Some Starters using Dynamic Geometry
1. Properties of Reflections & Lines of Symmetry
Y7 Teaching Objectives
 Understand and use the language and notation associated with reflections
 Recognise and visualise the transformation of a 2-D shape
 Reflection in given mirror line and line symmetry
Associated vocabulary:
Line of symmetry, mirror line, object, image, perpendicular
Used to support pupils understanding of properties of reflections (e.g. constructed line
between object and image point is perpendicular to and equidistant from mirror line) Helps to
address the common misconception which arises when mirror lines are limited to “vertical”
and “horizontal” lines
Start with a simple shape such as a triangle and a skew mirror line projected on to the IWB or
ordinary WB:
B
C
A
Invite volunteer pupil(s) to sketch in the
image on the large classroom IWB/WB.
Others could sketch this on prepared print
outs (possibly inside A4 plastic wallets and
using soluble OHP pens). Most common
response is shown in blue.
Computer image can be generated and compared. Pupils can be invited to suggest how we
might adjust our original triangle or mirror line to ensure the computer image matches the
drawn (blue)image. Line segments can be drawn between object and images (A to A’) etc.
and questions asked about the relation between these and the mirror line. A, B and/or C can
be moved to illustrate the invariability of this.
Additional Actvities/extensions:
Objects and mirror lines could be drawn on a square dotty grid with/without coordinates and
with/without equations of mirror lines/lines of symmetry. Invite pupils to create a dynamic
Rangoli pattern (see GSP example for simple Rangoli pattern, “Foursym” created on square
dotted grid)
Aditional Objectives:
 Use conventions and notation for 2-D coordinates in all four quadrants, find coordinates
of points determined by geometric information
2. Lines of Symmetry-Properties of 2-D Shapes
Teaching Objectives
Y7
 Use correctly the vocabulary, notation and labelling conventions for lines angles and
shapes
 Identify parallel and perpendicular lines
Y8
 Explaining reasoning with diagrams and text, classify (triangles and) quadrilaterals by
their geometric properties
 Know that if two 2-D shapes are congruent corresponding sides and angles are equal.
Associated vocabulary:
Line of symmetry, mirror line, object, image, perpendicular, parallel, quadrilateral,
arrowhead, kite, parallelogram, intersect, bisect, mid point, equidistant, diagonal, equal sides
(angles), congruent, adjacent, triangle, equilateral, isosceles, vertex, vertices
The blue line is a mirror line. Imagine moving any of the points D, C or E. Describe the
shapes you can/cannot make. Sketch them in your book/on your white board. Give reasons
for your answers.
C
D
D'
E
Invite pupil(s) to drag point D to create the shapes that they have drawn. If pupils have drawn
their shapes on acetate these could be projected onto the screen and superimposed on a GSP
diagram which could be manipulated to fit/not fit their drawing. Line segments and angles
can be measured to check/validate properties of the shape. Pupils can be questioned/prompted
with, for example “Why can a parallelogram or rectangle not be made and a rhombus and
square can”.Link to diagonals of these shapes and their lines of symmetry (Note pupils often
harbour the misconception that the diagonal of a rectangle is a line of symmetry). Link this
with possible classification of quadrilaterals through properties of their diagonals.
3. Rotations, Lines of Symmetry- Properties of 2-D Shapes
Y7 Teaching Objectives
 Understand and use the language and notation associated with rotations and reflections
 Identify parallel and perpendicular lines
 Recognise and visualise the transformation of a 2-D shape
 Reflection in given mirror line and line symmetry
 Rotation about a given point and rotation symmetry
Associated vocabulary:
Angle, degrees, centre of rotation, line of symmetry, mirror line, object, image, parallel
perpendicular, equal sides angles, line segment, vertex, square
Challenge pupils to create a square using transformations of a line segment. This line
segment could be defined as one side of our square or could be left ambiguous i.e it could
also be one of the diagonals of the square.
Display the vocabulary of transformations on the board or on large cards or alternatively give
them a copy of the words on a sheet of A4..Encourage pupils to use mathematical
terminology and precise, unambiguous instructions, for example ask pupils what they would
need to define a rotation (viz: centre of rotation, angle and direction). Pupils might do this
initially in groups/pairs and write out their instructions on paper. Then challenge different
groups to recreate their square using DGS such as GSP (whole class activity). The DGS
requires precise non-ambiguous “mathematical” instructions and offers useful non
judgemental feedback to the pupils.
Compare and contrast the different methods i.e some might do it by rotation only, others by a
combination of rotation and reflection. Tease out the how the method used to create their
square is linked to the property of the square eg equal sides, adjacent sides at right angles or
perpendicular, opposite sides are parallel. (You might relate this to the fact that in one of the
methods the square is obtained by rotating through say +90 then –90 about different points
and that two 90 rotations about different points produces a non-coincident parallel line
segment). Point out the invariant qualities of their constructions i.e each shape remains a
square no matter how we drag different segments or points.
Additional Activities/extensions
Challenge the pupils to generate a tile design (by rotations, reflections and/or translations
based on a single tile. DGS such as GSP offers pupils the opportunity for pupils to explore
dynamic alterations to their designs (see enclosed GSP file “Floors”).
e.g
Etc.
Which simple single “dynamic” tile design offers a good range of overall designs
Other activities such as creating a Kaleidoscope can be used to develop pupils understanding
of rotational symmetry.
4. Properties of 2-D Shapes, Constructing a Rectangle
Y7 Teaching Objectives
 Understand and use the language and notation associated with rotations and reflections
 Identify parallel and perpendicular lines
 Explore constructions using ICT
 Recognise and visualise the transformation of a 2-D shape
 Reflection in given mirror line and line symmetry
Y8
 Explaining reasoning with diagrams, classify quadrilaterals (rectangles and squares) by
their geometric properties
 Know that if two 2-D shapes are congruent corresponding sides and angles are equal.
Similar to starter 3 but this time ask pupils to create a rectangle from a line segment by
parallel and perpendicular constructions. Again emphasis is on precise unambiguous
instruction (and some knowledge of how the software works), eg creating a perpendicular
line to the line segment requires a given point.
A rectangle can be created in a variety of ways. Note how we can use the interior polygon
facility to illustrate symmetry properties of a rectangle and countering the misconception of a
line of symmetry along a diagonal. Dragging points, line segments illustrates the invariant
nature of their construction. Note how we can create a square by dragging an end point of
our original line segment. i.e a square is a special kind of rectangle and in this case the square
has a line of symmetry on the diagonal. The diagrams below illustrate one of the ways that
pupils might construct a rectangle and develop these points.
A
B
A
B
C
A
C
B
D
A
C
D
A
B
B
C
A
C
D
A
B
D
B