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There are 123 NRICH Mathematical resources connected to Exploring and noticing, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Exploring and noticingYour school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
If a sum invested gains 10% each year how long before it has doubled its value?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Can you describe this route to infinity? Where will the arrows take you next?
A game in which players take it in turns to choose a number. Can you block your opponent?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Can you work out how to produce different shades of pink paint?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
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.
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
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?
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?
There are lots of ideas to explore in these sequences of ordered fractions.
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
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.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
What do you notice about these families of recurring decimals?
Which set of numbers that add to 100 have the largest product?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Can you make sense of information about trees in order to maximise the profits of a forestry company?
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
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?
A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
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?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
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?
Can you explain the strategy for winning this game with any target?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.