# Analysing Alternative Approaches - November 2011, All Stages

This month, we invite you to consider a variety of ways of approaching the tasks, and encourage you to reflect on the merits of different routes to solutions.

## Problems

##### Age 5 to 7 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

##### Age 5 to 7 Challenge Level:

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

##### Age 5 to 11 Challenge Level:

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

##### Age 7 to 11 Challenge Level:

Why does the tower look a different size in each of these pictures?

##### Age 7 to 11 Challenge Level:

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

##### Age 7 to 11 Challenge Level:

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

##### Age 7 to 14 Challenge Level:

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

##### Age 11 to 14 Challenge Level:

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

##### Age 11 to 14 Challenge Level:

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

##### Age 11 to 16 Challenge Level:

There are lots of different methods to find out what the shapes are worth - how many can you find?

##### Age 14 to 16 Challenge Level:

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

##### Age 14 to 16 Challenge Level:

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

##### Age 14 to 18 Challenge Level:

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

##### Age 14 to 18 Challenge Level:

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

##### Age 14 to 18 Challenge Level:

Investigate constructible images which contain rational areas.

##### Age 16 to 18 Challenge Level:

These proofs are wrong. Can you see why?

## Featured Solutions

This was a complex challenge to solve with a number of parts to it.

There was consensus on how this game should be scored.

We had some clear explanations about the different shapes of distribution that can be made with two spinners.

We received lots of interesting comments on this selection of short statistics questions.

## Articles & Games

In this article, Malcolm Swan describes a teaching approach designed to improve the quality of students' reasoning.

In this article for teachers, Bernard gives some background about the theme for November 2011's primary activities, which focus on analysing different approaches.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.