Place value

article
Activities on the Gattegno chart

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
article
Place value: the ten-ness of ten

This article develops the idea of 'ten-ness' as an important element of place value.
article
Place value as a building block for developing fluency in the calculation process

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
article
How can I support the development of early number sense and place value?

This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas.
problem

Double digit

Age

11 to 14

Challenge level

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?
problem

Purr-fection

Age

16 to 18

Challenge level

What is the smallest perfect square that ends with the four digits 9009?
problem

Novemberish

Age

14 to 16

Challenge level

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.
problem

Lesser digits

Age

11 to 14

Challenge level

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
problem

Alphabet soup

Age

11 to 14

Challenge level

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
problem

Cayley

Age

11 to 14

Challenge level

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?