### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

### Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

# Medal Muddle

### Why do this problem?

This problem is an exercise in strategic thinking, accessible to lower Stage 3 students but hinting at work on sorting algorithms that they might meet at Stage 5 in Decision Maths.

### Possible approach

"I'm going to give you a problem to solve, and while you work on it, I'd like you to think about the strategies you are using. Imagine you had to solve lots of problems like this one. How would you ensure that you found the correct answer accurately and efficiently?"

Hand out this worksheet for students to work on in pairs (or individually at first if they wish).

These cards could be printed and handed out to students so they can manipulate the order as they work their way through the different clues.

Once they have had time to make progress (but not necessarily solve the problem completely), bring the class together to discuss the strategies they have tried. We have included a few ideas in the hint that you could share with your class if they don't come up with suggestions of their own.

Once students have had a chance to discuss the merits of different approaches, hand out this worksheet with the extension challenge, so that they can test how their chosen strategy works on a longer problem with more information to consider. Here is a set of cards for the extension activity.

### Key questions

Which representations or ways of organising your thinking help you to use the information given to solve the problem efficiently?

### Possible extension

Challenge students to create their own versions of the problem, which could be shared on the blog.

### Possible support

The visual representation shown in the hint is a very clear way of seeing the relationship between the different countries.