Conjecturing and generalising
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problemWhat is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes? -
problemA 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?
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problemFour coloured lights
Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up? -
problemShapely lines
This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?
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problemOur numbers
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?
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problemCounting cogs
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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problemI like ...
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
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problemGrowing rectangles
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
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problemTimes tables shifts
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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problemThree dice
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?