Conjecturing and generalising
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problemWhen if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators? -
problemLots of lollies
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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problemShare bears
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
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problemThe bridges of Konigsberg
Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
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problemTourism
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
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problemPainted 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?
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problemTilted 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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problemCoordinate patterns
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
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problemSeven squares - group-worthy task
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?