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Fruity totals
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
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The Number Jumbler
The Number Jumbler can always work out your chosen symbol. Can you work out how?
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Two and two
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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The remainders game
Play this game and see if you can figure out the computer's chosen number.
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Missing multipliers
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Consecutive numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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Isosceles triangles
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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Consecutive negative numbers
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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?
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Shady symmetry
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Stars
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Funny factorisation
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Sociable cards
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How many miles to go?
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Triangles in circles
Can you find triangles on a 9-point circle? Can you work out their angles?
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Weights
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Where can we visit?
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Which solids can we make?
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
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Right angles
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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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.
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Nine colours
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Number pyramids
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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Shapely pairs
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
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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.
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M, M and M
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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River crossing
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How far does it move?
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.
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Elevenses
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Opposite vertices
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
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Tilted squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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Speeding up, slowing down
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.
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Can they be equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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Number daisy
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Peaches today, peaches tomorrow...
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Up and across
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.
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American billions
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Semi-regular tessellations
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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Days and dates
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Power mad!
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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Changing areas, changing perimeters
How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?
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Ben's game
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Squares in rectangles
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Multiples Sudoku
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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1 step 2 step
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Changing areas, changing volumes
How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
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Cuboids
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
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An equilateral triangular problem
Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
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What's it worth?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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On the edge
If you move the tiles around, can you make squares with different coloured edges?
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Gabriel's problem
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Product Sudoku
The clues for this Sudoku are the product of the numbers in adjacent squares.
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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?
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Shopping basket
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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Magic letters
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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.
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Can you make 100?
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Factors and multiples puzzle
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Sticky numbers
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Triangles to tetrahedra
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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?
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Alison's quilt
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How steep is the slope?
On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?
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Reflecting squarely
In how many ways can you fit all three pieces together to make shapes with line symmetry?
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Perimeter possibilities
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
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Consecutive seven
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Going round in circles
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Cinema problem
A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?
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Wipeout
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Fence it
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Shifting times tables
Can you find a way to identify times tables after they have been shifted up or down?
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Pick's theorem
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Fair shares?
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Partly painted cube
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Funnel
A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?
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What's possible?
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LCM Sudoku
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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Which is cheaper?
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Parabolic patterns
The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.
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Training schedule
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Squirty
Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.
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Finding factors
Can you find the hidden factors which multiply together to produce each quadratic expression?
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Painted cube
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CD Heaven
All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?