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Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
Which set of numbers that add to 100 have the largest product?
Can you find the connections between linear and quadratic patterns?
Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
How much of the square is coloured blue? How will the pattern continue?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Is there an efficient way to work out how many factors a large number has?
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
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?
Can you do a little mathematical detective work to figure out which number has been wiped out?
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?
Can you find an efficent way to mix paints in any ratio?