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## Grades 11 and 12 Solve the triangle

*By toni On 18 August, 2018 · Leave a Comment*

The area of triangle PQR is 3√3 square centimetres. Angle PRQ is 60 degrees and RQ is 4 centimetres longer than PR.

Find the length of PQ.

Draw ΔPQR accurately.

Calculate all the angles in the triangle.

## UPPER SECONDARY FC2 LINES, CIRCLES AND TANGENTS

*By toni On 12 August, 2018 · Leave a Comment*

A sequence of activities in this guide takes you from familiar ideas about lines, then emphasises the ‘across’ and ‘up’ aspect of gradient to explain why the product of gradients of perpendicular lines is -1, then uses Pythagoras Theorem to produce the equations of circles and recaps on properties of perpendicular lines […]

## Grades 11 and 12 Kite

*By toni On 27 July, 2018 · Leave a Comment*

Take a sheet of A4 paper. First fold the top left corner to meet the bottom edge and press the fold flat. Then fold the top right corner to meet the edge that you folded down.

Can you prove that the quadrilateral you have made is a kite?

Can you find the perimeter of the […]

## UPPER SECONDARY G3 CIRCLE THEOREMS

*By toni On 22 July, 2018 · Leave a Comment*

The paper folding activities in this workshop guide provide experiences of discovering the properties of circles stated in seven basic theorems. Folding cut-out paper circles does not prove the theorems but it suggests recipes for the formal proofs. Teachers should do all the activities before using them in lessons even if they […]

## Grades 11 to 12 Cyclic

*By toni On 20 May, 2018 · Leave a Comment*

The diagram shows a circle centre O with points P, Q, R and S on the circumference. UST is a tangent to the circle. Angle RPS = 44º and angle PSO = 32º.

Find angles xº and yº.

## Grades 4 to 9 Durer’s Magic Square

*By toni On 16 March, 2018 · Leave a Comment*

Add the columns one by one, add the rows, then add the diagonals. What do you notice?

This is Albrecht Durer’s supermagic square from his famous engraving Melencolia dated 1514. Can you see it at the top right hand corner of the engraving under the bell? It has many […]

## Grades 7 to 10 Constructions with Circles

*By toni On 18 February, 2018 · Leave a Comment*

a. Draw 2 circles with equal radii, intersecting at C, so that each goes through the centre of the other.

b. Draw a third circle of the same radius with centre C.

c. Draw 4 more circles with centres on the circle centre A and passing through A.

## Grades 7 to 10 Constructions with Lines

*By toni On 18 February, 2018 · Leave a Comment*

Click here for Learner’s worksheet with instructions for measuring angles and doing geometrical constructions.

Accurately copy the following patterns and vary them to make your own designs.

1. ENVELOPE PATTERNS WITH STRAIGHT LINES

Draw two base lines and mark the same number of points at equal distances along each line. Join […]

## Grades 7 to 10 Constructing circle and line patterns

*By toni On 18 February, 2018 · Leave a Comment*

The picture shows you how to use a paper clip to draw circles. You just need to open out the paper clip as shown,

Draw a circle and mark 24 points equally spaced around the circumference. To do this, draw a circle and mark the centre, and mark your first point on […]

## PRIMARY G5 PYRAMIDS AND PRISMS

*By toni On 5 February, 2018 · Leave a Comment*

In these activities you will investigate the properties of prisms and pyramids. Full instructions are given as to how to roll scrap paper tightly around string to make paper sticks and tie the string together at the vertices to make ‘skeleton’ 3D polyhedra. There are activities for teachers to engage with together […]

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