Module 4 Understanding shape
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Can I describe and predict transformations of shapes?

Example review questions

Rectangular grid with co-ordinates a, b and c plotted

  • Predict the coordinates of vertex c after this shape is rotated about point a through:
    • 90° anti-clockwise
    • 180°
    Explain how you made your prediction.
  • On dotty paper, draw a parallelogram. Choose one side of the parallelogram to be the mirror line. Draw the reflection of the parallelogram in this mirror line. Which lines in your diagram are parallel?
  • A shape is translated 5 squares right and 2 squares down. It is then rotated 720° clockwise about its centre and translated 2 squares left and 7 squares up. Describe a reflection, translation or rotation that will return it to its starting position.

Teaching guidance

This teaching guidance document suggests some of the key vocabulary, models, images and practical equipment that children should experience and be able to use. It also includes some teaching tips to provide a few starting points for ways of supporting children with this area of mathematics.

PDF file Teaching guidance: Can I describe and predict transformations of shapes? | 137KB new window

These resources are to support children in guided or independent work. Roll over the highlighted resources for a description.

Consolidation and practice

SWF file Symmetry ITP | 31KB new window

SWF file Coordinates ITP | 69KB new window

SWF file Polygon ITP | 176KB new window

SWF file Fixing points ITP | 133KB new window

SWF file Isometric grid ITP | 53KB new window

SWF file Area ITP | 41KB new window

Visit the nrich website new window for further activities to support practice and application.

Symmetry

itp_symmetry

This interactive teaching program (ITP) is an ICT-based tool to support the exploration of shape and space. Symmetry ITP allows the child or teacher to represent and reflect shapes on a grid. An image of the original shape can be fixed to explore the effect on the reflection of moving towards, away from and along the mirror line.

Coordinates

itp_coordinates.png

This interactive teaching program (ITP) is an ICT-based tool to support the exploration of coordinates. Coordinates ITP allows the child or teacher to use a marker to identify the coordinates of points on different grids, mark points and draw lines and shapes, working in one, two or four quadrants to introduce both positive and negative coordinates. The ITP can also be used to explore the properties of 2-D shapes and to predict translations, rotations and reflections of various shapes in the different quadrants.

Polygon

itp_polygons

This interactive teaching program (ITP) is an ICT-based tool to support the exploration of shape, space and measure. Polygon ITP allows the child or teacher to represent regular polygons with three to ten sides. The ITP can then be used to explore the properties of regular and irregular shapes by dragging vertices and creating additional vertices. The ITP includes an on-screen protractor and ruler.

Fixing points

itp_fixing_points

This interactive teaching program (ITP) is an ICT-based tool to support the exploration of shape and space. Fixing points ITP allows the child or teacher to create one or more shapes by connecting a number of vertices on a grid. Angles can be estimated and measured, and the effect of moving different vertices can be explored.

Isometric grid

itp_isometric_grid

This interactive teaching program (ITP) is an ICT-based tool to support the exploration of shape and space. Isometric grid ITP allows the child or teacher to display equilateral triangles. The grid can be hidden or become an isometric pin board. An 'elastic band' can be stretched around the pins to create outlines. Rhombuses can be selected and dragged to different positions on the grid, and then locked together to form representations of 3-D shapes.

Area

itp_area

The Area interactive teaching program (ITP) is an ICT-based tool to support the exploration of number, shape and space and problem solving. Area ITP (version 2.2) allows the child or teacher to place counters or colour in whole or part cells on a grid, pinboard or blank screen, or to define a shape using a rubber band.

PDF file How to use symmetry ITP | 174KB new window

PDF file How to use coordinates ITP | 184KB new window

PDF file How to use polygon ITP | 176KB new window

PDF file How to use fixing points ITP | 31KB new window

PDF file How to use isometric grid ITP | 254KB new window

PDF file How to use area ITP | 156KB new window

Opportunities to use and apply

Possible contexts include:

  • Art, e.g. Produce wrapping paper designs using reflection, rotation and translation of shapes; Create Rothko-like pictures by translating rectangles; Translate patterns through block printing.
  • ICT, e.g. Use draw packages to design a pattern involving rotation, reflection or translation of shapes; use the repeat command in drawing software to produce a pattern and then produce translated versions.
  • Everyday objects, e.g. Identify objects that would map onto themselves exactly when reflected or rotated.
  • Coordinates, e.g. Find the coordinates of vertices of shapes after reflections, rotations and translations.

Confirming learning

Ask probing questions such as:

  • Decide whether you would use a reflection, rotation or translation or combination of these to turn the pink shape into the:
    • yellow shape
    • green shape
    • white shape
    Describe each transformation. Are there different possibilities?
    Pink, yellow, green and white shapes.
  • Point a is reflected in the line shown. Is it reflected onto point b, c or d? Explain how you know. Draw the original points for the other two reflected coordinates.
    Line at forty five degrees, with point a on one side, and points b, c and d on the other.
  • Using dotty paper, draw an equilateral triangle. Rotate it through 60° clockwise about one of its vertices. What shape is formed by the two triangles together?