
SILO 2.1 (DRAFT) Year 2, Term 1: Shapes and objects Focus: Dimensions Scope and sequence: Perimeter, Area, Volume, Capacity, Dimensions
Learning intention: Students recognise, represent and classify familiar two-dimensional shapes and three-dimensional objects.
NSW Syllabus	Australian Curriculum (version 9.0)
"A student recognises, describes and represents shapes including quadrilaterals and other common polygons." (MA1-2DS-01) "A student recognises, describes and represents familiar three-dimensional objects." (MA1-3DS-01)	"Students learn to make, compare and classify familiar shapes; recognise familiar shapes and objects in the environment, identifying the similarities and differences between them." (AC9M1SP01)

Introduction to the topic

What is the difference between a shape and an object?

In geometry, shapes are generally considered to be two-dimensional but objects have three dimensions.

Tangram activity

An introductory geometry activity using tangrams is as follows:

Give each student a piece of paper and ask them to rule up their own tangrams sheet by following verbal instructions.
After each step, draw the instruction for all to see.
For example; "Draw a straight line between the top-right corner and bottom-left corner."

Alternatively, you could print the tangrams from this A4 template or provide step-by-step instructions for children to draw their own tangrams using this slideshow.

Using the pieces which you just created, try to make the following shapes:

Symmetry

Shapes and objects are symmetrical if they can be divided into two equal parts along a straight line. Some shapes and objects have multiples lines of symmetry and shapes and objects which are not symmetrical are described as being asymmetrical.The following video (3:14) provides a good overview of symmetry.

Activity: Write out the 26 letters of the alphabet in capitals and also the 10 digits. Identify which characters are symmetrical and draw all lines of symmetry.

Students should be able to draw a 6 x 6 grid and add the letters and numbers for themselves. Alternatively, an A4 worksheet is available here in PDF format.

How many characters are not symmetrical?

Which characters have the most lines of symmetry?

Perimeter and area

Perimeter is the distance around a shape. Area is the space inside a shape.

Rope activity

Using a long rope joined together at both ends, find a large space such as outside.
Step inside the rope with the children so that the rope is behind your waist and everyone is facing in.
Try making different shapes and ask the children to estimate if the area of each shape is the same or different.
Return to the classroom and examine the following three shapes which all have the same perimeter of 12.
The teaching point is that area is affected by shape, not just perimeter.

Prisms

A prism is a three-dimensional object where the two ends are the same shape and size. Prisms are also 'polyhedrons' which are solid objects with flat faces. For this reason a cylinder is not classified as prism. Some examples of prisms are shown below:

Some prisms have more than one name. For example, a square prism is more commonly called a cube.

Capacity and 3D shapes

Introduction activity: Capacity is how much an object is able to hold. To begin, we will test what shape or object we can create to have the largest capacity, using only a piece of paper and tape. Each student will attempt to fold or bend their paper into an object they think can hold them most in it. When completed, the object’s capacity will be tested using classroom blocks to see which can hold the most.

The following formula is not formally introduced until Years 7 and 8 but the teaching points are:

Shape is a determining factor when dealing with volume and area.
Mathematics is not just about questions but can be a way of explaining things.
Mathematical formulas embody these relationships. Knowing that there is a formula is more important in Year 2 than knowing how to use the formula. There is a handy online calculator for cylinders at https://www.omnicalculator.com/math/cylinder-volume.

(Image source: https://www.mometrix.com/blog/what-is-the-formula-for-the-volume-of-a-cylinder/)

Drawing 3D objects

When an object has depth to it, making it able to be filled (such as the cylinder seen in the intro activity), we call this 3 dimensional, or 3D. These objects have different properties: they have a certain number of edges, vertices, and faces that classify them as cubes, prisms, spheres, etc. The diagram below shows where the edges, faces, and vertices of different objects are located. An important note is that edges refer to the area where TWO faces meet, whereas vertices are the locations where THREE OR MORE faces meet.

Wait a minute – the circular object looks somewhat confused! Why is that? Does anyone know what this object is called? What do you notice about it that is different from the other objects?

That’s right! It is called a sphere, and it has no edges or vertices! The primary property of a sphere is that it only contains ONE FACE.

Here are some common objects that you have likely seen around. Can anyone give examples of where they may have seen these objects in their everyday activities?

Activity #1:
The activity today is going to be building our own objects. Everyone is going to get a number of different pieces of paper, all coloured differently. You are going to try and fold them to create the following objects:

Activity #2:
The activity today is going to be building our own objects. Everyone is going to get a net that can be used to create a cube and a square-based pyramid. Your task is to cut along the solid lines, leaving the inside of the nets as-is until you are finished cutting. Then, you are going to fold along the dotted lines, and tape the tabs on the net to each of the faces to create your object.

An A4 sized worksheet is available here which has nets for the cube and pyramid on the same page.