Understanding Shape

2. Objectives To develop knowledge of the vocabulary and terminology of shape. To consider activities to develop children's understanding of shape. To examine progression in shape. Go through the objectives with staff. This session will move between 2D and 3D shapes as the idea of vocabulary building and the activities involved could be used with either. Go through the objectives with staff. This session will move between 2D and 3D shapes as the idea of vocabulary building and the activities involved could be used with either.

3. Stress the importance that we need to be placing on building up the correct vocabulary. In pre-school provision, and throughout Foundation and Key Stage 1, we should help children to make the gradual transition from using everyday words such as round, fatter, corner.....to the more precise mathematical vocabulary: circular, wider, angle ... There are good opportunities in primary schools for cross-curricular development of this language, for example, in PE, art and design and technology. But in the daily mathematics lesson, the aim is to focus on the development of mathematical understanding rather than the skills of art or technology. Look at the Mathematics Vocabulary Book (electronic copy provided in resources). Look at the range of language used for Shape and Space in YR. Explain how the vocabulary book builds up with new words in red text. Briefly look at progression through the year groups. Key Points: Teacher must know and use vocabulary Teacher must encourage, and leave time for, children to use the vocabulary (in sentences) Vocabulary should be displayed in the classroom so that children can make the link between hearing, seeing and saying the vocabulary. If there are any words that teachers are unsure about, they can use the shape and space dictionary (available from the Lancashire Mathematics Website) to check the definitions or look at a pictorial representation. The next activity illustrates the importance of vocabulary in supporting the learning of shape and space. Activity: Four-bidden (need whiteboards and pens) Explain that they are going to see four words on the next slide, uncovered one at a time. The task is to guess the word! If they guess the word after the first clue they get 4 points, after the second clue 3 points, and so on. Teachers write an answer for each clue and when answer is revealed, teachers mark their own, look in which space they have the correct answer and achieve 4 marks if correct after the first clue, 3 marks if correct after the second clue, 2 marks if correct after the third clue, 4 marks if correct after the last clue.Stress the importance that we need to be placing on building up the correct vocabulary. In pre-school provision, and throughout Foundation and Key Stage 1, we should help children to make the gradual transition from using everyday words such as round, fatter, corner.....to the more precise mathematical vocabulary: circular, wider, angle ... There are good opportunities in primary schools for cross-curricular development of this language, for example, in PE, art and design and technology. But in the daily mathematics lesson, the aim is to focus on the development of mathematical understanding rather than the skills of art or technology. Look at the Mathematics Vocabulary Book (electronic copy provided in resources). Look at the range of language used for Shape and Space in YR. Explain how the vocabulary book builds up with new words in red text. Briefly look at progression through the year groups. Key Points: Teacher must know and use vocabulary Teacher must encourage, and leave time for, children to use the vocabulary (in sentences) Vocabulary should be displayed in the classroom so that children can make the link between hearing, seeing and saying the vocabulary. If there are any words that teachers are unsure about, they can use the shape and space dictionary (available from the Lancashire Mathematics Website) to check the definitions or look at a pictorial representation. The next activity illustrates the importance of vocabulary in supporting the learning of shape and space. Activity: Four-bidden (need whiteboards and pens) Explain that they are going to see four words on the next slide, uncovered one at a time. The task is to guess the word! If they guess the word after the first clue they get 4 points, after the second clue 3 points, and so on. Teachers write an answer for each clue and when answer is revealed, teachers mark their own, look in which space they have the correct answer and achieve 4 marks if correct after the first clue, 3 marks if correct after the second clue, 2 marks if correct after the third clue, 4 marks if correct after the last clue.

4. Reveal one clue at a time. Teachers mark their own. For the next game, play the other way round. Give the answer word and ask teachers to write down what they think will be the four connecting words. They get a point for every one that is correct.Reveal one clue at a time. Teachers mark their own. For the next game, play the other way round. Give the answer word and ask teachers to write down what they think will be the four connecting words. They get a point for every one that is correct.

5. 1 point for each correct word. Give out Handout � Polygons This is a useful sheet for focusing on different shapes with their properties. Give out Handout � 3D shape This is all the vocabulary that should be in place in Year 6. Allow participants time to look at handouts and pick up any key issues. See next slide. 1 point for each correct word. Give out Handout � Polygons This is a useful sheet for focusing on different shapes with their properties. Give out Handout � 3D shape This is all the vocabulary that should be in place in Year 6. Allow participants time to look at handouts and pick up any key issues. See next slide.

6. Definitions � A rectangle is any quadrilateral with four right angles. This either has to have a length which is different from its width (a shape that is correctly called an oblong) or it has all four sides equal (which is called a square).� Some people find the terms �rectangle� and �oblong� confusing. Dictionary definitions vary, so you might like to explain them as follows: A rectangle is any quadrilateral with four right angles, that is equiangular. There are two types of rectangle: A shape which has a length different from its width (an oblong); A shape with four equal sides, that is, equilateral (a square). Some people are in the habit of saying �rectangle� only when they are talking about an oblong. Point out that children need to hear the term �rectangle� applied to both squares and oblongs. Ask everyone to have a pencil and paper handy and to close their eyes for a visualisation activity. Visualisation activity: imagine a large white rectangle on the table in front of you now imagine two smaller black right-angled triangles inside the rectangle slide one of the triangles so that its right angle fits into one corner of your rectangle slide the second triangle to fit into one of the other corners of your rectangle now without saying anything open your eyes and sketch the white shape that is left compare drawing with someone nearby and name white shapes as precisely as they can The next slide shows the shapes that could be made. Some people find the terms �rectangle� and �oblong� confusing. Dictionary definitions vary, so you might like to explain them as follows: A rectangle is any quadrilateral with four right angles, that is equiangular. There are two types of rectangle: A shape which has a length different from its width (an oblong); A shape with four equal sides, that is, equilateral (a square). Some people are in the habit of saying �rectangle� only when they are talking about an oblong. Point out that children need to hear the term �rectangle� applied to both squares and oblongs. Ask everyone to have a pencil and paper handy and to close their eyes for a visualisation activity. Visualisation activity: imagine a large white rectangle on the table in front of you now imagine two smaller black right-angled triangles inside the rectangle slide one of the triangles so that its right angle fits into one corner of your rectangle slide the second triangle to fit into one of the other corners of your rectangle now without saying anything open your eyes and sketch the white shape that is left compare drawing with someone nearby and name white shapes as precisely as they can The next slide shows the shapes that could be made.

7. Can participants name these shapes as precisely as they can. They can use the polygons handout to help them if required. They are as follows: Isosceles triangle Scalene Triangle Trapezium Trapezium Quadrilateral Parallelogram (or rhombus) Irregular Pentagon Irregular Pentagon Irregular Hexagon Irregular Hexagon Say that this form of visualisation exercise makes a good starting point for a mental and oral session on shape and space. 3D shapes can also be used for this type of activity. A selection of similar ideas, for use in the classroom, is provided in the booklet Shape and Space activities. (Included in staff meeting resources.) Give teachers time to look through the booklet. Ask people to consider: How often they start a lesson with a shape-related topic. Discuss starter ideas for shape and space from P2/3 of Spring Term 2008 newsletter. How might these be adapted for different ages and abilities? Can participants name these shapes as precisely as they can. They can use the polygons handout to help them if required. They are as follows: Isosceles triangle Scalene Triangle Trapezium Trapezium Quadrilateral Parallelogram (or rhombus) Irregular Pentagon Irregular Pentagon Irregular Hexagon Irregular Hexagon Say that this form of visualisation exercise makes a good starting point for a mental and oral session on shape and space. 3D shapes can also be used for this type of activity. A selection of similar ideas, for use in the classroom, is provided in the booklet Shape and Space activities. (Included in staff meeting resources.) Give teachers time to look through the booklet. Ask people to consider: How often they start a lesson with a shape-related topic. Discuss starter ideas for shape and space from P2/3 of Spring Term 2008 newsletter. How might these be adapted for different ages and abilities?

8. Orientation of Shapes Children need to see shapes in different orientations. Before showing statement ask staff to draw a rectangle. Note the orientation of the shape most people draw it with a landscape orientation. It is really important that children see shapes that are in different orientations so they can recognise and identify them correctly.Before showing statement ask staff to draw a rectangle. Note the orientation of the shape most people draw it with a landscape orientation. It is really important that children see shapes that are in different orientations so they can recognise and identify them correctly.

9. Tree diagrams are one method we can use to help children sort shapes by focusing on their properties. Most people are familiar with the tree diagram method of sorting. This tree diagram has been designed to reinforce understanding of the properties of shape we have just been looking at on the polygons handout. Click to make the first shape appear. Ask what shape it is. It is a right-angled isosceles triangle. At each question, ask which branch of the tree the shape will follow to be sorted correctly. Click the mouse after each choice has been decided and see if the decision was correct. How do we know two of the sides are equal? Because we know it is an isosceles triangle and one of the features of an isosceles triangle are that it has two equal sides. Click to make the second shape appear. Ask what shape it is. It is an isosceles triangle. At each question, ask which branch of the tree the shape will follow to be sorted correctly. Click the mouse after each choice has been decided and see if the decision was correct. Give out handouts Sorting Shapes 1 and 2. (Either ensure shapes are cut out already or ask teachers to cut them out) and sort into the correct place using the tree diagram on Sorting Shapes 2 (copied onto A3). Teachers should write the correct name onto each shape before sorting. Can the teachers think of extra questions at the end of the arrows that still have more than one shape to sort? Teachers should refer to the Polygons handout if they need help to name the shapes or recognise the properties. During this activity, circulate around the groups, using the opportunity to clarify definitions and sort out misunderstandings. Take feedback about sorting and extra questions.Tree diagrams are one method we can use to help children sort shapes by focusing on their properties. Most people are familiar with the tree diagram method of sorting. This tree diagram has been designed to reinforce understanding of the properties of shape we have just been looking at on the polygons handout. Click to make the first shape appear. Ask what shape it is. It is a right-angled isosceles triangle. At each question, ask which branch of the tree the shape will follow to be sorted correctly. Click the mouse after each choice has been decided and see if the decision was correct. How do we know two of the sides are equal? Because we know it is an isosceles triangle and one of the features of an isosceles triangle are that it has two equal sides. Click to make the second shape appear. Ask what shape it is. It is an isosceles triangle. At each question, ask which branch of the tree the shape will follow to be sorted correctly. Click the mouse after each choice has been decided and see if the decision was correct. Give out handouts Sorting Shapes 1 and 2. (Either ensure shapes are cut out already or ask teachers to cut them out) and sort into the correct place using the tree diagram on Sorting Shapes 2 (copied onto A3). Teachers should write the correct name onto each shape before sorting. Can the teachers think of extra questions at the end of the arrows that still have more than one shape to sort? Teachers should refer to the Polygons handout if they need help to name the shapes or recognise the properties. During this activity, circulate around the groups, using the opportunity to clarify definitions and sort out misunderstandings. Take feedback about sorting and extra questions.

10. Shapes can also be sorted using Venn and Carroll diagrams. Initially, children can be given the headings and asked to sort the shapes. To extend the thinking involved, the teacher can place some shapes and ask pupils to place their own shapes and identify the labels. What would the labels be in this example? Click to reveal. Remember to include shapes that do not fall into either sorting criteria. 3D shapes could be used for this activity, but that is more effective when done with real shapes, rather than 2D representations, initially.Shapes can also be sorted using Venn and Carroll diagrams. Initially, children can be given the headings and asked to sort the shapes. To extend the thinking involved, the teacher can place some shapes and ask pupils to place their own shapes and identify the labels. What would the labels be in this example? Click to reveal. Remember to include shapes that do not fall into either sorting criteria. 3D shapes could be used for this activity, but that is more effective when done with real shapes, rather than 2D representations, initially.

11. Show the slide with the shapes on but no labels. Ask participants to talk in pairs to decide what either pairs of labels may be. Remind them that for Carroll diagrams the labels come in pairs with a �has� the property and a �does not have� the property. Click to reveal one pair of labels and then again for the next pair. Again, this activity could be done with 3D shapes.Show the slide with the shapes on but no labels. Ask participants to talk in pairs to decide what either pairs of labels may be. Remind them that for Carroll diagrams the labels come in pairs with a �has� the property and a �does not have� the property. Click to reveal one pair of labels and then again for the next pair. Again, this activity could be done with 3D shapes.

12. This slide shows an example question from a test paper which requires the children to identify which shape is sorted incorrectly. Again, this allows the children to use and apply their knowledge in a less straightforward way than simple sorting.This slide shows an example question from a test paper which requires the children to identify which shape is sorted incorrectly. Again, this allows the children to use and apply their knowledge in a less straightforward way than simple sorting.

13. Tangram Children need to be able to use and apply their knowledge of shapes and explain their reasoning. Show this slide and explain that this is a two piece tangram puzzle. Give teachers these two pieces (cut from bottom left hand corner to centre of top side). Using these two pieces touching along an edge, how many different shapes can you make? Can you name them all? Give teachers time to work in pairs to solve this. The next slide shows some examples. Have they got all the examples? Is there any they can add?Children need to be able to use and apply their knowledge of shapes and explain their reasoning. Show this slide and explain that this is a two piece tangram puzzle. Give teachers these two pieces (cut from bottom left hand corner to centre of top side). Using these two pieces touching along an edge, how many different shapes can you make? Can you name them all? Give teachers time to work in pairs to solve this. The next slide shows some examples. Have they got all the examples? Is there any they can add?

14. Take care regarding shape 6 because the adjoining lines are not the same length so create an irregular hexagon with one particularly short side.Take care regarding shape 6 because the adjoining lines are not the same length so create an irregular hexagon with one particularly short side.

15. To make a link between 2D and 3D shapes, we can look at the features of 3D shapes in terms of their faces, e.g. cubes. An objective focus from Y3 onwards is to relate 2-D shapes and 3-D solids to drawings of them. In the example on the slide, the squares create a net of a cube. Ask questions such as: When the cube is constructed: What colours will border blue? What colours will border red? What colours will share an edge with green? If pink is on the top, what colour will be on the bottom? What colour is opposite brown?To make a link between 2D and 3D shapes, we can look at the features of 3D shapes in terms of their faces, e.g. cubes. An objective focus from Y3 onwards is to relate 2-D shapes and 3-D solids to drawings of them. In the example on the slide, the squares create a net of a cube. Ask questions such as: When the cube is constructed: What colours will border blue? What colours will border red? What colours will share an edge with green? If pink is on the top, what colour will be on the bottom? What colour is opposite brown?

16. The grey squares show another net of a cube. Can the teachers colour it so that when the two nets are folded, the cubes look identical. Teachers can record this on Handout � Nets. The solution is on the next slide.The grey squares show another net of a cube. Can the teachers colour it so that when the two nets are folded, the cubes look identical. Teachers can record this on Handout � Nets. The solution is on the next slide.

17. One solution for Handout � Nets.One solution for Handout � Nets.

18. The next two slides are reproductions of the renewed framework for the strand � Understanding Shape. Ask teachers to look at the Renewed Framework Core Learning for Maths by Strand for Understanding Shape (Handout 8). Explain that this document is useful in terms of identifying the progression in understanding shape. This is useful to support with differentiation and also mixed age classes. In the renewed framework, objectives for this strand appear in Block B - Securing number facts and understanding shape and Block D � Calculating, measuring and understanding shape. Emphasise the following points: Very little time in the Renewed Framework is spent on naming shapes (or colouring shapes), a more important focus is their properties. The emphasis on exploring and discussing the properties of shapes provides opportunities for mental and oral interactive sessions. Draw their attention to the Shape and Space activities booklet (in the attached resources) Children will be expected to use their knowledge of the properties of shapes to sort, classify and generalise; some work (particularly in upper KS2) might involved them in identifying extra properties from known properties.The next two slides are reproductions of the renewed framework for the strand � Understanding Shape. Ask teachers to look at the Renewed Framework Core Learning for Maths by Strand for Understanding Shape (Handout 8). Explain that this document is useful in terms of identifying the progression in understanding shape. This is useful to support with differentiation and also mixed age classes. In the renewed framework, objectives for this strand appear in Block B - Securing number facts and understanding shape and Block D � Calculating, measuring and understanding shape. Emphasise the following points: Very little time in the Renewed Framework is spent on naming shapes (or colouring shapes), a more important focus is their properties. The emphasis on exploring and discussing the properties of shapes provides opportunities for mental and oral interactive sessions. Draw their attention to the Shape and Space activities booklet (in the attached resources) Children will be expected to use their knowledge of the properties of shapes to sort, classify and generalise; some work (particularly in upper KS2) might involved them in identifying extra properties from known properties.

20. 1999 Framework Supplements of Examples Reception Section 4 Pages 24-25 Years 1-3 Section 5 Pages 80-83 Years 4-6 Section 6 Pages 102-105 This is the reference for the 1999 framework supplement of examples. These pages are still useful in identifying ideas to support learning and teaching. This document is available electronically from the Lancashire Mathematics Team website.This is the reference for the 1999 framework supplement of examples. These pages are still useful in identifying ideas to support learning and teaching. This document is available electronically from the Lancashire Mathematics Team website.

21. Pitch and Expectations The Pitch and Expectations documents are available from the Primary Strategy Renewed Frameworks website (www.standards.dfes.gov.uk/primaryframework). They take each objective for each year group and exemplify the appropriate �pitch and expectations� by linking them to SATs questions/real life problems. Give out the Handouts � Pitch and Expectations (if you wish, just copy the section on Understanding Shape). Ensure that teachers are looking at the section for the strand Understanding Shape. Explain that although this session focused purely on 2D and 3D shape, there are many other aspects to the Understanding Shape strand. The appropriate objectives are in the Renewed Framework strand and the expectations for these are outlined in this document.The Pitch and Expectations documents are available from the Primary Strategy Renewed Frameworks website (www.standards.dfes.gov.uk/primaryframework). They take each objective for each year group and exemplify the appropriate �pitch and expectations� by linking them to SATs questions/real life problems. Give out the Handouts � Pitch and Expectations (if you wish, just copy the section on Understanding Shape). Ensure that teachers are looking at the section for the strand Understanding Shape. Explain that although this session focused purely on 2D and 3D shape, there are many other aspects to the Understanding Shape strand. The appropriate objectives are in the Renewed Framework strand and the expectations for these are outlined in this document.

22. Key Stage 1 Level 3 2003 Sita had a square She cut a triangle of this size off each corner What is the name of the shape that is left? Tick it. square pentagon hexagon heptagon octagon Another useful source of questions which can be used to develop children�s skills of using and applying, and useful for plenary sessions, is Testbase. The question above is from Testbase, originally from the KS1 Level 3 paper in 2003. Ask teachers to have a go in pairs at this question. Discuss how they would model this question to ensure that children could understand. Take feedback. Mention modelling using interactive whiteboard / shape and scissors etc. This could also then be used in the same context with other shapes to see if children could apply that knowledge.Another useful source of questions which can be used to develop children�s skills of using and applying, and useful for plenary sessions, is Testbase. The question above is from Testbase, originally from the KS1 Level 3 paper in 2003. Ask teachers to have a go in pairs at this question. Discuss how they would model this question to ensure that children could understand. Take feedback. Mention modelling using interactive whiteboard / shape and scissors etc. This could also then be used in the same context with other shapes to see if children could apply that knowledge.

23. Key Stage 2 2003 These diagrams show the diagonals of three quadrilaterals. Write the names of the quadrilaterals in the boxes. Ask teachers again to have a go at this question. How could this be modelled to ensure understanding? Take feedback.Ask teachers again to have a go at this question. How could this be modelled to ensure understanding? Take feedback.

24. ICT Polygon Fixing Points Calculating Angles Isometric Grid Symmetry ICT Pack (What�s My Angle?) Modelling is important in mathematics to ensure that children�s understanding is developed. The Library section of the renewed framework contains many resources available to support teachers with modelling. Show the ITPs shown above (which are in the resources file attached). Show how these could be used to model key aspects of learning to develop children�s understanding. Ensure that teachers are aware of the following: Questioning is one of the most important tools to run alongside these resources.Modelling is important in mathematics to ensure that children�s understanding is developed. The Library section of the renewed framework contains many resources available to support teachers with modelling. Show the ITPs shown above (which are in the resources file attached). Show how these could be used to model key aspects of learning to develop children�s understanding. Ensure that teachers are aware of the following: Questioning is one of the most important tools to run alongside these resources.

25. Key Messages The vocabulary associated with shape and space is crucial to extending children�s learning. Children must be provided with lots of opportunities to explore, investigate and reason about shapes. Take any questions and reinforce key messages from the slide.Take any questions and reinforce key messages from the slide.