Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing

problem

Favourite

Sums of pairs

Age

11 to 16

Challenge level

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?”

problem

Favourite

Twisting and turning

Age

11 to 14

Challenge level

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

problem

Favourite

Crossed ends

Age

11 to 14

Challenge level

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

problem

Favourite

Cyclic quadrilaterals

Age

11 to 16

Challenge level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

problem

Favourite

Dotty six

Age

5 to 11

Challenge level

Dotty Six is a simple dice game that you can adapt in many ways.

problem

Favourite

Biscuit decorations

Age

5 to 7

Challenge level

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?

problem

Favourite

One to eight

Age

11 to 14

Challenge level

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.

problem

Favourite

Egyptian rope

Age

7 to 11

Challenge level

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

problem

Favourite

Frogs

Age

11 to 14

Challenge level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

problem

Favourite

Eggs in baskets

Age

5 to 7

Challenge level

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

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For younger learners

Exploring and noticing

Sums of pairs

Twisting and turning

Crossed ends

Cyclic quadrilaterals

Dotty six

Biscuit decorations

One to eight

Egyptian rope

Frogs

Eggs in baskets