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### Number and algebra

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### Working mathematically

### For younger learners

### Advanced mathematics

# Year 10 Exploring and Noticing

### Differences

### A Chance to Win?

### Arithmagons

### Pair Products

### Standard Index Form Matching

### Warmsnug Double Glazing

### A Little Light Thinking

### Pick's Theorem

### Plus Minus

### Fair Shares?

### What's Possible?

### Perpendicular Lines

### Attractive Tablecloths

### Tiny Nines

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Age 11 to 14

Challenge Level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Age 11 to 14

Challenge Level

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Age 11 to 16

Challenge Level

Can you find the values at the vertices when you know the values on the edges?

Age 14 to 16

Challenge Level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Age 14 to 16

Challenge Level

Can you match these calculations in Standard Index Form with their answers?

Age 14 to 16

Challenge Level

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Age 14 to 16

Challenge Level

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Age 14 to 16

Challenge Level

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.

Age 14 to 16

Challenge Level

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Age 14 to 16

Challenge Level

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?

Age 14 to 16

Challenge Level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Age 14 to 16

Challenge Level

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Age 14 to 16

Challenge Level

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?

Age 14 to 16

Challenge Level

What do you notice about these families of recurring decimals?