List

Year 10 Exploring and Noticing

Arithmagons
problem
Favourite

Arithmagons

Age
11 to 16
Challenge level
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Can you find the values at the vertices when you know the values on the edges?

Differences
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Differences

Age
11 to 14
Challenge level
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Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
A Chance to Win?
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A Chance to Win?

Age
11 to 14
Challenge level
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Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Pair Products
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Pair Products

Age
14 to 16
Challenge level
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Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Warmsnug Double Glazing
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Warmsnug Double Glazing

Age
14 to 16
Challenge level
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How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
A little light thinking
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A little light thinking

Age
14 to 16
Challenge level
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Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Standard Index Form Matching
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Standard Index Form Matching

Age
14 to 16
Challenge level
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Can you match these calculations in Standard Index Form with their answers?
Plus Minus
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Plus Minus

Age
14 to 16
Challenge level
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Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Fair Shares?
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Fair Shares?

Age
14 to 16
Challenge level
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A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
What's Possible?
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What's Possible?

Age
14 to 16
Challenge level
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Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Attractive Tablecloths
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Attractive Tablecloths

Age
14 to 16
Challenge level
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Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Tiny Nines
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Tiny Nines

Age
14 to 16
Challenge level
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What do you notice about these families of recurring decimals?
Pick's Theorem
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Pick's Theorem

Age
14 to 16
Challenge level
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Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Perpendicular lines
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Perpendicular lines

Age
14 to 16
Challenge level
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Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
Filling the gaps
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Filling the gaps

Age
14 to 16
Challenge level
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Which numbers can we write as a sum of square numbers?