# Secondary Maths ITE

Document Sample

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Stage         Secondary                                     Year             7
Subject       mathematics                                   Term

Transforming triangles
Module contents

Module focus
Curriculum focus

Using dynamic geometry to explore angles, side and symmetry in

Learning objectives

By the end of the lesson pupils will:

    understand where a shape will be after a reflection;
    begin to understand the geometrical properties of quadrilaterals.

Learning outcomes

Most pupils will:

    draw a mirror line along one side of an equilateral, isosceles and scalene
triangle and accurately reflect them to create a quadrilateral;
    identify the angle and symmetrical properties of the quadrilaterals they
have constructed.

Pupils making slower progress will:

    draw a mirror line along a suggested side on an equilateral triangle and
accurately reflect the triangle to create a quadrilateral;
    identify the line of symmetry and pairs of equal angles in the quadrilateral
they have constructed.

Pupils making faster progress will:

    create a triangle and investigate a number of ways to reflect that triangle
to form a range of quadrilaterals;
    identify the angle and symmetrical properties of the quadrilaterals they
have created and suggest quadrilaterals which do not have a diagonal
line of symmetry.

This document is part of a range of materials designed to help teachers teach using ICT.

Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
www.teachernet.gov.uk/supportpack

References

Strategy Framework references

Shape, space and measures

Geometrical reasoning: lines, angles and shapes

    Begin to identify and use angle, side and symmetry properties of triangles
and quadrilaterals; solve geometrical problems involving these properties,
using step-by-step deduction and explaining reasoning with diagrams and
text.

Transformations

    Understand and use the language and notation associated with
reflections, translations and rotations.
    Recognise and visualise the transformation and symmetry of a 2D shape:
- reflection in given mirror lines, and line symmetry;
- rotation about a given point, and rotation symmetry;
- translation;
explore these transformations and symmetries using ICT.

The Framework for teaching mathematics can be found at:

www.standards.dfes.gov.uk/keystage3/respub/mathsframework/forewo
rd/.

National Curriculum references

Ma3 Shape, space and measures

Geometrical reasoning

Pupils should be taught to:

Properties of triangles and other rectilinear shapes

d use angle properties of equilateral, isosceles and right-angled
triangles; understand congruence, recognising when two triangles are
congruent; explain why the

angle sum of any quadrilateral is 360 degrees

This document is part of a range of materials designed to help teachers teach using ICT.

Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
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f recall the essential properties of special types of quadrilateral,
including square, rectangle, parallelogram, trapezium and rhombus;

geometric properties

Transformations and coordinates
Pupils should be taught to:
Properties of transformations
b recognise and visualise rotations, reflections and translations,
including reflection symmetry of 2-D and 3-D shapes, and rotation
symmetry of 2-D shapes;
transform 2-D shapes by translation, rotation and reflection,
recognising that these transformations preserve length and angle, so
that any figure is congruent to its
image under any of these transformations

The National Curriculum programme of study can be found at:
www.nc.uk.net/nc/contents/Ma-3-2-POS.html.

Use of ICT

Teacher use of ICT

This module will give you the opportunity to:

    use dynamic geometry software to select and reflect objects and drag the
resulting images;
    move between pages within dynamic geometry software files;
    save files to and import files from the shared area of the computer
network.

Pupil use of ICT

It will support your pupils to:

    explore reflection using dynamic geometry software.

Requirements

Hardware

    A computer

This document is part of a range of materials designed to help teachers teach using ICT.

Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
www.teachernet.gov.uk/supportpack

    Data projector and large screen display or interactive whiteboard (IWB)
    An ICT suite

Software

    Dynamic geometry software, such as The Geometer's Sketchpad and
Cabri Geometry Software

Other

    Sheets of paper, rulers, compass and pencils

You can download the viewers needed for these files on the Software

Lesson preparation

A key element of this module is a lesson for you to adopt and adapt to
impact of using ICT for learning and teaching. Display and discuss the
objectives and key vocabulary for this lesson with the pupils.

Make sure this equipment is set up prior to the lesson, taking into
account strong light sources and potential obstructions. Dynamic
geometry software is used in this lesson and you will need to install the
resource files on to the school network for the pupils to access them
during the main activity. (This lesson is best carried out in an ICT
suite).

Some resources have been pre-prepared for this lesson and you will
with the resources before the lesson. The resources Transforming
triangles and Find the mirror line have been provided in two different
formats, a Geometer's Sketchpad version and a Cabri Geometry
version.

Before the lesson begins ensure the key vocabulary is displayed where
pupils can easily refer to it.

Vocabulary

congruent line of symmetry, equilateral, images, isosceles, mirror line,
object, perpendicular bisector, reflect, reflection, scalene triangles,
symmetrical, transformation, vertex, vertices

Health & Safety

This document is part of a range of materials designed to help teachers teach using ICT.

Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
www.teachernet.gov.uk/supportpack

All standard safety procedures with computers need to be in place.
Information can be found at www.ictadvice.org.uk.

ICT skills guidance

The guidance in this section supports the ICT skills described in the
Module contents.

Pupils' prior knowledge and skills

    be able to identify and name an equilateral and isosceles triangles;
    recognise parallel and perpendicular lines, and properties of rectangles.

ICT skills

    know how to open up a file from a shared location on the network.

Starter

Display resource Find the mirror line and give pupils some time to
look carefully at the object and image. Invite a pupil to suggest where
the mirror line would be.

Join some corresponding points on the object and image making sure
that pupils understand that these lines will always be parallel. Inform
pupils that the line of symmetry must pass through the midpoint of this
set of lines and that it is called the 'perpendicular bisector'.

As dynamic geometry software is being used, any of these shapes can
be dragged to convince pupils that these geometrical features are
always true.

Main

Using a data projector and interactive whiteboard, open the resource
Transforming triangles. Alternatively, ask pupils to open this file from

This document is part of a range of materials designed to help teachers teach using ICT.

Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
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a shared location on the school network. Firstly look at the page
Equilateral triangle.

Invite a pupil to drag a vertex of the equilateral triangle and explain to
pupils what is meant by equilateral. (All three angles and all three sides
are equal and therefore the triangle has three lines of symmetry.)

Model how to reflect an object, so that pupils are able to define the line
of symmetry as one of the sides of a triangle and reflect the remaining
sides and vertex to form a quadrilateral (i.e. any shape with four edges.
Quad - is the Latin name for four). Demonstrate to the class how the
resulting shape can be dragged and ask them to describe the features
of the resulting quadrilateral. Inform pupils that the two triangles are
congruent shapes and that the corresponding angles and sides are
equal.

Give pupils the opportunity to do this for themselves and conclude that
there is only one possible quadrilateral, a rhombus that can be
constructed from this starting point. ( This rhombus is unique and has
opposite interior angles of 60º and 120º.)

Then, keeping with the resource Transforming triangles ask the
pupils to click the page titled Isosceles triangle. Give pupils the
opportunity to drag the vertices and deduce for themselves that the
triangle is, by construction, isosceles. Ask the pupils to explore
reflecting it onto a chosen side to produce a quadrilateral and explore
the features of the resulting shape. You may want pupils to sketch
shapes and record observations or conclusions on paper as they are
working. The pupils can repeat this reflection using a different side.
and a rhombus.)

Many pupils share a misconception that irregular quadrilaterals are
those without a specific name. Establish that pupils understand that
there is only one regular quadrilateral. (Square)

Finally, ask pupils to click on the page titled Scalene triangles and
continue their investigation. No new quadrilaterals can be constructed,
but each of those previously discovered can be 'rediscovered' as the
scalene triangle appears to be equilateral or isosceles. Show pupils
how to use the text tool in the right hand toolbar, to add names,
descriptions and any observations to pages.

Discuss the outcomes of the investigation with the class and invite
pupils to show and discuss their findings.

This document is part of a range of materials designed to help teachers teach using ICT.

Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
www.teachernet.gov.uk/supportpack

Plenary

Display the resource table Classifying quadrilaterals and give pupils
a few minutes to discuss, in pairs, into which cells in the table they
would place the quadrilaterals that they have produced.

Remind pupils that each quadrilateral was constructed from two
possible to construct using this approach and why.

and why. (For example, parallelograms and non-square rectangles as
the diagonals are not also lines of symmetry.)

In both cases encourage pupils to use correct mathematical names
and terms in their descriptions.

Assessment

In assessing for learning you should consider the following points.

1. Ensure objectives are expressed in language that pupils understand.
2. Give pupils clear success criteria related to these objectives.
3. Give pupils opportunities to discuss their successes and challenges
focusing on the objectives.
4. Provide oral and written feedback to pupils.
5. Encourage pupils to explain their thinking and reasoning in a secure
environment.
6. Provide time for pupils to reflect upon what they have learned and
understood and identify any difficulties.

You can find information on assessment for learning at:

www.standards.dfes.gov.uk/keystage3/respub/afl_ws.

Pupils making faster progress could begin with a new dynamic
geometry software file and be asked to construct equilateral and
isosceles triangles using their knowledge of their respective properties,
consequently exploring the construction features of the software.

This document is part of a range of materials designed to help teachers teach using ICT.

Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
www.teachernet.gov.uk/supportpack

    Can you find more than one strategy to construct an equilateral triangle?
    Can you use the same approach to draw an equilateral triangle using a
pencil, compasses and straight edge?

Pupils making slower progress may benefit from spending more time
exploring the nature of the shapes by dragging the vertices and getting
a feel for which side lengths and angles can vary and which are
constant. Further support could be provided by having keywords on
cards available and encouraging pupils to use them in their discussion
and their contributions to the plenary session.

    When a shape is reflected, what can you say about the appearance of the
new shape?

In the plenary, may benefit from being given a version of the resource
Classifying quadrilaterals which contains some completed cells.

Evaluation

Lesson reflection

These prompts are designed to help you reflect on how the use of ICT
affected your teaching and pupils’ learning.

Prompts for reflection:

1. How did the use of ICT:
o      help pupils to make better progress towards achieving the learning
objectives?
o      affect the pace of learning?
o      affect pupils’ motivation, interest and time spent on task?
learning?
2. What knowledge or skills have you gained and extended in teaching this
lesson?
3. What adaptations would you make to the lesson and its resources to suit

You may wish to create a record of your evaluation and save it as
template containing these prompts and spaces for your responses.

This document is part of a range of materials designed to help teachers teach using ICT.

Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
www.teachernet.gov.uk/supportpack

Materials evaluation

These prompts are designed to help you consider why, how and when
you would incorporate these lesson activities and resources into your
curriculum and teaching plans.

Prompts for evaluation:

1. What are the benefits of using these teaching and learning approaches
and resources to achieve the subject objectives?
2. How do the suggested activities fit with your existing curriculum and
teaching plans?
3. What adaptations would be required to the activities or resources to suit
4. Are there any requirements for ICT equipment, other resources, space,
etc. that might limit how and where the lesson is taught?

You may wish to make a note of your thinking for your own records
containing these prompts and spaces for your notes.

resources, supplementary information and extension activities using
the link below. The pack is in a zipped file to minimise file size, but

To extract the files within the module pack you will need either Winzip
or Microsoft Windows Extraction Wizard. This software is freely
page.

This document is part of a range of materials designed to help teachers teach using ICT.