Resources tagged with: Curious

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Broad Topics > Habits of Mind > Curious

Trapezium Four

Age 14 to 16 Challenge Level:

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Opposite Vertices

Age 11 to 14 Challenge Level:

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

Circles in Quadrilaterals

Age 14 to 16 Challenge Level:

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

Triangles and Petals

Age 14 to 16 Challenge Level:

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Pick's Theorem

Age 14 to 16 Challenge Level:

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Curvy Areas

Age 14 to 16 Challenge Level:

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

Triangle Midpoints

Age 14 to 16 Challenge Level:

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Fit for Photocopying

Age 14 to 16 Challenge Level:

Explore the relationships between different paper sizes.

Perimeter Possibilities

Age 11 to 14 Challenge Level:

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

On the Edge

Age 11 to 14 Challenge Level:

If you move the tiles around, can you make squares with different coloured edges?

Can They Be Equal?

Age 11 to 14 Challenge Level:

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Blue and White

Age 11 to 14 Challenge Level:

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

Hexy-metry

Age 14 to 16 Challenge Level:

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Marbles in a Box

Age 11 to 16 Challenge Level:

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Right Angles

Age 11 to 14 Challenge Level:

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Partly Painted Cube

Age 14 to 16 Challenge Level:

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Where to Land

Age 14 to 16 Challenge Level:

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

Arclets

Age 14 to 16 Challenge Level:

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

Cola Can

Age 11 to 14 Challenge Level:

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

More Number Pyramids

Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Same Number!

Age 14 to 16 Challenge Level:

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Charlie's Delightful Machine

Age 11 to 16 Challenge Level:

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Statement Snap

Age 7 to 14 Challenge Level:

You'll need to know your number properties to win a game of Statement Snap...

Which Spinners?

Age 14 to 18 Challenge Level:

Can you work out which spinners were used to generate the frequency charts?

Cosy Corner

Age 11 to 14 Challenge Level:

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Two's Company

Age 11 to 14 Challenge Level:

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Mathsland National Lottery

Age 14 to 16 Challenge Level:

Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

Beelines

Age 14 to 16 Challenge Level:

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

Sending a Parcel

Age 11 to 14 Challenge Level:

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Non-transitive Dice

Age 11 to 14 Challenge Level:

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

Last One Standing

Age 14 to 16 Challenge Level:

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

Litov's Mean Value Theorem

Age 11 to 14 Challenge Level:

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Searching for Mean(ing)

Age 11 to 16 Challenge Level:

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Cuboid Challenge

Age 11 to 16 Challenge Level:

What's the largest volume of box you can make from a square of paper?

Vector Journeys

Age 14 to 18 Challenge Level:

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?

Dicey Operations

Age 11 to 14 Challenge Level:

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Nice or Nasty

Age 7 to 14 Challenge Level:

There are nasty versions of this dice game but we'll start with the nice ones...

Arithmagons

Age 11 to 16 Challenge Level:

Can you find the values at the vertices when you know the values on the edges?

Stars

Age 11 to 14 Challenge Level:

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

How Much Can We Spend?

Age 11 to 14 Challenge Level:

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

A Chance to Win?

Age 11 to 14 Challenge Level:

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Number Pyramids

Age 11 to 14 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Pair Products

Age 14 to 16 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Square Coordinates

Age 11 to 14 Challenge Level:

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

What's Possible?

Age 14 to 16 Challenge Level:

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Multiplication Arithmagons

Age 14 to 16 Challenge Level:

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Semi-regular Tessellations

Age 11 to 16 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Which Solids Can We Make?

Age 11 to 14 Challenge Level:

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Odds and Evens Made Fair

Age 14 to 16 Challenge Level:

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

Your Number Was...

Age 11 to 14 Challenge Level:

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?