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There are **53** NRICH Mathematical resources connected to **Exploring and noticing**, you may find related items under Thinking mathematically.

Problem
Primary curriculum
Secondary curriculum
### Rhombus It

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parallelogram It

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Standard Index Form Matching

Can you match these calculations in Standard Index Form with their answers?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square Number Surprises

There are unexpected discoveries to be made about square numbers...

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Difference of Two Squares

What is special about the difference between squares of numbers adjacent to multiples of three?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Going to the Cinema

A cinema has 100 seats. Is it possible to fill every seat and take exactly Â£100?

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### Steel Cables

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factorising with Multilink

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Vector Journeys

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Training Schedule

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Generating Triples

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Charlie's Delightful Machine

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Little Light Thinking

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cyclic Quadrilaterals

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Countdown Fractions

Here is a chance to play a fractions version of the classic Countdown Game.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Power Countdown

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Legacy

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Root Hunter

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Connect Three

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Matchless

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dating Made Easier

If a sum invested gains 10% each year how long before it has doubled its value?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sums of Pairs

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?”

Age 11 to 16

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Factors and Multiples Game

A game in which players take it in turns to choose a number. Can you block your opponent?

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Magic Potting Sheds

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Warmsnug Double Glazing

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Spinners

How do scores on dice and factors of polynomials relate to each other?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Arithmagons

Can you find the values at the vertices when you know the values on the edges?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Where to Land

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square It

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pair Products

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pick's Theorem

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tiny Nines

What do you notice about these families of recurring decimals?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shopping Basket

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's it Worth?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tree Tops

Can you make sense of information about trees in order to maximise the profits of a forestry company?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Attractive Tablecloths

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Marbles in a Box

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's Possible?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Beelines

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fair Shares?

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plus Minus

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Old Am I?

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Simply Graphs

Look for the common features in these graphs. Which graphs belong together?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Guessing the Graph

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Impossible Triangles?

Which of these triangular jigsaws are impossible to finish?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### There's Always One Isn't There

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

Age 14 to 16

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Last Biscuit

Can you find a strategy that ensures you get to take the last biscuit in this game?

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polite Numbers

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?

Age 16 to 18

Challenge Level