There are 96 NRICH Mathematical resources connected to Being curious, you may find related items under Developing positive attitudes.
Broad Topics > Developing positive attitudes > Being curious
Can you find rectangles where the value of the area is the same as the value of the perimeter?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
Can you work out which spinners were used to generate the frequency charts?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
These clocks have only one hand, but can you work out what time they are showing from the information?
The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Can you find the values at the vertices when you know the values on the edges?
Can you work out what step size to take to ensure you visit all the dots on the circle?
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?
Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
If you move the tiles around, can you make squares with different coloured edges?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
There are many different methods to solve this geometrical problem - how many can you find?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
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.
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Which set of numbers that add to 100 have the largest product?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
There are lots of different methods to find out what the shapes are worth - how many can you find?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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".
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.