Multiplication and division

problem

Powerful Factorial

Age

11 to 14

Challenge level

3 out of 3

6! = 6 × 5 × 4 × 3 × 2 × 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4) = 45. What is the highest power of two that divides exactly into 100!?
problem

Please Explain

Age

11 to 14

Challenge level

3 out of 3

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.
problem

Skeleton

Age

11 to 14

Challenge level

3 out of 3

Can you reconstruct the long division calculation from the 'skeleton'?
problem

What Is the Question?

Age

11 to 16

Challenge level

1 out of 3

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?
problem

Times Right

Age

11 to 16

Challenge level

3 out of 3

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
problem

Factorial

Age

14 to 16

Challenge level

2 out of 3

How many zeros are there at the end of the number which is the product of first hundred positive integers?
problem

Number Rules - OK

Age

14 to 16

Challenge level

2 out of 3

Can you produce convincing arguments that a selection of statements about numbers are true?
problem

Vedic Sutra - All From 9 and Last From 10

Age

14 to 16

Challenge level

3 out of 3

Vedic Sutra is one of many ancient Indian sutras which involves a cross subtraction method. Can you give a good explanation of WHY it works?
problem

Galley Division

Age

14 to 16

Challenge level

3 out of 3

Can you explain how Galley Division works?
article
Multiplication Series: Illustrating Number Properties With Arrays

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials, but it can also assist them in forming useful mental pictures to support memory and reasoning.