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There are 305 NRICH Mathematical resources connected to Exploring and noticing, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Exploring and noticingThe planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
Find at least one way to put in some operation signs to make these digits come to 100.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
What do you notice about these squares of numbers? What is the same? What is different?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
There are six numbers written in five different scripts. Can you sort out which is which?
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?
Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?
Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of three dominoes?
Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?
Make one big triangle so the numbers that touch on the small triangles add to 10.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Use these four dominoes to make a square that has the same number of dots on each side.
Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
How many faces can you see when you arrange these three cubes in different ways?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.