords a-leaping 8 maids a-milking 6 geese a-laying 7 swans a-swimming
27 Christmas maths Introductions I like to introduce this by inviting children out to the front. I have pictures of the various presents so as we recite the poem I ask the first child to hold up a picture of a partridge in a pear tree. For the 2nd day two children come out, one to hold another partridge and one to show two turtle doves. I build this up until about day 5. Without an indication about the start of the pattern many children just add up the present total for day 12 rather than realising they have to add day 1 and day 2 and day 3 etc. to get a total. If you are more musically adept you may wish to suggest that your colleagues perform the song, with actions, and leave it at that… Extensions/alternatives You could: with older pupils help them to look for a pattern and generalise to more days work out what would happen to the pattern if, on day one, there were 12 partridges, on day two 12 partridges and eleven turtle doves etc. Does the total work out the same? play ‘my aunt went shopping’ and alter the number of items each day to be an even number…..my aunt went shopping and she bought 2 buns….. my aunt went shopping and she bought 2 buns and 4 bananas……. my aunt went shopping and she bought 2 buns and 4 bananas and 6 apples - what happens to the patterns? Note – the answer is 364 – 12x1, 11x2, 10x3, 9x4, 8x5, 7x6, 6x7, 5x8, 4x9, 3x10, 2x11, 1x12, or (12x1, 11x2, 10x3, 9x4, 8x5, 7x6) x2 Resources: Christmas maths The twelve days of Christmas
28 Magic squares ….. Put the numbers 1,2,3,4,5,6,7,8,9 anywhere you like. See what patterns you can find…….. Name: Class: These are my patterns Help for grown-ups: Cut out pieces of paper or card with the numbers 1-9. Explore what sorts of patterns you can make – for example can you put the numbers so that each row adds up to an even number? Or an odd number? Or the same number? There are endless possibilities. Record the most interesting array above and note down the patterns. Date back to school:
29 Magic squares Introductions Another very open ended question which can produce all sorts of interesting answers. The typical magic square is of course the one where each row, column and diagonal adds to the same number – for numbers 1-9 this would be 15 with 5 in the middle square (why?). But I introduce this by putting the numbers in order and asking what patterns anybody notices. In this case the sums of each row, column and diagonal add up to a multiple of 3. This encourages the children to look for other ways of entering the numbers – usually the older ones have seen the original magic square so this gives them an opportunity to be more creative. Extensions/alternatives You could: tell the Chinese story of Lo Shu, the divine turtle with a magic square on his shell ask the children how many solutions to the 3x3 magic square there are and how they relate to each other (through rotational and reflective symmetry) set up a display with a 4x4 grid and Velcro backed numbers 1-16 explore the history of magic squares across different nations explore one of the magic square websites for interactive activities. Resources: Magic squares Lo Shu math forum website magic squares website 1 4 7 2 5 8 3 6 9
30 Dice and digits: make a game Introductions My favourite resource is a box of dice – all sorts and shapes, including 1-6 cubes and blank ones. The following activities although having a common objective, are at three different levels for different ages or abilities of children. The simpler grid is the one I give to KS 1 children and their parents as 0-99 is just too difficult – however if you offer a free choice it can be interesting to see which the children pick. The one which produced the most talk was the 0-99 grid as the children tried to work out which were the good numbers The blank grid is interesting as there is a lot of arithmetic and underlying probability theory underlying decisions about which numbers to put on the grid and where. Extensions/alternatives You could: choose the best and, once you are sure they worked, decorate them, laminate them and keep them for choosing time at playtime and wet play use the blank grid as a data handling exercise. Everyone in the class throws the two dice and records the number of times each of the different scores is made by whatever rule is being used (adding, multiplying, squaring etc). Some scores occur often – why? Some never occur – why? Then choose suitable numbers based on the classes findings, to fill in the grid. Resources: Dice and digits 1,2,3 and which were the awkward ones - either difficult or impossible to make using two 1-6 dice.
31 Dice and digits 1 Use the board and one or two dice, or a spinner. You may want to use buttons for counters too. Write the rules of your game on the back. Name: Class: Name of my game: Help for grownups: If you’ve got dice at home, you could use the number of spots to decide which numbers to cover, perhaps by multiplying, or adding, or squaring…. If you don’t have dice you could make spinners from card board circles and matchsticks. Choose the rule for covering the numbers on the grid. Say what you have to do to win (for example cover three in a row). Playing the game several times will help to iron out any unfairness or problems. Date back to school: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
32 Dice and digits 2: Use the board and one or two dice, or a spinner. You may want to use buttons for counters too. Write the rules of your game on the back. Name: Class: Name of my game: Help for grown-ups: If you don’t have dice you could make a spinner from a card board circle and a matchstick. Playing the game several times will help to iron out any unfairness or problems. Choose your dice or spinners. Choose the rule for covering the numbers on the grid (for example, add the dots). Say what you have to do to win (for example cover three in a row). Date back to school: 1 7 3 8 5 10 6 8 2 9 4 11 5 9 1 10 3 12 4 10 6 11 2 7 3 11 5 12 1 8 2 12 4 7 6 9
33 Dice and digits 3: Use the board and one or two dice, or a spinner. You may want to use buttons for counters too. Write the rules of your game on the back. Name: Class: Name of my game: Help for grown-ups: If you don’t have dice you could make a spinner from a card board circle and a matchstick. Playing the game several times will help to iron out any unfairness or problems, and may help to choose more suitable numbers for the grid. Choose your dice or spinners. Choose the numbers to put on the grid (you might want to use pencil until you are sure). Choose the rule for covering the numbers on the grid (for example, add the dots). Say what you have to do to win (for example cover three in a row). Date back to school:
34 Partners …… Choose pairs of numbers from the ones below and say why they make good partners Name: Class: Help for grown-ups: There are lots of possibilities here – there may be one reason to connect lots of different pairs (they add up to a certain number for example) or your child may find lots of different reasons for connecting two numbers. There’s no right or wrong – the reason just needs to be stated. You might want to use a coloured pencil to join the numbers and write the reason along the line. There’s a space for you to add one of your own too. Can you use them all up? Date back to school: 1 9 12 18 4 24 6 18 36 48 9 8 16 3 2 7 5 5 19 17 1 19 13 11
35 Partners Introductions I introduce this by telling the story of ten, much as the introduction to the ‘The answer is 6’ activity. Then we discuss the idea of partners and how numbers can be connected by adding or multiplying, or some other type of connection. I put up an OHT with a selection of different numbers and ask the children to suggest partners and why. It’s an excuse to look at number bonds, but the older children will find lots of other possibilities too. Extensions/alternatives You could: ask the children to make up their own sets of partners according to a certain rule and give them to a friend as a challenge link this activity to the counter or function machine activities in the ‘magic box’ activity investigate target numbers rich in factors such as 36 and see how many multiplication partners can be found in an ordered way. Resources: Partners
36 Clown Make both sides match. You could add a hat, or a bow tie, too! Name: Class: Name of my clown: Help for grown-ups: This could be done by drawing, or painting, or perhaps by making a collage. To make the face symmetrical, you could cut out shapes from a folded piece of paper, and stick one on each side of the centre line so that both sides match. Older pupils could use ruler and compasses to construct and measure accurately. You could use a real mirror to check! Date back to school:
37 Clown Introductions Symmetry is fascinating to most children. You could introduce this activity through the ‘magic mirror’ where a child has to copy exactly what you do. Or cut a set of dancing dolls from a concertina of paper to show how both sides match. Or produce examples from nature in which line symmetry is evident. From older children you could tease out what exactly they mean by ‘matching’ and draw out the idea of object and image (corresponding shapes) being the same distance away from the mirror line. Or if you are really daring take some face paints and draw a symmetrical pattern on the face of a child ……..or a colleague.. Extensions/alternatives You could: challenge the children to bring in symmetrical faces or other pictures to supplement a whole school display use half faces in art so that the children have to complete the face use a digital camera to take photos of the children and, by reflecting each half in turn, show that we would look slightly strange if we were symmetrical suggest that older children use more sophisticated drawing equipment eg rulers and compasses to ensure accuracy. Resources: Clown
38 Stars What is a star? You could draw one here, or make a model of one as part of our display. Name: Class: Help for grown-ups: Try to tease out your child’s understanding of a star. Young children may draw them freehand, but you could encourage them to try to make all the points the same…or different…or make a 3-d star from straws………the possibilities are endless! Date back to school
39 Stars Introductions I have often used this as our Christmas assembly as the resulting products make a very festive display. I begin by asking for a description of a star, and once several children have had a go we make a communal agreement – usually something like ‘ a centre bit with lots of points coming off it’. Not very scientific or mathematical but enough to get us started. I then show them some pictures of fantastic stars - both 2-d and 3-d and suggest that a judicious use of glitter might enhance the end products. Extensions/alternatives You could: make links to the Circle pattern activity and encourage star production within a circle. How do we make sure the points are equally spaced? Is it possible to draw stars by connecting the points on the circumference of a circle in a continuous line? suggest that older children use more sophisticated drawing equipment eg rulers and compasses to ensure accuracy investigate some of the mathematical models of stellated polyhedra and perhaps make them as a class project try out some of the wonderful folded tissue paper window stars from the Tarquin publication – they make a stunning classroom decoration. Resources: Stars Robert Webb Kaleidometrics Altair grids Reproduced with permission from Robert Webb
40 What a space! ……. What can you make with 20 squares? Cut them out and make a picture. Give it a name. Name: Class: Name of my picture: What is the l o n g e s t shape you can make? What is the w i g g l i e s t shape you can make? What is the most interesting shape you can make? Help for grown-ups: The picture could be made with whole squares, or the squares can be cut up to make other shapes. But all of every square must be used! Date back to school:
41 What a space! Introductions The idea of conservation of area is a sophisticated one. In this activity I like to start by showing a couple of 2-d shapes which have the same area and asking what’s the same about them. Then I rearrange the first shape into the other and we talk about the area or the space they take up being the same. Extensions/alternatives You could: ask for the shape with the longest perimeter……shortest perimeter suggest that the shape should be symmetrical – either line or rotational symmetry have look at the investigations about area on the ‘nrich’ website. The GRRRRRREAT SQUARES one has lots of open ended questions for older children. Resources: What a shape! nrich from nrich GRRRREAT squares
42 Pop-ups ……. Surprise a friend by making a pop-up card. Name: Class: My card is for: Instructions 1. Take two identical pieces of paper and fold them in half. 2. On one of the pieces, cut a line into the fold 3. Fold the flaps back to make triangles 4. Open the flaps and then open up the paper 5. Push the triangle through from the outside to the inside to make a mouth 6. Make a picture using the mouth then glue the other piece of paper onto the outside Help for grown-ups: If your child is young, you may need to help with the mechanics the first time, but do let them have go by themselves. Older children might like to try making more than one flap, or different sized flaps, or different shaped flaps….. Date back to school:
43 Pop-ups Introductions If you have collection of pop - up cards then showing them to the children can be a good enough introduction. The one on the sheet is a simple mouth flap, but if you have them you can take apart more mathematical ones that use rectangular steps onto which pop-up shapes can be stuck. Extensions/alternatives You could: make a display of the various cards suggest that older children have to have more than one flap investigate how you make a flap on top of a flap – expect more sophisticated and accurate examples from the older children support younger children by using squared paper for the inside sheet of paper. Resources: Pop-ups Fractal cuts Robert Sabuda from Robert Sabuda website cut out rectangular flaps and stick shapes onto the front of them
44 Tangram Cut out the pieces and make a picture which uses all of them. Give your picture a name. Name: Class: My picture is: Help for grown-ups: You may like to cut off the heading and stick it onto another sheet together with your child’s picture. The picture must use all the pieces. Colouring may emphasise the picture, too. Date back to school:
45 Tangram Introductions There are several good books that have tangram activities suitable for all ages of children, and a good source of ideas for you. Using an OHP you can show how to disassemble the square and make it into a variety of different shapes or pictures to illustrate the idea. You might wish to suggest that the pictures are on a certain theme, or, together with the title, tell a story. If you have access to the internet in your assembly venue, you could show some of the interactive ‘nrich’ challenges to provide further ideas. Extensions/alternatives You could: use a different tangram – for example at spring time you might choose to use the Egg tangram (see below) challenge the children to create certain mathematical shapes using all the pieces at any one time eg a large isosceles triangle, or a hexagon introduce the children to the stories and challenges from the tangram activities on the ‘nrich’ web site let the children make up their own tangram and offer challenges to their classmates with older children label each piece as a fraction of the whole square and ask the children to make a picture using pieces summing to 3/8, 3/4 etc. Resources: Tangram nrich Cundy and Rollett Egg Tangram
46 Make a box What shaped box can you make from one A4 piece of card? You can use lots of sticky tape or glue but no other bits of card! Name: Class: If you want to make this box copy the net below onto your card. If you want to make a box without a lid, you can leave out the bottom rectangle. This box uses two circles and one rectangle This box uses two triangles and three rectangles Help for grown-ups: Practice with old card first – the box doesn’t have to have lid. You could add some flaps for ease of sticking. Date back to school:
47 Make a box Introductions You could introduce the idea of a net by taking apart several cereal and other boxes. Older children will already have seen nets several times, so you could set a different challenge such as using the card to make the biggest box possible – ie the one with the biggest volume. Emphasise that the whole box must be made from one piece of card only. Extensions/alternatives You could: set up the interactive display with polydron to make polyhedra, and boxes which can be taken apart challenge the children to create boxes which fulfil certain conditions o to hold a tennis ball, o a cream egg, o having a curved face, o holding at least a named volume. use the boxes to estimate volume ask for suggestions for measuring the volume of the various boxes and arrange them in order set up an investigation comparing the areas of all the surfaces of a box with the volume. Resources: Make a box
48 Rangoli patterns ……………. Join the dots to make a doorstep pattern. Name Class: Name of my pattern: Help for grown-ups: Rangoli patterns are typically made of coloured powders and painted on the ground on doorsteps by Indian women between Dec 15th and Jan 15th of each year. They are usually symmetrical. Date back to school:
49 Rangoli Introductions Rangoli patterns are made by joining dots arranged in a grid. Usually the patterns have either reflective symmetry or rotational symmetry, and some have both. You could introduce Rangoli patterns by beginning with a single line of symmetry - photocopy the grid opposite and draw a mirror line down the centre, joining the dots. Join dots on one side of the mirror to make a simple pattern and then invite a child to come and draw the reflection. You could then show some other more complicated examples. Extensions/alternatives You could: challenge the children to bring in symmetrical pictures start a display with some Rangoli patterns that have been begun, leaving them for children to complete try using coloured sand to make a Rangoli pattern on a board suggest that older children use more sophisticated drawing equipment eg rulers and compasses to ensure accuracy invite a parent or friend who knows how to do them properly to come and demonstrate. Resources: Rangoli illustrations from www.kamat.com
50 Snail’s trails ……………Snail needs to go from A to B. How many different paths can he take? What is the shortest? What is the longest path? (He can’t use any point more than once, but he doesn’t have to use them all. He can’t go diagonally – only up or down, or across.) Name: Class: Snail’s shortest is units and longest is units Help for grown-ups: There are four grids here to have go but you might want to draw a lot more to try different ideas. Date back to school: A B
51 Snail’s trails Introductions I like to introduce this using a 3 x 3 array and tell a story about a creature trying to move along the paths from one corner to another. Younger children will enjoy just finding lots of different paths whilst older ones can be encouraged to do this systematically – which may mean inventing some sort of recording code. Don’t give any ideas though - let them invent their own. This activity could easily lead on to topology – the study of networks and pathways - the ‘nrich’ site has a whole section of such linked activities. Extensions/alternatives You could: ask how many ways there are of getting the longest line and make a display of them ask how many ways there are of getting the shortest line and make a display of them change the rules so that diagonal lines are allowed change the size of the grid to 5 by 5 change the numbers of times you are allowed to visit each dot change the rules so that you have to go over each line joining the dots once and once only. Is it possible? ask the children for some ‘what ifs’ and let them design their own investigations. Resources: Snails trails © nrich website nrich
52 Matchstick maths What can you make with 24 matchsticks? Name: Class: Name of my matchstick challenge: Help for grown-ups: Of course make sure the match sticks are used ones! 24 is a large number for a young child so you may wish to suggest grouping the matches in some way to make more sense. Try to encourage your child to do something mathematical – it would be relatively easy to make some sort of picture, but a pattern or a puzzle requires more mathematical thinking. Date back to school:
53 Matchstick maths Introductions You could introduce this by putting up a few simple matchstick puzzles on the OHP such as those below. Some children might choose to use all their matchsticks to make a selection of puzzles such as these – they are a good way to encourage the accurate use of mathematical language. Extensions/alternatives You could: challenge the children to make the widest enclosed shape – the tallest shape – or even a 3-d shape by glueing them together use the matches to make numbers and hence sums set some challenges – what is the widest 2-d shape that can be made? Let the children have a go at making up some puzzles – see ‘Maths on fire’ for examples. take way four matches and leave five squares Resources: Matchstick maths Maths on fire
54 Just a minute …. What can you do in a minute? Write or draw what you found out. Name: Class: I can: Help for grown-ups: The passing of time is a sophisticated concept even to grown-ups. A minute can seem a very long time when you’re standing on one leg but no time at all when you’re enjoying yourself. Explore some of the more usual and unusual tasks that can be done in a minute. Date back to school:
55 Just a minute Introductions The programme of the same name is introduced by the ‘Minute Waltz’ by Chopin and if you can get hold of a copy it makes a suitable introduction. Or you could set a stopwatch going, ask everyone to close their eyes and estimate a minute. They put their hands up and open their eyes when they think a minute has gone by. You could ask for a volunteer to come and see if they could stand on one leg for a minute – or see how many times they can bounce a ball… or whatever. Extensions/alternatives You could: set up a display of different types of clocks with challenges of the ‘how long would it take….’questions have a sponsored silence make a display of time words and everyday sayings to do with time play the ‘just a minute’ game (children have to speak on a given subject for one minute without repetition, deviation or hesitation). You might want to start with half a minute and be quite generous about applying the rules to begin with explore sundials and how they work. Resources: Just a minute Sundials
56 Resources linked to activities Show a hundred Million dots poster www.universalworkshop.com/pages/MIL.htm 102 book and poster ACT 029 ATM Matchboxes Powers of ten website www.microcosm.web.cern.ch/microcosm/P10/english/welcome.html Powers of ten flipbook Eames and Eames pub Freeman ISBN 0716734419 Powers of ten Philip Morrison pub Freeman ISBN 0716760037 The answer is 6 Numbers, facts, figures and fiction Richard Phillips pub Badsey ISBN 095465620-2 Magic Box Annos mysterious multiplying jar Anno and Anno pub Philomel ISBN 0698117530 Counting machine, function machine www.standards.dfes.gov.uk/numeracy/publications/ict_resources/ Crossword Make your own crosswords www.edhelper.com/crossword.htm Cross number interactive site http://kreuzzahl.de/ Hangman www.interativestuff.org/sums4fun/ Fourbidden card game ACT 012 ATM What’s the question? Numbers, facts, figures and fiction Richard Phillips pub Badsey ISBN 095465620-2 Which Wally nrich website search under combinatorics www.nrich.maths.org.uk Nature trail Fibonacci numbers in nature library.thinkquest.org/27890/applications5.html or www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html Circle patterns nrich website www.nrich.maths.org.uk Path to the Stars (Feb 2002) smile Inscribe see smilemathematics.co.uk Show a half Take part www.standards.dfes.gov.uk/primary/teaching resources/
57 Christmas maths The Twelve days of Christmas John Julius Norwich pub Transworld ISBN 038541028X Magic squares maths forum website mathforum.org/alejandre/magic.square/adler/ magic squares website www.magic-squares.de/magic.html Stars Kaleidometrics Sheillah Shaw pub Tarquin ISBN 0-906212-21-9 star and other beautiful patterns from circles Symmetry Patterns Alan Wiltshire pub Tarquin ISBN 0-906212-73-1 photocopiable grids to make stars and other symmetrical patterns Window Patterns William Gibbs pub Tarquin ISBN 1-899618-31-7 tissue paper star Altair creative colouring books pub Longman ISBN -0-582-35040-4 well known grids for spotting patterns including stars Robert Webb website home.aanet.com.au/robertw/Stellations.html fantastic pictures What a space! nrich website search under area www.nrich.maths.org.uk Pop ups Up-pops Mark Hiner pub Tarquin ISBN 0-906212-79-0 uses elastic bands to produce Fractal cuts Diego Uribe pub Tarquin ISBN 0-906212-88-X www.makersgallery.com/joanirvine/index.html www.enchantedlearning.com/crafts/cards/flowerpopup/ robertsabuda.com/popmakesimple.asp Tangram nrich website search under tangrams www.nrich.maths.org.uk directory of tangram sites tangrams.ca/inner/diver.htm Mathworld Weisstein Egg Mathworld Rangoli patterns smile website search for Rangoli smilemathematics.co.uk www.kamat.com/kalranga/rangoli/rangani.htm snaithprimary.eril.net/rangoli.htm Snail’s trails nrich website search under networks www.nrich.maths.org.uk Matchstick maths Maths on Fire: Matchstick Maths John Dabell pub Millgate House Take a minute www.sundials.co.uk/projects.htm
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