## The first topic they meet in high school

Like most calendar years, I am teaching Year 7 in 2012.  The first topic they encounter is “Whole Numbers”, which includes:

• understanding the Hindu-Arabic number system, in part by comparing it to others
• place value and expanded notation ($2049=2\times10^3+4\times10^1+9\times10^0$)
• the four operations; order of operations
• divisibility tests
• factors and multiples
• highest common factor
• prime and composite numbers
• prime factors; factor trees
• squares, cubes and roots

Some of those topics are quite interesting, but much of it is expected background knowledge. However, the students have come from a variety of primary schools and are now meekly having their first taste of high school mathematics. My Year 7 classes have always had a great variety in ability and background knowledge, so it becomes hard to avoid plodding through this material.

I’ve always wanted to spice it up with some fun activities, and every now and then I get an idea in my head or some inspiration from somewhere.  But it’s impossible to recall all those ideas when planning an attack.  Anyway, here are some ideas, in no particular order.  I’d love to hear of others.

• Give them a page with lots of prime numbers scattered all over it.  Get them to answer questions like: write all the numbers with a digital sum of 13; write the numbers that multiply to give 731, add to give 98, etc.; write all primes between 1-10, 11-20, 21-30, etc.  Think of some more, hopefully better, questions which get them immersed in the numbers and practising other skills.  Next day, give them two separate quizzes: write all the prime numbers you can think of; circle all the primes in this list.
• Every year we have some year-group “relays” where students answer puzzle questions in small groups. It has not escaped my notice that many of the questions practise the skills listed above.  I need to track down a set of good puzzle questions.
• Lots of number statement jigsaw puzzles. For example, get to the number 45 using 2, 5, 6 and 13.  Answer: $13\times(5-2)+6=45$ .  Check your answer with a calculator to be sure you are obeying order of operations.  Some variations: change one thing to make the answer 22 (answer: $13+5-2+6=22$); write and evaluate the same expression without brackets (answer: $13\times5-2+6=69$; get as many different values as you can using the numbers 2, 5, 6 and 13 in that order.
• Lots of “fill in the blank”, like $15-(blank)\times 2=7$. This can cover many levels of difficulty and even allow for multiple answers, like $3\times(blank) + 7\times(blank)=29$.
• Learn the GCD algorithm (repeated subtraction). Not everyone will be amenable to this, so an independent worksheet for more capable students would be good.  Demonstrate the algorithm a few times and get them to practise it.
• Binary, octal, hexadecimal and other bases. Time permitting, you can develop a lot of understanding by really working with other bases.

This is not a bad set of ideas, but I have a frustrating feeling that I’ve been aware of many others in the past and can’t think of them now.

Pointers and ideas would be most welcome. Keep in mind that calculators are not used at this stage unless permission is given (e.g. to check answers).