# Geometrical properties of plane shapes

Students are required to identify properties of a variety of shapes including identifying shapes which contains sides of equal lengths, the properties of circles, the properties of different types of triangles, quadrilaterals and other plane figures. Students are also required to be able to use appropriate language to describe the properties of different shapes.

Visit the secondary mathematics webpage to access all lists.

### Transforming Shapes SS7

In this DfE Standards Unit resource, students learn to recognise and visualise transformations of 2D shapes and translate, rotate, reflect and combine these transformations. Students unfamiliar with the terms ‘rotation’, ‘reflection’ and ‘translation’ will need some introduction to these. The session also assumes some acquaintance with equations of lines of reflection,

e.g. y = 4, x = 4, y = x, y = –x.

It is not essential, however, that all learners understand these ideas fully at the outset; during the session they will learn from each other through discussion.

Students work in pairs or small groups or pairs to start by linking two Picture cards using a Word card. They should then try to link up more pairs and, ultimately, aim to end up with a connected network using as many of the cards as possible. Encourage learners to explain carefully to each other why cards are linked and perhaps demonstrate this to you using the acetates on their table. Encourage students to discuss the changes and invariance achieved by combinations of rotations, reflections and translations

### Rods and Triangles

Students are presented with five rods of different lengths. The rods can be joined to make different triangles. Students are challenged to form as many triangles with as many different properties as possible. They are required to identify triangles, describe angles, justify their responses and present their work in such a manner that their reasoning can be followed. This activity can be used to assess students understanding of the properties of triangles and can identify misconceptions students may have.

### Polygons

The text, Polygons, begins with a revision of simple angle facts such as: angles at a point add to three hundred and sixty degrees. Students are provided with explanations, examples and exercises to complete. The next section requires students to explore the angle properties of polygons and the properties of interior and exterior angles of polygons. The third section begins with a recap of what is meant by a line of symmetry and progresses to look at the line and rotational symmetry of polygons. The final section invites students to explore the properties of quadrilaterals, asks students to name quadrilaterals and to identify them given their properties.

The activities sheet contains five activities exploring line and rotational symmetry. The symmetry of regular polygons is an activity which requires students to complete a table showing the properties of quadrilaterals.

### Paper Magic: Folding Polygons

One of the challenges facing the teacher is how to produce lessons which are active, engaging, contain problem solving and also meet the objectives of the lesson objectives. Given a piece of A4 paper, challenge the students to fold the paper into a square, an equilateral triangle, an isosceles triangle, kites, rhombi, a regular pentagon, a regular hexagon or a regular octagon. Suggest students consider the properties of the shape to help them make it. Students can peer assess each other’s efforts.

It is important that students have a chance to succeed in their challenge once they have attempted to solve the problem themselves.

This resource contains step by step illustrated instructions of how to fold a variety of polygons, using A4 size paper. There are also investigations on polygon properties and suggestions for further activities. The resource also includes a full colour wall poster showing window, nesting and stacking patterns using the folded polygons.

All that is needed is a plentiful supply of coloured A4 paper. No glue, compasses or protractors are required to produce the polygons.

### Properties of Shape Mystery

Students always like a challenge. This activity is ideal for consolidating learning, assessing understanding and identifying misconceptions. Students are presented with fifteen cards, each with a statement about 2-D shapes and where they should be placed on the 3 by 3 solution grid. Students should work in groups and be encouraged to discuss the possible options and work towards a solution. Extension questions are also posed.

**2-D Shape cards** contains a grid with a solution to the mystery and six additional cards displaying rogue shapes. These cards can be included to add an extra challenge or retained to make the solution more accessible.

### 2D and 3D Shapes

This resource contains a number of ideas for activities which provide students with the opportunity to explore the properties of two dimensional and three dimensional shapes.

2D and 3D shapes - requires students to recognise and name shapes in the real world when studying a photograph.

2D shapes naming and classification - students are given a variety of shapes and are required to classify the shapes, justifying their decisions.

2D shapes – vocabulary requires students to place the shapes presented to them into categories. Groups then view other solutions to attempt to decide what criteria were used to form the grouping.

2D shapes - using technology creatively and appropriately, students are required to identify two dimensions shapes around them and use appropriate technology such as camera, phone or tablets to take pictures of the objects. Students can then identify the properties of the shapes they have found.

### Circles

This resource contains six activities for use in the classroom when exploring the properties of circles. It progresses from the basic reminder of the formula for circumference and area. Each section includes a basic introduction with examples or short investigations. This is then followed by a range of question. Could be used by students working in pairs or small groups to consolidate existing knowledge and then working independently to extend their learning. The sections are:

**The Circle:** Contains a variety of questions requiring students to calculate the circumference and the area of circles. Given values for the diameter or radius of the circle. The second section contains questions requiring students to find the diameter or the radius given the circumference or the area. The third section has problems set in context.

**Drawing Circles:** Begins by defining the radius, diameter and circumference and asking students to draw circles with a given radius, circumference or area. The following section is more challenging requiring students to draw two circles with the same centre, one property of each circle being given.

**The Annulus:** the shape formed between two circles. Students explore the properties of the annulus by completing a table with values of pertaining to the properties of the inner circle, the outer circle and the annuls.

**Circles 2:** Contains a series of questions set in a variety of contexts.

**Sectors:** Begins by defining major and minor sector, and explaining how to calculate the arc length and the area of a sector of a circle. Students are then required to complete a table of values of properties of a circle and a sector of that circle given different properties from which to start with.

**Circles 3:** Contains further questions set in a variety of contexts.

### Mensuration

This resource is a mixed selection of worksheets requiring students to answer questions about the dimensions of the square, the circle, sectors of circles, the cube, the cylinder and the sphere. The resource begins with teacher notes to provide some additional background information. These notes are intended only to provide some additional background alongside some suggestions to guide teaching and learning. This resource would probably be best used for revision or to challenge learners existing knowledge. Many of the examples are of a practical nature. The others require the ability to manipulate the appropriate formulas. It includes:

**Circles:** Students are presented with a range of different diagrams containing circles within circles, compound shapes made up of parts of circles and are required to answer questions such as find the area of the shaded section of the diagram.

**Squares and circle:** Students answer questions relating to compound shapes made from circles, squares and triangles.

**Sectors: **Requires students to find the sector angle, the radius of the circle, the arc length and the area of a variety of sectors.

### Parallelogram in a Quadrilateral (grid version)

There are a series of quadrilaterals presented on a grid. The initial task is to form the shape derived by joining the midpoints of each side. The resulting quadrilateral is in each case a parallelogram. Not only that but each parallelogram is similar. The second part of the investigation involves proving that the area of the parallelogram is the same in each case