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Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
What can you see? What do you notice? What questions can you ask?
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
Can you use the given image to say something about the sum of an infinite series?
What fractions can you divide the diagonal of a square into by simple folding?
This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.
Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles
Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.
Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.
Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
A Short introduction to using Logo. This is the first in a twelve part series.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?
What is the total number of squares that can be made on a 5 by 5 geoboard?
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ
A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?