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Parallel lines
How does the position of the line affect the equation of the line?
What can you say about the equations of parallel lines?
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Reflecting Lines
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.
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Translating Lines
Investigate what happens to the equation of different lines when
you translate them. Try to predict what will happen. Explain your
findings.
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Cyclic Quadrilaterals
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
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Diminishing Returns
How much of the square is coloured blue? How will the pattern continue?
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Growing Surprises
Can you find the connections between linear and quadratic patterns?
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Days and Dates
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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Picturing Triangular Numbers
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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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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Tower of Hanoi
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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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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What numbers can we make now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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Wipeout
Can you do a little mathematical detective work to figure out which number has been wiped out?
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Terminating or not
Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
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Counting Factors
Is there an efficient way to work out how many factors a large number has?
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Legs Eleven
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?
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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?
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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?
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Generating Triples
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?