Section 3 : Exploring 3D shapes

Transcription

1 Section 3 : Exporing 3D shapes Copyright 2016 The Open University

2 Contents Section 3: Exporing 3D shapes 3 1. Using practica work 3 2. A cross-curricuar approach 4 3. Using practica work to consoidate earning 6 Resource 1: Coecting and making shapes and objects 7 Resource 2: Photograph of a pyramid 7 Resource 3: Nets 8 Resource 4: 3D objects 13 Resource 5: Recording resuts 15 Acknowedgements 16 2 of 16 Wednesday 18 May 2016

3 Section 3: Exporing 3D shapes Section 3: Exporing 3D shapes Key Focus Question: How can you use practica tasks to investigate the reationship of 2D to 3D shapes? Keywords: poyhedra; investigation; patterns; surfaces; edges; vertices; poygons; subject knowedge Learning Outcomes By the end of this section, you wi have: deveoped your own subject knowedge of reguar poygons (2D shapes) and poyhedra (3D objects); expored practica activities to hep pupis investigate the reationship between poygons and poyhedra. Introduction The process of buiding rea geometric soids provides an informa and practica way for pupis to get to know and understand geometric objects. Because pupis are abe to touch the shapes and objects being studied, they fee more confident about thinking in a more abstract way. If these shapes are inked to objects in everyday ife, this heps pupis thinking and visuaisation. 1. Using practica work To expore and investigate poyhedra, it is important to have exampes in your cassroom. There are severa commercia pastic buiding sets to make 3D objects that can be bought to use in the cassroom, but it is as easy to make your own from recycabe materias such as pastic, card and thick paper. Making their own shapes heps pupis understand the properties of shapes better. Pastic drinking straws can be used with thread and wire to buid skeetons of 3D modes. As a teacher, make it a habit to keep objects that may be usefu in the cassroom for exampe, aways keep a straw whenever you buy a coo drink. Ready-made nets of various soids that fod up for storage can be used to hep pupis expore the difference between 2D shapes and 3D objects. Case Study 1: Differentiating between 3D objects and 2D shapes Mrs Yomba, a primary teacher in Lindi, Tanzania, wanted her pupis to be aware of the difference between 3D objects and 2D shapes. She knew this was sometimes a difficut concept for them. 3 of 16 Wednesday 18 May 2016

4 Section 3: Exporing 3D shapes She described 3D objects as those one can pick up, ike books, pens, desks, etc.. She said that 2D shapes are things you can see but that you cannot pick up: an image of a horse on a photograph, or a painting of a person, even a square drawn on paper. She said, athough one can pick up the photograph or the painting, one cannot pick the horse out of the photograph or the person out of the painting. She then invited them to suggest other things that coud be regarded as either 2D or 3D in the cassroom. Some pupis were quite excited about the distinction, but others reay strugged to beieve that a piece of paper or a window are 3D objects because they were too thin. Mrs Yomba decided then to give her pupis homework. She asked them to go home and te their parents about what they had earned, and that their homework task was to bring a ist of at east ten things from home or the oca environment that are 3D. She beieved that by doing this they woud consoidate the work they had done in cass. Activity 1: Understanding 3D shapes or poyhedra Before you teach this esson, you need to coect or make some 3D objects and keep these in a box (see Resource 1: Coecting and making shapes and objects). Organise your cass into groups of between six and eight. Ask your pupis to ook carefuy at the shapes and objects in the box. Ask your pupis what shapes, ike squares and rectanges, they can see in the objects. Te them the names of the objects: Prism e.g. cube, cuboid, cyinder Pyramid e.g. cone, sphere Ask them if they know other objects that ook ike these shapes around the schoo and near their homes. Expain that a the soids, except the cyinder and sphere, are aso caed poyhedra. Ask them: Why do you think cyinders and spheres are not considered poyhedra? (See Key Resource: Using expaining and demonstrating to assist earning for some ideas to hep you.) Te them that the word poyhedron is from a Greek word for a seat. Prisms and pyramids have many fat surfaces ike seats but a cyinder is not a poyhedron as it has a curved surface. Finish the activity by asking each group to count the surfaces on each object. Ask them to record their answers in their books. Share each group s answers as a cass. For homework, ask them if they can see any of these shapes on their way home or at home and report back the next day. 2. A cross-curricuar approach Look at Resource 2: Photograph of a pyramid. Pyramids interest pupis. Here we expore how to visuaise different pyramids. The teacher in Case Study 2, by doing some cross-curricuar work, showed his pupis that 4 of 16 Wednesday 18 May 2016

5 Section 3: Exporing 3D shapes mathematics has connection to other subjects and to rea ife. Activity 2 ooks at the mathematics of pyramids by asking pupis to make their own, using nets. Case Study 2: Looking at groundnut pyramids to motivate pupis in mathematics When Mr Ahmadu panned his esson, he wanted to invove other teachers and to give his pupis more than just a mathematica experience. He spoke to his coeagues in socia studies and they gave him a pictures of groundnut pyramids in Maiduguri, Nigeria (see Resource 2). He dispayed the picture where a his pupis coud see it and asked them to te him what they knew about the picture. Mr Ahmadu made a mind map of what they knew about how the pyramids were buit. (See Key Resource: Using mind maps and brainstorming to expore ideas.) Next, he organised them into sma groups to discuss the pyramids and ist any questions they had about them. He coected a their questions together and sorted out those that were about the structure of the pyramids and their shape. He gave each group a pyramid that he had made from cards (see Resource 3: Nets). He asked the groups to think about the shape and structure and any common features i.e. sides, edges and surfaces on each. Next, he asked them to think how peope were abe to buid such arge structures as the pyramids in Maiduguri. He showed them more pictures of how pyramids were buit and this reay interested his cass. As a resut they asked their socia studies teacher to te them more about the pyramids. Mr Ahmadu fet that this mixing of mathematics and socia studies heped his pupis motivation as they began their mathematics work. Activity 2: Making paper pyramids You wi need copies of Resource 3, paper, scissors and sticky tape or gue. If you ony have enough materias for one group to work at a time you can spread this activity over a week. Expain to your pupis that pyramids can have bases of any number of sides the simpest have equiatera trianges on a four surfaces, but pyramids can be made with any reguar poygon as a base: the groundnut pyramids are made of trianguar sides, but have square bases. Give out the nets of trianguar- and square-based pyramids, and ask pupis to cut, fod and gue these to make paper pyramids. Mount a dispay of them. Next, pace some straws or matches on each group s desk and ask if they can, using string or sticky tape, make a pyramid out of these materias. Go around and support the groups whie they work. Let them share what they did to make their pyramids. 5 of 16 Wednesday 18 May 2016

6 Section 3: Exporing 3D shapes 3. Using practica work to consoidate earning In this part, we move to a more forma exporation of different shapes through using activities that invove pupis making carefu observations before making some different 3D objects themseves. Resource 4: 3D objects provides a usefu summary of pupis earning so far. Case Study 3: Making poyhedra into mobies Mrs Bako wanted to extend her Primary 5 cass s understanding by buiding some poyhedra to make a new set of mobies to hang in her cassroom. She asked her pupis to group themseves into teams of six to eight and gave each group scissors, card and gue. She asked each group to make 32 equiatera trianges, 6 squares and 12 pentagons. She wrote the dimensions for each shape on the board. She asked them to investigate how many different poyhedra they coud make with their poygons by foowing these rues: Use one type of poygon at a time to make the poyhedron. The poyhedron must be a cosed shape. A the edges must join up. The pupis reay enjoyed the task. Next, she gave them nets of reguar poyhedra and asked them to cut them out neaty, fod them and paste them to make poyhedra (see Resource 3). They found that the shapes they buit were the same as the poyhedra they had discovered. She discussed whether it was easier to make the nets into poyhedra or easier having the shapes oose. Most pupis agreed the nets were quicker. Key Activity: Features of reguar 2D shapes and 3D objects First, consoidate pupis earning from earier activities. For this, you wi need your box of shapes and objects and charts to record resuts (see Resource 5: Recording resuts) or ask your pupis to draw the two charts in their books. Organise your pupis into pairs or sma groups. Give them one of the items from your shapes box, and ask them to carefuy ook at the shape and compete the chart as best they can. Suggest they compete a row at a time. Ask them to return their shape to the box and take another one unti they have ooked at every shape. After an appropriate time, ask one pair or group to give their answers to the cass for one shape. Go round the cass unti a the shapes features have been shared and each pair has been abe to check their answers against everyone ese s. Ask them if they noticed any patterns in their observations. Which shapes and objects are reated? Dispay their charts. You might want to use the game Shape Chaenge in Resource 5 to finish this topic and assess their understanding as they pay. You coud divide the cass into teams to pay. You may need to use a doube esson for this activity. 6 of 16 Wednesday 18 May 2016

7 Section 3: Exporing 3D shapes Resource 1: Coecting and making shapes and objects Teacher resource for panning or adapting to use with pupis You wi need to draw/make cardboard cut-outs of the foowing 2D shapes: Triange Square Pentagon Hexagon Septagon Octagon You can now ook at 3D objects. Resource 2: Photograph of a pyramid Teacher resource for panning or adapting to use with pupis 7 of 16 Wednesday 18 May 2016

8 Section 3: Exporing 3D shapes Pyramids of peanut (groundnut) bags, Maiduguri, Nigeria Origina Source: Encycopaedia Britannica Concise Resource 3: Nets Pupi use Beow are tempates for different 3D objects that your pupis can make. 8 of 16 Wednesday 18 May 2016

9 Section 3: Exporing 3D shapes Tetrahedron tempate 9 of 16 Wednesday 18 May 2016

10 Section 3: Exporing 3D shapes Net Square based pyramid 10 of 16 Wednesday 18 May 2016

11 Section 3: Exporing 3D shapes Cube tempate 11 of 16 Wednesday 18 May 2016

12 Section 3: Exporing 3D shapes Octahedron tempate 12 of 16 Wednesday 18 May 2016

13 Section 3: Exporing 3D shapes Dodecahedron tempate Resource 4: 3D objects Background information / subject knowedge for teacher You wi find usefu resources on the website beow: This website provides background information on shape, space and measures. The revision bite on 3D objects is particuary reevant. 3D objects have surfaces (sides), edges and vertices (corners). 13 of 16 Wednesday 18 May 2016

14 Section 3: Exporing 3D shapes The exception is the sphere, which has no edges or vertices. Origina Source: (Accessed 2008) 14 of 16 Wednesday 18 May 2016

15 Section 3: Exporing 3D shapes Resource 5: Recording resuts Pupi use Origina Source: (Accessed 2008) 15 of 16 Wednesday 18 May 2016

16 Section 3: Exporing 3D shapes Acknowedgements Gratefu acknowedgement is made to the foowing sources: Photographs and images Pyramids of peanut (groundnut) bags, Maiduguri, Nigeria : Encycopaedia Britannica Concise Other Resource 4 : 3D objects : Origina Source: (Accessed 2008) Resource 5 : Recording resuts : Origina Source: (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 16 of 16 Wednesday 18 May 2016