Enlargement and similarity
Term 3 starting in week 1 :: Estimated time: 2 weeks
- Recognise enlargement and similarity
- Enlarge a shape by a positive integer scale factor
- Enlarge a shape by a positive integer scale factor from a point
- Enlarge a shape by a positive fractional scale factor
- Work out missing sides and angles in a pair of given similar shapes
For higher-attaining pupils:
- Enlarge a shape by a negative scale factor
- Solve problems with similar triangles
- Explore ratios in right-angled triangles
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Activities for pupils
Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.
Transformations Video A demonstration of the four basic transformations: reflection, translation, rotation and enlargement.
Construct a congruent triangle Construction (with compass and straight edge) of a triangle congruent to a given triangle.
Transformations Draw transformations online and have them instantly checked. Includes reflections, translations, rotations and enlargements.
Congruent Triangles Video Learn the conditions for two triangles to be congruent and then use this information to solve problems.
Congruent Triangles Test your understanding of the criteria for congruence of triangles with this self-marking quiz.
Scale Factors Video The scale factor, area factor and volume factor of similar shapes are quite different.
Similar Shapes Questions about the scale factors of lengths, areas and volumes of similar shapes.
Blow Up Click on all the points that could be the centre of enlargement of the shape if the image does not go off the grid.
Congruent Parts Use the colours to dissect the outlines into congruent parts.
Similar Parts Use the colours to dissect the outlines into similar parts.
Click on a topic below for suggested lesson Starters, resources and activities from Transum.
- Construction In a way this topic is quite different to all of the other topics in school mathematics. It requires a practical skill as well as the understanding of the geometrical concepts. It also requires a sharp pencil, a sturdy ruler and a decent pair of compasses. Younger children should practise using the drawing instruments to make patterns. They will then progress to constructing accurate diagrams, plans and maps. Older pupils are taught to derive and use the standard ruler and compass constructions for the perpendicular bisector of a line segment, the perpendicular to a given line from a given point and the bisector of a given angle.
- Enlargements When areas and volumes are enlarged the results are far from intuitive. Doubling the dimensions of a rectangle produces a similar shape with four times the volume! Doubling the dimensions of a cuboid produces a similar shape with eight times the volume! The activities provided are intended to give pupils experiences of dealing with enlargements so that they better understand the concept and are able to produce diagrams, make models and answer questions on this subject. Once positive scale factors have been mastered the notion of fractional and negative scale factors await discovery!
- Transformations A transformation in mathematics is an operation performed on a shape (or points) which changes the view of that shape (or points). This topic includes four transformations namely reflection, translation, rotations and enlargement. A reflection can best be described as the mirror image of a shape in a given line (which acts as the mirror). After reflection the shape remains the same size but the orientation is the mirror image of the original. The transformation known as a translation can be thought of as a movement or shift in position. The size and orientation of the shape remains the same but the position on the plane changes. A rotation can be described as turning. This transformation is defined by the angle of turning and the centre of rotation (the point which does not move during the turning). Finally enlargement is the term we use when a shape increases in size but maintains the same shape. The shape after enlargement is defines as being similar to the shape before enlargement. His use of the word similar has a precise mathematical meaning. All of the angles in the enlarged shape are the same as the angles in the original shape and the lengths of the sides are in the same proportion. An enlargement is defines by the scale factor of the enlargement and the centre of enlargement. We use the term enlargement even if the shape becomes smaller (a scale factor between minus one and one). A negative scale factor will produce an enlarged mirror image of the original shape.
Lesson Starters
Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.
1st Lesson
Star Wars Day
Estimate the size of an alien given the size of their hand. This could be an introduction to scale factors.
2nd Lesson
Analogies
Make more of analogies to help remember mathematical concepts.
3rd Lesson
Consecutive
Three consecutive numbers multiplied together give a given product. Pupils are asked to figure out what the numbers are.
4th Lesson
Khmer's Homework
Check a student's homework. If you find any of the answers are wrong write down a sentence or two explaining what he did wrong.
5th Lesson
Oblongs
Find the dimensions of a rectangle given the perimeter and area.
6th Lesson
Rounding 1dp
Round off the given numbers to 1 decimal place then add the answers together.
Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.
