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Resources tagged with Squares similar to Trig Rules OK:

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Broad Topics > 2D Geometry, Shape and Space > Squares

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Trig Rules OK

Stage: 5 Challenge Level: Challenge Level:1

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...

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Squaring the Circle and Circling the Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

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Semi-square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

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A Tilted Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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Zig Zag

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Square It

Stage: 1, 2, 3 and 4 Challenge Level: Challenge Level:1

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.

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Square it for Two

Stage: 1, 2, 3 and 4 Challenge Level: Challenge Level:1

Square It game for an adult and child. Can you come up with a way of always winning this game?

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Take a Square II

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What fractions can you divide the diagonal of a square into by simple folding?

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Folding Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Semi-detached

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Take a Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Gold Yet Again

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."

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Something in Common

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Similarly So

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Baravelle

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

What can you see? What do you notice? What questions can you ask?

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Triangles in a Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Circle Box

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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LOGO Challenge - the Logic of LOGO

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Just Opposite

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Fitting In

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Compare Areas

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

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Vector Journeys

Stage: 4 Challenge Level: Challenge Level:1

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?

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Logo Challenge 3 - Star Square

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles

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LOGO Challenge 7 - More Stars and Squares

Stage: 3 and 4 Challenge Level: Challenge Level:1

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

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LOGO Challenge 4 - Squares to Procedures

Stage: 3 and 4 Challenge Level: Challenge Level:1

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

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LOGO Challenge - the Humble Square

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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.

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LOGO Challenge 5 - Patch

Stage: 3 and 4 Challenge Level: Challenge Level:1

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

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LOGO Challenge 1 - Star Square

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

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First Forward Into Logo 1: Square Five

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

A Short introduction to using Logo. This is the first in a twelve part series.