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#### Resources tagged with Circles similar to Angle Measurement: an Opportunity for Equity:

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##### Other tags that relate to Angle Measurement: an Opportunity for Equity
Investigations. Group worthy. Mathematical Thinking. Angle measurer (protractor). Rich Tasks. Enrichment. Pedagogy. Problem solving. Angles. Learning mathematics.

### There are 62 results

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

### Witch's Hat

##### Stage: 3 and 4 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

### Three Tears

##### Stage: 4 Challenge Level:

Construct this design using only compasses

### Circle Packing

##### Stage: 4 Challenge Level:

Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...

##### Stage: 4 Challenge Level:

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

### Efficient Cutting

##### Stage: 3 Challenge Level:

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

### What Is the Circle Scribe Disk Compass?

##### Stage: 3 and 4

Introducing a geometrical instrument with 3 basic capabilities.

##### Stage: 4 Challenge Level:

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

### Arclets Explained

##### Stage: 3 and 4

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

### Roaming Rhombus

##### Stage: 4 Challenge Level:

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point. . . .

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

A metal puzzle which led to some mathematical questions.

### Track Design

##### Stage: 4 Challenge Level:

Where should runners start the 200m race so that they have all run the same distance by the finish?

### A Rational Search

##### Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.

### Some(?) of the Parts

##### Stage: 4 Challenge Level:

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

### Circumspection

##### Stage: 4 Challenge Level:

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.

### Efficient Packing

##### Stage: 4 Challenge Level:

How efficiently can you pack together disks?

### Squaring the Circle and Circling the Square

##### Stage: 4 Challenge Level:

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

### Approximating Pi

##### Stage: 4 and 5 Challenge Level:

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

### Fitting In

##### Stage: 4 Challenge Level:

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. . . .

### Polycircles

##### Stage: 4 Challenge Level:

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

### Circles, Circles Everywhere

##### Stage: 2 and 3

This article for pupils gives some examples of how circles have featured in people's lives for centuries.

### Semi-detached

##### Stage: 4 Challenge Level:

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.

### First Forward Into Logo 4: Circles

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

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

### LOGO Challenge 11 - More on Circles

##### Stage: 3 and 4 Challenge Level:

Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .

### Partly Circles

##### Stage: 4 Challenge Level:

What is the same and what is different about these circle questions? What connections can you make?

### Curvy Areas

##### Stage: 4 Challenge Level:

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

### Gym Bag

##### Stage: 3 and 4 Challenge Level:

Can Jo make a gym bag for her trainers from the piece of fabric she has?

### LOGO Challenge 12 - Concentric Circles

##### Stage: 3 and 4 Challenge Level:

Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.

### LOGO Challenge - Circles as Animals

##### Stage: 3 and 4 Challenge Level:

See if you can anticipate successive 'generations' of the two animals shown here.

### An Unusual Shape

##### Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

### Salinon

##### Stage: 4 Challenge Level:

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

### Square Pegs

##### Stage: 3 Challenge Level:

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

### Rolling Around

##### Stage: 3 Challenge Level:

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

### LOGO Challenge 10 - Circles

##### Stage: 3 and 4 Challenge Level:

In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.

### Illusion

##### Stage: 3 and 4 Challenge Level:

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

### Coins on a Plate

##### Stage: 3 Challenge Level:

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

### Not So Little X

##### Stage: 3 Challenge Level:

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

### Round and Round

##### Stage: 4 Challenge Level:

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

### A Chordingly

##### Stage: 3 Challenge Level:

Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.

### Floored

##### Stage: 3 Challenge Level:

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

### Intersecting Circles

##### Stage: 3 Challenge Level:

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

### Get Cross

##### Stage: 4 Challenge Level:

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

### Rolling Coins

##### Stage: 4 Challenge Level:

A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .

### Squaring the Circle

##### Stage: 3 Challenge Level:

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

### Rotating Triangle

##### Stage: 3 and 4 Challenge Level:

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

### Pericut

##### Stage: 4 and 5 Challenge Level:

Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

##### Stage: 4 Challenge Level:

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .

### Tied Up

##### Stage: 3 Challenge Level:

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .

### The Pillar of Chios

##### Stage: 3 Challenge Level:

Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .

### Crescents and Triangles

##### Stage: 4 Challenge Level:

Triangle ABC is right angled at A and semi circles are drawn on all three sides producing two 'crescents'. Show that the sum of the areas of the two crescents equals the area of triangle ABC.

### Blue and White

##### Stage: 3 Challenge Level:

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?