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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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.
"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). 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.
Which representations or ways of organising your thinking help you to use the information given to solve the problem efficiently?
Challenge students to create their own versions of the problem, which could be shared on the blog.
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.
The visual representation shown in the hint is a very clear way of seeing the relationship between the different countries.