Estimating and approximating

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Building patterns

Can you deduce the pattern that has been used to lay out these bottle tops?
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Let's get flexible!

In this article for primary teachers, Ems outlines how we can encourage learners to be flexible in their approach to calculation, and why this is crucial.
problem
Shedding some light

Age

7 to 11

Challenge level

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?
problem
Interstellar

Age

11 to 14

Challenge level

What number could replace * so that */5 is between 3 and 4?
problem
Silver line

Age

11 to 14

Challenge level

Weekly Problem 40 - 2008
A class raises money for charity by placing 10p pieces edge to edge in a 'silver line'. If the line was 25m long, how much money did they make?
problem
Thunder and lightning

Age

11 to 14

Challenge level

How far away was the lightning if the flash and the thunderclap were 6 seconds apart?
problem
Counting sweets

Age

7 to 14

Challenge level

How might you use mathematics to improve your chances of guessing the number of sweets in a jar?
problem
Growing

Age

16 to 18

Challenge level

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)
problem
Whole numbers only

Age

11 to 14

Challenge level

Can you work out how many of each kind of pencil this student bought?
problem
Squaring the circle

Age

11 to 14

Challenge level

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.