Section 2 : Practica ways from sheet to cube Copyright 2016 The Open University
Contents Section 2: Practica ways from sheet to cube 3 1. Organising an investigation of 3D shapes 3 2. Using group work to understand nets 5 3. Deveoping probem-soving skis 6 Resource 1: Net of a tin (a cyinder) 7 Resource 2: 11 nets for a cube 8 Resource 3: Dice facts 9 Resource 4: Pictures of containers 10 Resource 5: Numbered dice net 11 Acknowedgements 13 2 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Section 2: Practica ways from sheet to cube Key Focus Question: How can you hep pupis see and mentay transform geometric shapes? Keywords: nets; geometry; visuaisation; transformation; boxes; dice; investigations Learning Outcomes By the end of this section, you wi have: expored practica ways to use the oca environment and simpe nets to hep pupis understand 3D objects; used investigation and probem soving to extend your pupis thinking about the different nets to make cubes; used dice to encourage menta visuaisation and transformation of cubic nets. Introduction Imagine you have to draw a shape on a piece of paper, which can be cut out and foded into a cube. On the paper you wi draw the six squares that wi fod up to make the six sides of the cube. Can you imagine the shape you woud draw on the paper to make the cube? It is not easy to do, as this imaginary exercise requires two important mathematica skis menta visuaisation (being abe to see with your mind s eye a two-dimensiona [2D] or three-dimensiona [3D] mathematica image) and menta transformation (being abe to manipuate or change that image in some way). This section expores practica ways to deveop these skis in your pupis as they make nets. (A net is a 2D representation of a 3D shape, with dotted ines to represent fods, and soid ines to represent cuts.) Manipuating a rea object wi hep your pupis visuaise the transformations of this object and reate their understanding of shape to their own ife. 1. Organising an investigation of 3D shapes As your pupis work it is important that they fee that they are doing the investigation, that they are soving the probem. As a teacher, you need to be abe to stand back and watch your pupis taking over the centra stage. At first, this is often difficut to do, but if you can find a way to set up your cassroom that gives pupis the space to think, tak and expore, many of them wi surprise you with their imagination and understanding. For more information, see Key Resource: Using investigations in the cassroom. Activity 1 and Case Study 1 expore ways of aowing pupis to discover the nets for different shapes themseves. 3 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Case Study 1: Investigating a net for a tin Mrs Sawua in South Africa was doing work on shape. First, she took her cass out into the oca environment to ook at a the different shapes they coud find. The next day, she wanted to start her esson on nets by having her pupis discover a simpe net for themseves. Mrs Sawua asked them to think how they coud make a paper pan of some of the shapes they had seen. She istened to some of these ideas. Then, having asked her pupis to bring in a tin (she coected a few hersef for those who forgot or coudn t bring one in), she asked them this question to discuss in pairs: Your tin can was made from a fat piece of tin. Imagine your piece of paper is a piece of tin to be made into a can what shape woud have to be cut from the paper? Can you use the can to hep you draw this shape on your paper? Resource 1: Net of a tin (a cyinder) shows how a 2D net can be foded to make a 3D object. She gave the pupis time to try and sove this puzze. Mrs Sawua enjoyed watching her pupis working and did not interfere uness she saw they were stuck. She was peased at how many were abe to produce the net. Activity 1: Identifying the net of an open box For this activity ask each pupi to bring in an empty box. You shoud coect some too. Give each group of four some gue or sticky tape and four sheets of A4 paper. Te pupis that together they are going to expore how to make a box the same shape as the box (a rectanguar prism see beow), using one A4 sheet and by drawing, foding and sticking. Ask them to work together and discuss how to do it before they start. Once they are happy with what they are doing, ask them to use one piece of paper to test their ideas. If some groups are stuck, give them a cue about how to start by suggesting they undo the box to make it fat. Wak around sienty; ony hep if a group is stuck or asks for support. 4 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Ask each group to show their work to the cass. In the next esson, ask pupis to decorate their boxes and hang them from the ceiing. Finay, ask them to draw their pans or nets for the box they made and dispay these too. 2. Using group work to understand nets In this part, you wi hep pupis extend their understanding by moving from open to cosed boxes. This means adding a id to the box and expaining what changes need to be made to the net. Using the same groups working together, means that pupis can buid on their coective ideas. Putting your pupis into new groups, in this case, woud mean they woud have to revisit earier ideas first, which woud sow down the deveopment of new ideas. In this part, you show your pupis how there is not just one correct answer, but many possibe answers. By not teing them too much, but asking questions to guide their thinking, you are giving them the satisfaction of discovering things for themseves. This wi buid their confidence and give them courage to try new ideas. Case Study 2: Designing nets for cosed boxes Mr Chishimba was peased with the progress of his pupis in Activity 1. He expained that, in mathematics, some words have specia meanings. In mathematics, for exampe, the word net is sometimes used to mean a pane shape (a fat, 2D shape), which can be foded to form a soid 3D object. He asked his pupis to add this term to their mathematica dictionary and put in a definition. As they had made a net of an open box previousy, he asked them to make a net of a cosed box. He suggested they ooked at the nets they had drawn ast time and think how they coud add a id. Using the same groups, Mr Chishimba asked them to discuss together how to add a id and draw the new net. He gave the groups ten minutes and then asked each group to draw what they found on the board. Then he asked each group to ook at the different nets and agree whether they a worked. Activity 2: Which nets wi fod to make a cube? Make sure pupis understand what a cube is, then ask pairs of pupis to find as many different nets for a cube as they can. They shoud first draw each net, then cut it out and check that it makes a cube, before trying to draw a different net. (You may want to show one or more exampes such as those beow to get them started.) 5 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube You might ike to set this up as a competition, with a reward for the group that can make the most nets for cubes (see Resource 2: 11 nets for a cube). Again, do not interfere or tak too much during this esson; make space for the pupis to tak through their ideas and to enjoy the activity. Listen carefuy to them and identify how they are abe to sove their own probems. Dispay the finished cubes and, if there is time, aow them to decorate them to ceebrate what they have achieved. Discuss how many different nets they have found. Ask them to make a wa chart of the 11 possibiities of a net for a cube. 3. Deveoping probem-soving skis Having estabished famiiarity with nets, and making cuboid shapes from them, you now move on to ways of heping your pupis to visuaise and transform these nets mentay. One way to do this is by using a dice. Another way is to ook at shapes in the environment. A dice is a specia kind of cube, where each surface has a unique number between 1 and 6, and where the numbers on opposite surfaces add up to 7. See Resource 3: Dice facts. In order to correcty number the squares on a cubic net, before it is foded into a cube, the pupi must be abe to visuaise the transformation from 2D to 3D in their mind s eye. Case Study 3 and the Key Activity expore these ideas in different ways. Case Study 3: Drawing nets for different shapes Mrs Moyo wanted to deveop her pupis awareness of mathematics around them in everyday ife and so she went to the nearby ZCBC supermarket and took some pictures of various containers with her mobie phone (see Resource 4: Pictures of containers). She printed the pictures and took them to her cass. She asked her pupis to make neat drawings of what they thought the nets for these containers woud be, and abe them with the product names. When they had drawn the nets, they cut them out and made them into 3D objects so Mrs Moyo coud hang them in the cassroom. The pupis were very peased with what they produced and so she asked them to invite their parents to come and see their work. Mrs Moyo knows that it is important to have good parent cooperation, as this enhances teaching. 6 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Key Activity: Making dice nets Before the esson, coect up or make severa dice to show your cass. Ask pupis in pairs to ook at a dice, and ook carefuy at the numbers they shoud be abe to identify that each side has a number between 1 and 6; you may have to prompt them to see that opposite sides add to 7. Aow them time to check if this rue is foowed on a their dice. Now give each pair two sets of empty 5 x 5 square grid papers. Ask them to design different nets for a dice: a cube net with numbers written on the squares so that they obey the rues above. When they think they have soved the probem, they may cut out the nets and check that they have correct dice. After the pairs have soved this probem, they coud mark dice numbers on some of the other 11 cube nets that they identified. Ask each pair to make a poster to dispay the different numbering patterns for each net. You coud extend this activity by asking your cass to make a board game about shape and use their own dice to pay it Resource 5: Numbered dice net shows an exampe of a correct soution and a tempate for your more abe pupis to investigate how many different ways they can pace the numbers on the dice so it sti works. You may wish to use a doube esson for this activity. Resource 1: Net of a tin (a cyinder) Teacher resource for panning or adapting to use with pupis A net is a fat or 2D shape that can be foded to make a 3D object. Beow is the net of a tin, known as a cyinder. A 2D net The 3D object beow (a cyinder) is what the 2D net ooks ike when it has been foded. 7 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube A 3D object (a cyinder) Resource 2: 11 nets for a cube Teacher resource for panning or adapting to use with pupis 8 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Resource 3: Dice facts Background information / subject knowedge for teacher A dice is a cube, each face marked with a number between one and six. The sum of the two numbers on the opposite faces is aways 7, so the opposite pairs are: 1 and 6 2 and 5 3 and 4 9 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Origina source: http://casses.maxwe.syr.edu/ecn521/pair-of-dice.jpg (Accessed 2008) Dice can be used to pay games on their own or as part of a board game where by throwing a dice a payer is abe to move their counter towards a goa. The first person to reach the goa is the winner. Such games incude Snakes and Ladders and Ludo (see Modue 1, Section 1, Resource 2 for how to pay these). Resource 4: Pictures of containers Teacher resource for panning or adapting to use with pupis Origina source: http://www.greenpeace.org/ebanon/ar/photosvideos/sideshows/ge-poution-guf?mode=index (Accessed 2008) 10 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Origina source: http://www.serengetionine.com/images/junge%20oats%201kg.jpg (Accessed 2008) Origina source: http://www.uniever.co.za/ourbrands/homecare/omo.asp (Accessed 2008) Origina source: http://www.tigerbrands.com/investor/investorcentre/2006resuts/annuareport/divreview_domestic_- food.htm (Accessed 2008) Resource 5: Numbered dice net Teacher resource for panning or adapting to use with pupis This is an exampe of a correct soution: 11 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Numbering dice nets How many ways can your pupis set out the numbers on a dice net and sti keep to the rue? 12 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Acknowedgements Gratefu acknowedgement is made to the foowing sources: Photographs and images Pair of dice : http://casses.maxwe.syr.edu/ecn521/pair-of-dice.jpg (Accessed 2008) Quaker Corn Mea : http://www.greenpeace.org/ebanon/ar/photosvideos/sideshows/ge-poution-guf?mode=index (Accessed 2008) Junge Oats : http://www.serengetionine.com/images/junge%20oats%201kg.jpg (Accessed 2008) 13 of 14 Wednesday 18 May 2016
Section 2: Practica ways from sheet to cube Omo : http://www.uniever.co.za/ourbrands/homecare/omo.asp (Accessed 2008) Tinned food : http://www.tigerbrands.com/investor/investorcentre/2006resuts/annuareport/divreview_domestic_food.htm (Accessed 2008) Every effort has been made to contact copyright hoders. If any have been inadvertenty overooked the pubishers wi be peased to make the necessary arrangements at the first opportunity. Return to Numeracy (primary) page 14 of 14 Wednesday 18 May 2016