Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing
Cut Nets
problem
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Cut nets

Age
7 to 11
Challenge level
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Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Number Differences
problem
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Number differences

Age
7 to 11
Challenge level
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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?
Brush Loads
problem
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Brush loads

Age
7 to 11
Challenge level
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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.

Magic Vs
problem
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Magic vs

Age
7 to 11
Challenge level
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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

How much can we spend?
problem
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How much can we spend?

Age
11 to 14
Challenge level
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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?
Training schedule
problem
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Training schedule

Age
14 to 16
Challenge level
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The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
Consecutive Numbers
problem
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Consecutive numbers

Age
7 to 14
Challenge level
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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Writing Digits
problem
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Writing digits

Age
5 to 7
Challenge level
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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?
Birthday Cakes
problem
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Birthday cakes

Age
5 to 7
Challenge level
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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?
Got It
problem
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Got it

Age
7 to 14
Challenge level
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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.