Constructions and congruency
Term 1 starting in week 10 :: Estimated time: 3 weeks
- Draw and measure angles (review)
- Construct and interpret scale drawings (review)
- Locus of distance from a point
- Locus of distance from a straight line/shape
- Locus equidistant from two points
- Construct a perpendicular bisector
- Construct a perpendicular from a point
- Construct a perpendicular to a point
- Locus of distance from two lines
- Construct an angle bisector
- Construct triangles from given information (review)
- Identify congruent figures
- Explore congruent triangles
- Identify congruent 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.
Congruent Triangles Test your understanding of the criteria for congruence of triangles with this self-marking quiz.
Congruent Triangles Video Learn the conditions for two triangles to be congruent and then use this information to solve problems.
Constructions Construct the diagrams from the given information then check your accuracy.
Loci Construction Pairs Match the description of the loci to the diagram of the construction.
Loci Land Make scale drawings of real life situations using ruler, compasses and pencil to answer questions about loci.
Map Scales Test your understanding of map scales expressed as ratios with this self marking quiz.
Measuring Angles Measure the size of the given angles to within two degrees of their actual value.
Perpendicular Bisector Video A step-by-step guide showing how to construct the perpendicular bisector of a line segment.
Ruler and Compass Constructions Video A demonstration of standard ruler and compass constructions.
Scale Drawings Measure line segments and angles in geometric figures, including interpreting scale drawings.
Sheep Herding Arrange the sheep in the field according to the instructions. An introduction to loci.
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.
- Loci A locus (plural: loci) is a set of points whose location satisfies or is determined by one or more specified conditions. This topic links to Geometry and Shape and provides opportunity for accurate drawing and 'people maths' where pupils can position themselves in the classroom according to certain conditions.
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
Goat Grazing
Find the loci of the goat's position as it eats the grass while tethered to the rope.
2nd Lesson
The Power of Christmas
Find a power of 2 and a power of 3 that are consecutive numbers.
3rd Lesson
Christmas Eve
Is there a pattern in the number of palindromic numbers to be found less than powers of 10?
4th Lesson
Christmas Tables
Which of the two shapes has the largest area? You will be surprised!
5th Lesson
Cube Calendar
What numbers should be on each face of the two cubes to make this perpetual calendar?
6th Lesson
Christmas Ornaments
A Maths Starter activity requiring students to arrange Christmas ornaments in a square box.
7th Lesson
Santa's Sleigh
Work out the number of clowns and horses given the number of heads and feet.
8th Lesson
Three Wise Gifts
Find as many sets of three of the available numbers as possible which add up to the given total.
9th Lesson
Last Day
The 31st of December is the last day of the year. What mathematical lasts do you know?
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.
