Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing
Exploring cubic functions
problem
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Exploring cubic functions

Age
14 to 18
Challenge level
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Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Zios and Zepts
problem
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Zios and zepts

Age
7 to 11
Challenge level
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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?
Fractions in a Box
problem
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Fractions in a box

Age
7 to 11
Challenge level
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The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Clocks
problem
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Clocks

Age
7 to 11
Challenge level
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These clocks have been reflected in a mirror. What times do they say?

The Tall Tower
problem
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The tall tower

Age
5 to 7
Challenge level
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As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Board Block Challenge
problem
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Board block challenge

Age
7 to 11
Challenge level
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Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Domino Sorting
problem
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Domino sorting

Age
5 to 7
Challenge level
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Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
What's in the Box?
problem
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What's in the box?

Age
7 to 11
Challenge level
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This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Root hunter
problem
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Root hunter

Age
16 to 18
Challenge level
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In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Four-digit targets
problem
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Four-digit targets

Age
7 to 11
Challenge level
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You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?