MATHEMATICAL CONTENT KNOWLEDGE -
MCK of geometry includes properties of 2D and 3D shapes, classification including hierarchical
thinking, transformations, relationships between 2D and 3D figures/objects, representations,
visualisation, and location.
Shapes:
- 3D shapes are categorised into curved surfaces, flat surfaces, and curved and flat surfaces.
- Polyhedrons are 3D solid shapes with flat faces
- Prisms have two identical parallel faces joined together by rectangles
- Pyramids have one face with at least 3 straight edges which are joined together by triangles meeting at one centre point (apex)
- Spheres have no vertices and no edges
- Cones are solid with one face and one vertex that is not on the face
- Cylinders have two congruent, parallel face
- Platonic solids are a special type of polyhedron, where all faces are identical in shape, size, length of edges, angles and vertices
Location and mapping: There needs to be an understanding of the representation of position
including the use of coordinates. Additionally, the use of positional language with distance/
measurement is a crucial skill for location and mapping.
Transformation and symmetry: Ensure to understand change of position, orientation, size
and shape. It is appropriate to understand symmetry in shapes and arrangements. The focus
in transformations is on the process by which the original shape is transformed into a new one.
The two focuses in symmetry include bilateral symmetry and rotational symmetry.
PEDAGOGICAL CONTENT KNOWLEDGE -
When teaching 2D shapes, students must be able to recognise examples and non-examples
of shapes, as well as models for real objects. They must learn the names of common shapes
and common vocabulary. Teachers are to give opportunities to students to explore the properties
or solve problems. Look at different shapes in the classroom and go through each property such
as it’s number of sides and corners, symmetry lines or reflections, lengths of sides, sizes of angles,
parallel and perpendicular sides, convexity and concavity, and altitude. Teachers can use tangram
puzzles, mosaic puzzles, and geoboards to teach composing and decomposing shapes. With 3D
shapes, examine objects with curved surfaces (spheres) , flat surfaces (prisms), and those with
flat and curved surfaces (cones). Many educators choose to do describing and sorting games,
such as ‘Who am I?’ where students must identify the shape with information about its edges,
vertices and faces.
Reference: (Van et al., 2015)
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Activity - Creating Composite Shapes
Year Level - 4
Classroom Context -
As this lesson is made up of multiple small activities and ICT tools, students with learning difficulties
or special needs may experience some challenges with keeping up to task. Using iPads and
hands-on materials can be distracting or cause students to fall off-track. For students with
learning disabilities, the teacher should plan for the student to complete the activity in a
desk away from distractions. The teacher should also provide explicit individual scaffolding
for these learners to reduce frustration or anxiety.
Content Descriptor -
Compare and describe two dimensional shapes that result from combining and splitting common
Learning Objectives -
This learning activity is designed for students to further their knowledge on geometric shapes.
The lesson is made up of three different activities. First, students will dive into their pre-existing
knowledge on two-dimensional shapes and demonstrate what they know. Second, students will
learn and demonstrate their skills on identifying and re-creating composite shapes. Finally, students
will learn to create composite shapes from written/verbal instruction. This lesson is important because
when students reach the older grades, they will begin to look at measuring areas of shapes, which
is often done by breaking down the individual common shapes.
Resources -
Key Mathematical Language:
2-dimensional, 2D, shapes, geometric, composite, sketch, graph, symmetry/symmetrical,
rotational
Materials:
Notebooks, pencils, sheet of composite shapes, grid paper, iPads
Use of ICT:
The use of iPads and software in this lesson will allow students to learn how to create geometric
shapes using online tools. Use of these resources will help engage students in their learning.
It is also beneficial for their future classes where they may be presented the opportunity to create
more shapes in subject areas such as Graphics, Science or Art.
Prior Knowledge -
Uses everyday language to describe and compare shapes and objects
Finds similar shapes or objects in the environment
Identifies and describes features of shapes and objects
Represents shapes and objects (sketching, model building, digital drawing packages)
Instructions -
- Ask the students to find things that represent 2D shapes around the classroom or school (can step outside the classroom) and list/draw as many they can find in their notebooks
- Write these up onto the whiteboard and discuss the properties these shapes have (similarities and differences)
- Provide each student with a sheet of composite shapes and explain that these shapes are results of the combining and splitting of common shapes (like the ones listed on the whiteboard)
- Using grid paper, allow each student to re-create these composite shapes by individually sketching the common shapes first. Ensure they label each common shape
- Once finished, hand out iPads to each student and ask them to access ‘Sketchometry,’ a digital tool for creating geometric constructions
- Ask students to create composite shapes responding to your verbal instructions. E.g. ‘Can everyone please sketch a composite shape using 2 triangles and 1 rectangle,’ etc.
- Give students time and further assistance if needed, allow students to work together if they wish to, as particular students can also provide learning support to others
Questions to ask -
Is this a 2D shape or a 3D shape? How can you tell?
What are some 2D shapes around the classroom?
Can you tell me some properties of a 2D shape?
What is a composite shape?
How can these 2D shapes join together to form a composite shape?
Enabling Prompts -
Have students practice identifying and drawing common basic shapes on grid paper.
Once confident, encourage them to join these basic shapes together.
Extending Prompts -
Challenge students to research or list names of composite shapes that has not yet been
studied during this activity. Encourage them to draw these on the digital tool.
Images -
The sheet of composite shapes they must recreate and label
An example of how they would sketch/label the composite shape on grid paper
Using iPads, students must go onto this website to digitally sketch composite shapes
An example of how they would use Sketchometry to sketch their new shapes
Reflection -
In week 8, our focus topic was geometry and how students can develop shape awareness
and knowledge, as it promotes visual thinking and communication skills. Research on the
teaching and learning of geometry indicates that physical experience, especially physical
manipulation of shapes, is important at all ages, that a wide variety of geometrical experiences
are necessary in order for children to gain a solid understanding of geometrical relationships
(Jones and Mooney, 2003).
Children need many opportunities to learn about shapes and to identify their different parts,
as they are exposed to shapes everyday in their environment, as well as interact with them
everywhere. They must be able to recognise shapes, verbalise what they see, and understand
why they are there. For example, we want a child to have the ability to make the connection of
knowing that the wheel of a car is a circle. As children learn each geometric concept, they will
develop into further stages of understanding to learn more complex geometry concepts later.
This is why the above activity/lesson plan allows the students to observe the shapes they see
around their classrooms and school. This is then followed by an activity where they must construct
shapes with a digital tool. In the future, I would like to help my students develop an understanding
of shapes by encouraging questions and having discussions about them. This can be done simply
just by allowing a child to share with the class about shapes they see in their environment. It is
important to make fun and engaging geometry activities daily in maths lessons and play times.
References -
Jones, K., & Mooney, C. (2003). Making space for geometry in primary mathematics.
Enhancing primary mathematics teaching, 3-15.
Van, D. W. J. A., Karp, K. S., & Bay-Williams, J. M. (2015). Elementary and middle
school mathematics: teaching developmentally, global edition. Retrieved from https://ebookcentral-proquest-com.ezproxy.library.uq.edu.au
