Directions for Using Worksheets on Thinking about 3D Shape based.docx

1、Directions for Using Worksheets on Thinking about 3D Shape basedDirections for Using Worksheets on Thinking about 3D Shape (based on Owens unpublished 3D test)EquipmentRectangular prisms (e.g., Cuisenaire rods, boxes or Lego pieces (3 shapes including thin one), cone, cylinder, cube, open cubes whic

2、h can be opened out, a square of paperIntroduction Say these worksheets are about thinking in 3D space and about 3D shapes or solids. Show at least 5 different-sized rectangular prisms such as cuisinaire rod, box for disks, a thin and thicker Lego blocks. Whenever showing objects or 3D shapes turn t

3、hem slowly around and over. Ask What do you call these? (expect rectangular prisms but if they say cuboid or square prism say that we will include them all as rectangular prisms. All the sides are rectangles and they sit flat on the table with the top parallel). Show a closed cube and an open cube.

4、Ask for the names and why the difference in name. Ask for the number of sides (6 and 5 respectively).Show a triangular pyramid and a square pyramid. Ask What do you call these? (expect pyramid and prompt for the two kinds). Show the difference in the bases and that the pyramids come to a point with

5、triangular side faces. Ask the class to repeat the name and to say why they call it by that name. Show a cone, a cylinder. Ask for the names.Worksheet A: Are the shapes the same? Recognising Rotated 3D Shapes Say The diagrams or pictures on these pages are of 3D Shapes or solids. Look at the front p

6、age. What is the first picture? (cone) Second? (cylinder). Read the instructions. Student does the example first with help and then completes the questionsWorksheet B: Can you see the 3D shape?- Embedding and Disembedding 3D ShapesJoin together 3 cuisinaire rods to form a rectangular prism. Ask what

7、 3D shape has been made? (rectangular prism). How many blocks of the same size were needed? (3)Say This section is about putting blocks together and seeing which ones might fit together to make rectangular prisms.Worksheet C: Can You See it Another Way? - Folding and Unfolding 3D ShapesShow the bloc

8、ks together and sketch the front view on the board.Take a piece of paper and fold it and tear out a shape in the middle of the open sides. Ask a student to copy what it might look like when opened out. Take the pyramids and cubes partially apart carefully and note the triangles and squares.Worksheet

9、 A: Are they the same?ExampleLook at the 3D shape under Smiley. If you turn it around or over can it look like the shape shown below.Circle Yes or No. 1. Yes No 2. Yes NoLook at the 3D shape under Smiley. If you turn it around or over can it look like the shape shown below.Circle Yes or No. 1. Yes N

10、o 2. Yes No 3. Yes No 4. Yes No 5. Yes No 6. Yes No Three blocks have fallen on the floor. One block has a circle face, one has a triangle face, and one has a rectangle face. We are looking down on them. Which one is underneath on the bottom?Circle the shape. 7.Three sticks are marked with Which one

11、 is underneath on the bottom.Circle the shape of its mark.8. 9.Worksheet B: Can you See the 3D shape?ExampleUnder Smiley is a finished picture. The picture below is not complete. Put in the lines to complete it like the finished one.Under Smiley is a finished picture. The picture below is not comple

12、te. Put in the lines to complete it like the finished one. Example Under Smiley is a building of blocks. Is the 3D shape below one of the blocks?Circle Yes or No. Yes No Yes NoUnder Smiley is a building of 3 blocks. Is the 3D shape one of the blocks?Circle Yes or No. 1. Yes No 2. Yes No 3. Yes No 4.

13、 Yes No 5. Yes NoExampleA 3D shape can be joined to the 3D shape under Smiley. Can the shape below be joined to it to make a rectangular prism? Circle Yes or No. Yes No Yes NoUnder Smiley are two blocks. Can they be joined to make the shape below.Circle Yes or No. Yes No Yes No Yes No Yes NoExampleA

14、 3D shape can be joined to the 3D shape under Smiley. Can this shape be joined to make a rectangular prism? Circle Yes or No. Yes No Yes NoA 3D shape can be joined to the 3D shape under Smiley. Can the shapes make a rectangular prism? Circle Yes or No. 1. Yes No 2. Yes No 3. Yes No 4. Yes No 5. Yes

15、No 6. Yes NoExampleLook at the block under Smiley. If you had some morelike this could you make the solid 3D shape below. Circle Yes or No. If Yes, write how many blocks you need. Yes_ No Yes _ No 1. Yes _ No 2. Yes _ No 3. Yes _ No 4. Yes _ No 5. Yes _ No 6. Yes _ NoWorksheet C: Can You See it Anot

16、her Way?ExampleYou can look from A straight down onto the object under Smiley. You can look at the sides from either B or C.A,looking down From which position do you see the view shown? Circle A, B or C.CB A B C No A B C No A B C NoFrom which position are you looking at the object?Circle A from the

17、top, B from in front, C from the side, or if you dont know, circle No.ABC A B C No A B C No A B C NoACB A B C No A B C No A B C NoABC A B C No A B C No A B C NoExampleA square piece of paper is folded in half taking the top to the bottom.A hole is punched in and then it is opened up again. Will it l

18、ook like the one shown?Circle Yes or No. Yes No Yes NoA square piece of paper is folded in half taking the top to the bottom.A hole is punched in it or a corner cut off and then it is opened up again.Will it look like the one shown?Circle Yes or No. Yes No Yes No Yes No Yes NoExampleThe shape under

19、Smiley is folded up. Can it form the 3D shape?Circle Yes or No. Yes No Yes No The shape is folded up. Can it form the 3D pyramid?Circle Yes or No. Yes No Yes No Yes NoCan the rectangular paper be folded to make the hollow 3D shape shown?Circle Yes or No.If so, draw in the where you would fold the pa

20、per, if any hard fold is needed. Yes No Yes No Yes NoCan the triangular paper be folded to make the hollow 3D shape shown?Circle Yes or No.If so, draw in the where you would fold the paper, if any fold is needed. Yes No Yes No Yes NoS2 Lesson 1 - Pop-up CardsDescriptionStudents make simple pop-up ca

21、rds in an investigative mode.PurposeStudents experience how 3D can be generated and modified by folding backwards or forwards. The cuts provide symmetrical changes.OutcomesSGS2.1 Makes, compares, describes and names three-dimensional objects including pyramids, and represents them in drawingsKnowled

22、ge and skillsStudents learn aboutWorking MathematicallyStudents learn to identifying three-dimensional objects in the environment and from drawings, photographs or descriptions describe three-dimensional objects using everyday language and mathematical terminology (Communicating) explore what can be

23、 created from folding and cutting to make three-dimensional objectsKey ideasCreate nets from everyday packagingExpected learning strategiesThe student uses pattern and movement in her/his mental imagery and is developing conceptual relationships. The student: Predicts changes mentally modifying shap

24、es and their attributes using motion or pattern analysis Discusses patterns and movements associated with combinations of shapes and relationships between shapes.MaterialsPaper or cardboard per student and scissors. Coloured pencils. Examples of bought and homemade pop-up cards.S2 Lesson 1 - Pop-up

25、CardsActivitiesTeaching Points and QuestionsIntroduction Show the student some purchased pop-up cards and your own home-made ones. Take a card and fold it. Ask students to predict what might happen if you make a cut at a slope on the fold. Try it and open up the card. Ask student how you might make

26、the fold poke inwards. Try it and fold it hard. Re-close the card and slowly reopen. Ask students what it looks like and then draw a face, say of a bird if they say it looks like a beak. These activities can become art problem solving activities.Pop-ups can be made by sloping cuts on fold, by two pe

27、rpendicular cuts, by diagonal folds at the top when sides are cut away.They can be decorated by gluing on pieces or just colouring in to make a picture.What will happen if we make a cut at this point?What happens if we fold it inwards?How can we make these cuts stick out?Symmetry is a key feature of

28、 this work.Push into cardActivity (individual)Students may find the beak easiest to do and they can easily draw eyes around it.Discuss the symmetry of the folds that go inwards or outwards.Glue a heart or similar cut-out on the front of the rectangular folded cut.If they are making cards, students c

29、an decide what is an appropriate message to write inside.Conclusion (whole class)Some students display their cards and show how they open up.Which lines are symmetrical about the fold?Could you predict what might happen if you made another cut (or fold) parallel to this one?Students share ideas and

30、help each other to develop their cards.S2 Lesson 2 Shadow ShapesDescriptionStudents investigate the shadows made by a variety of 3 dimensional objectsPurposeStudents need to experience and imagine what a shape will look like from a different perspective. They disembed the face-on view and realise so

31、me parts are then hidden from view. OutcomesSGS2.1 Makes, compares, describes and names three-dimensional objects including pyramids, and represents them in drawings.Knowledge and skillsStudents learn aboutWorking MathematicallyStudents learn to comparing and describing features of prism, pyramids, cylinders, cones and spheres sketching three-dimensional objects f