Exploring and Noticing
Consecutive Numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Magic Letters
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
How Much Can We Spend?
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?
Calendar Capers
Choose any three by three square of dates on a calendar page...
Shifting Times Tables
Can you find a way to identify times tables after they have been shifted up or down?
Have You Got It?
Can you explain the strategy for winning this game with any target?
Summing Consecutive Numbers
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Number Pyramids
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
What Numbers Can We Make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Interactive Spinners
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Tilted Squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Keep it Simple
Can all unit fractions be written as the sum of two unit fractions?
1 Step 2 Step
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Seven Squares
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Route to Infinity
Can you describe this route to infinity? Where will the arrows take you next?
Cyclic Quadrilaterals
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Arithmagons
Can you find the values at the vertices when you know the values on the edges?
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?
Marbles in a Box
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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?
Pair Products
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Painted Cube
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
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?
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.
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?
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?
Impossible Triangles?
Which of these triangular jigsaws are impossible to finish?
Exploring and Noticing - Short Problems
A collection of short Stage 3 and 4 problems on Exploring and Noticing.
Treasure Hunt
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Factors and Multiples Game
A game in which players take it in turns to choose a number. Can you block your opponent?
In the Bag
Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?
Cinema Problem
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Fence It
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Dicey Operations
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Sending a Parcel
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
How Many Miles to Go?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
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.
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.
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?
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.
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?
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?
Where to Land
Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
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?
Tree Tops
Can you make sense of information about trees in order to maximise the profits of a forestry company?
Root Hunter
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.