Digging Deeper into … 2D Shapes (3rd – 6th)

For practical suggestions for families, and helpful links to digital resources, to support children learning about the topic of 2-D shapes, please check out the following post: Dear Family, your Operation Maths Guide to 2-D Shapes

Overview of 2D-Shapes:

The following are the new 2D shapes, to which the children are formally introduced, in the senior end of primary school:

• 3rd class: hexagon
• 4th class:  Equilateral, isosceles and scalene triangles; rhombus & parallelogram; pentagon and octagon
• 5th class: Polygons, quadrilaterals, trapezium
• 6th class: Kite*

* while the kite is not specified on the Primary Mathematics Curriculum (1999) for sixth class, it has been included in Operation Maths 6 as it features on the curricula for 5th/6th grade in many other countries.

As with every topic in Operation Maths, a CPA approach is also recommended for 2D shapes:

Concrete: Using concrete geometric shapes for classifying and sorting; identifying examples of 2D shapes and tessellations in the environment.
Pictorial: Tracing around shape templates to make reproductions that can be manipulated, folded, partitioned and combined; using lollipop sticks, geostrips or geoboards to create representations of 2D shapes; using the Operation Maths Scratch lessons accessible on edcolearning.ie to draw various shapes.
Abstract: Answering shape questions with no visual references/supports; suggesting the number of lines of symmetry on a shape without folding or drawing to explore the same; identifying the resulting shape when a given shape is rotated, flipped etc.

Properties of 2D Shapes:

Don’t let the list above, of 2D shapes by class, fool you; it shouldn’t create an incorrect impression that the primary focus is on identifying shapes, or that we should look at one type of 2D shape exclusive of others. Rather, the focus should be on the children examining the properties of each 2-D shape, describing it according to these properties and contrasting it with, and comparing it to, the properties of other shapes, rather than on just naming the shape. For example, what makes a square a square? How is a square similar to, or different from, a rectangle? Could an argument be made to say a square is also a rectangle? Could an argument be made to say a rectangle is also a square?

Therefore, any new 2D shapes that the children encounter should be compared to the 2D shapes with which they are already familiar. And, as the 2D shapes chapter in Operation Maths always follows on from the topic of Lines and Angles, when exploring properties, reference should also be made to the number and type of angles within the shape, the number and types of sides (parallel, perpendicular etc) and whether the shape is regular or irregular.

Common misconceptions:

Categorising 2D shapes  separately: As mentioned previously, children often don’t recognise a square as a type of rectangle, a rectangle as a type of parallelogram, a rhombus as a type of parallelogram etc. This can often be the case if the children are focused primarily on naming the shape and then compartmentalising it in a category, as opposed to examining its properties and exploring how it may have proprieties in common with other shapes.

It can be useful here to display 2D shapes to the class using a subgroup structure (like this one here) so that the children can appreciate how, for example, a square is also a rectangle, is also a parallelogram, is also a quadrilateral, is also a polygon.

Constancy of shapes: Many children don’t recognise that a  shape remains constant, irrespective of its placement in space. In particular, a square sitting on its vertex is often incorrectly labelled as a diamond. The children should be encouraged to draw or trace around shapes on their MWBs and then rotate the shape in order to appreciate its constancy.

Regularity: Children may not recognise a five-sided figure with sides of same length as being a regular shape. It is as if the terminology “regular” implies to them that the shape should be common-place i.e. regularly occurring. For this same reason, a child will often say a rectangle and a circle are regular shapes, given their familiarity with these shapes from the junior classes, even though they are officially classified as irregular shapes. Challenging this misconception will require plenty of sorting activities where shapes are classified as regular or irregular (see Ready to Go activities below).

When creating a class display of shapes eg rectangles, triangles, etc., instead of using just one qualifying shape to illustrate the term, use many and use varied ones. Enlist the help of the class: “I want to make a display of triangles/parallelograms but I want the triangles/parallelograms to all be different. Can you draw and cut some out for me?” Such an activity would quickly reveal those who appreciate the required properties for each shape and those who don’t. Remember to also position the shapes in various ways so as to reinforce that the shape remains constant, irrespective of placement.

Identifying 3D objects as 2D shapes: This is a very problematic area. It often happens that when asked to find a circle in the environment, a child suggests a ball (a sphere) or a cube might be suggested as a square. When asking to identify 2D shapes in the classroom or at home, we must be careful how we respond to the answers so as not to reinforce these misconceptions. For example, if a child suggests that the door is a rectangle, when it is in fact a cuboid, emphasise that a part of the door is rectangular eg

• Which part of the door is like a rectangle?
• Are there any other parts of the door that are like a rectangle?
• Can you see any other rectangles on the outside of the door? How many?
• Are they all the same or different?

Asking the children to draw around solid 3D objects in order to produce flat 2D shapes can also be useful here.

Coordinates (6th class)

The concept of plotting and reading coordinates is introduced in 6th Class. There are plenty of examples of coordinates in the children’s environment, e.g. map reading, car parks and board games such as chess and Battleship. Allow the children to practise reading coordinates on maps and on board games, then progress to using two digit coordinates in maths. Make sure they first read the horizontal coordinate and then the vertical coordinate.

Operation Maths Digital Resources:

Don’t forget to access the linked digital activities on the digital version of the Pupil’s book, available on edcolearning.ie . These include:

Ready to go Activities: based on the Sorting eManipulative, these enable the various shapes to be sorted according to class-appropriate criteria, or enable tessellating patterns to be made. The Ready to go activities all have suggested questions inbuilt on the left-hand side of the screen that the teacher can just click to reveal and hide. Remember, when sorting, the focus should be on the properties of the shapes not their names; that said, you can also ask the children to identify the shapes, if known, as an extra dimension to the activity.

Create activities: (all classes) again using the Sorting eManipulative, these are less structured that their Ready to go counterparts. Instead, the teacher should click on the yellow “Create new example” button on the bottom of the screen, and then use the sorting eManipulative to explore the shapes as they see fit. The teacher can use a previous Ready to go activity to inspire the create activity or come up with a completely different activity of their own using the almost limitless possibilities of the sorting eManipulative.

Write-Hide-Show videos: These explore tessellations (3rd class) and different types of triangles (5th class). They encourage the children to look and respond to the questions by answering orally or on their MWBs.

Maths Around Us video (6th class): which examines different types of triangles from the environment.

Scratch-based programming lessons with instructions on how to draw 2D shapes  (3rd class) and hexagons (3rd, 4th, 5th classes), scalene triangle, pentagon and octagon (4th class), different types of triangles (5th class) and plot 2D shapes on a grid (6th class).

Further Reading and Resources

• Dear Family, your Operation Maths Guide to 2-D Shapes includes practical suggestions for supporting children, and links to a huge suite of digital resources, organised according to class level.
• The Operation Maths Digital Resources have specific resources designed to support this strand unit. Full details of these can be found in your TRB. Click here for the Quick Start Guide to the Digital Resources.
• Shape and Space Manual from PDST
• 2D shapes Pinterest Board