- Geometry is "an organised, logical and cohern system for the study of shape, space and measurement...[and] involves the study of 1D (lines), 2D (planes) & 3D (solid)" (Jamieson-Proctor, 2016a, p. 5)
- There are 5 basic skills in geometry:
- Visualising
- Communication
- Drawing and modelling
- Thinking and reasoning
- Applying geometric concepts and knowledge (Jamieson-Proctor, 2016a) - There are three different categories to determine 3D shapes:
- "Those with all curved surfaces(spheres & egg shapes) they can roll
- Those with all flat surfaces (prisms & pyramids) called polyhedrons they do not roll only
slide
- Those with both flat and curved surfaces (cylinders & cones) they will roll or
slide" (Jamieson-Proctor, 2016a, p. 3) - Platonic solids are a sub-class of polyhedrons. Platonic solids include:
- Tetrahedron
- Hexahedron
- Octahedron
- Dodecahedron
- Icosahedron (Jamieson-Proctor, 2016a) - 2D shapes do not have any depth, they only have length and width (Jamieson-Proctor, 2016b)
- Common 2D shapes include:
- Quadrilaterals
- Pentagon
- Hexagon
- Octagon
- Decagon
- Dodecagon (Jamieson-Proctor, 2016b) - Students begin with 3D shapes because it is the world of students - begin with shapes such as balls and blocks (Reys et al., 2012)
- Face models can be made easily from heavy construction paper and edge models can be made from straws, pipe cleaners and toothpicks and then connected with clay or tape (Reys et al., 2012)
- Two lines are parallel if they never intersect (Reys et al., 2012)
- Two lines are perpendicular if they intersect at right angles (Reys et al., 2012)
- Geometry has never been my strong suit but I went in to this week with an open mind. I learnt a lot about geometry that I didn't know about before, or that I knew at a base level and was able to expand on this knowledge.
- The big ideas changed my understanding about 1D, 2D and 3D shapes
Demonstrate your understanding of the mathematical concept and related skill and strategies children need to assimilate and be able to use, that are related to the topic of geometry
Language model for concept- There are many different concepts covered this week including; geometry, 1D shapes, 2D shapes, 3D shapes
- Geometry is the study of shapes, including 2D and 3D shapes
- The skills for geometry include:
- Visualising
- Communication
- Drawing and modelling
- Thinking and reasoning
- Applying geometric concepts and knowledge (Jamieson-Proctor, 2016a) - Teaching strategies for geometry include:
- Sorting and classifying shapes
- Build individual shapes (clay, cardboard, straws or paper)
- Modelling
- Creating solids from nets
- Feeling and identifying
- Matching
- Solid jigsaws
- Drawing (Jamieson-Proctor, 2016b)
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| Figure 1.40: Language model for geometry |
Specific teaching strategies and resources that could assist children to understand the key mathematical concept of geometry include:
Describe/demonstrate a specific misconception children might have in relation to geometry
- A specific misconception that children have in relation to geometry is that cardboard and paper shapes are 2D when in actual fact they are 3D because there is a thickness, however thin it is, to the shape (Reys et al., 2012)
- A way to remediate this misconception is to explain to students that although this a way for us to demonstrate their shape it is technically 3D because of its thickness
Provide appropriate URL links to the ACARA year, strand, substrand, content description, elaborations and Scootle resources for the earliest mention of geometry
- Geometry is first seen in the Foundation year, ACMMG009, Measurement and Geometry strand, shape substrand.
- The content descriptor for ACMMG009 is "Sort, describe and name familiar two-dimensional shapes and three dimensional objects in the environment" (ACARA, 2016, p. 1)
- The elaboration for ACMMG009 is: "Sorting and describing squares, circles, triangles, rectangles, spheres and cubes" (ACARA, 2016, p. 2)
- The following are some Scootle resources that would aid in the teaching of ACMMG009:
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| Figure 1.41: Scootle Resource One Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG009&userlevel=(0) |
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| Figure 1.42: Scootle Resource Two Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG009&userlevel=(0) |
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| Figure 1.43: Scootle Resource Three Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG009&userlevel=(0) |
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| Figure 1.44: Scootle Resource Four Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG009&userlevel=(0) |
Resources for students to understand the concept of geometry:
Resources for students to understand the skills of geometry:
- 2D shape identifying and applying to real world knowledge - also teaches students how to draw the shapes
- 3D shape identifying and applying to real world knowledge
- 1D, 2D and 3D volume, area and length - would explain the inches to centimetre conversions
Resources for students to understand the teaching strategies of geometry:
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| Figure 1.45: Edge models of 3D shapes Retrieved from http://proactiveplay.com/modelling-2d-and-3d-shapes-with-toothpicks-and-plasticine/ |
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| Figure 1.46: 2D shape edge models Retrieved from http://proactiveplay.com/modelling-2d-and-3d-shapes-with-toothpicks-and-plasticine/ |
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| Figure 1.47: 3D shape nets Retrieved from http://www.math-salamanders.com/geometry-nets.html |
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| Figure 1.48: 3D shape models Retrieved from http://proactiveplay.com/3d-shape-models-for-play/ |
Chapter 16: Geometry
- Students begin with 3D shapes because it is the world of students - begin with shapes such as balls and blocks (Reys et al., 2012)
- Models play an important role in all geometry (Reys et al., 2012)
- One of the difficulties that children have with 3D geometry is visualising the solids (Reys et al., 2012)
- Face models can be made easily from heavy construction paper and edge models can be made from straws, pipe cleaners and toothpicks and then connected with clay or tape (Reys et al., 2012)
- Children need to be able to recognise geometric shapes as models for real objects (Reys et al., 2012)
- Children should know the names of common shapes, i.e. traingle, square, rectangle, circle and parallelogram,
- as well as words that are associated with shapes, such as centre, radius, diameter and circumference (Reys et al., 2012)
- There are two types of symmetry:
1. Line/reflectional symmetry
2. Point/rotational symmetry (Reys et al., 2012) - Properties of angles:
- The sum of the angles of a triangle is 180 degrees
- The sum of the angles of a quadrilateral is 360 degrees
- The base angles of an isosceles triangles are equal
- The angle opposite the longest side of a scalene triangle is the largest
- Opposite angles of a parallelogram are equal
- A polygon with more than 3 sides can have some equal sides without having equal angles
- Regular polygons have equal angles
- Angles of a quadrilateral sum to 360 degrees (Reys et al., 2012, p .386) - Two lines are parallel if they never intersect (Reys et al., 2012)
- Two lines are perpendicular if they intersect at right angles (Reys et al., 2012)
- Polygons are named according to their number of sides (Reys et al., 2012)
- Two shapes are congruent if they have the same size and the same shape (Reys et al., 2012)
ABCkidTV
Nursery Rhymes. (2014). Shapes song: 31
kids songs and videos. Retrieved from https://www.youtube.com/watch?v=mAE79M9lCbg
Australian
Curriculum Assessment and Reporting Authority. (2016). Mathematics. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Education
Services Australia. (2016). Scootle:
Mathematics. Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG009&userlevel=(0)
Harry
Kindergarten Music. (2014). 3D shapes I know:
Solid shapes song – including sphere, cylinder, cube, cone and pyramid).
Retrieved from https://www.youtube.com/watch?v=2cg-Uc556-Q
Hartmann,
J. (2015). Shapes for kids: 2D shapes:
Shapes song: Educational songs: Children’s song’s: Jack Hartmann. Retrieved
from https://www.youtube.com/watch?v=beTDz9HSNOM
Jamieson-Proctor,
R. (2016a). EDMA202/262 mathematics
learning and teaching 1: Week 9 Part 1. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36561
Jamieson-Proctor,
R. (2016b). EDMA202/262 mathematics
learning and teaching 1: Week 9 Part 2. Retrieved from http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36562
Math
Salamanders. (2016). Geometry nets
information & worksheets. Retrieved from http://www.math-salamanders.com/geometry-nets.html
Reys,
R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S.,
& Bennett, S. (2012). Helping
children learn mathematics. Queensland, Australia: John Wiley & Sons
Australia, Ltd.
Rynhart,
P. (2013). 3D shapes models for play.
Retrieved from http://proactiveplay.com/3d-shape-models-for-play/
Rynhart,
P. (2013). Modelling 2D and 3D shapes
with toothpicks and plasticine. Retrieved from http://proactiveplay.com/modelling-2d-and-3d-shapes-with-toothpicks-and-plasticine/
Sisk,
D. (2012). 3D vs 2D vs 1D: Volume, area
and length. Retrieved from https://www.youtube.com/watch?v=b0_eCFUB_Ag
