Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing
Carroll Diagrams
problem
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Carroll diagrams

Age
5 to 11
Challenge level
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Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Roll these Dice
problem
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Roll these dice

Age
7 to 11
Challenge level
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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?

Let's Investigate Triangles
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Let's investigate triangles

Age
5 to 7
Challenge level
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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?

Missing Middles
problem
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Missing middles

Age
5 to 7
Challenge level
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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?
What's it worth?
problem
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What's it worth?

Age
11 to 16
Challenge level
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There are lots of different methods to find out what the shapes are worth - how many can you find?

Two Primes Make One Square
problem
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Two primes make one square

Age
7 to 11
Challenge level
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Can you make square numbers by adding two prime numbers together?
What Shape and Colour?
problem
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What shape and colour?

Age
5 to 7
Challenge level
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Can you fill in the empty boxes in the grid with the right shape and colour?

Sending a Parcel
problem
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Sending a parcel

Age
11 to 14
Challenge level
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What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
How far does it move?
problem
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How far does it move?

Age
11 to 14
Challenge level
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

Four Go
problem
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Four go

Age
7 to 11
Challenge level
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This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?