A little way through the delivery of these types of number, I gave each student a set of 10 random numbers from 11200 (there are 19 in the class, and I did 110 as examples). The numbers were randomly distributed, so each student got a mixture of higher and lower numbers. I then explained that they were going to need to fill a card like the one to the right for each number they had been given. I printed out the cards on as many different colours of card as I could find, and gave each student 2 sheets of cards (giving them 14 cards allowing them to make a few mistakes along the way). I explained that for each of their 10 numbers, they would need to fill the number in at the top, and then record the appropriate information in the other boxes on the card. 
With open day fast approaching, it has been that time of the year when all the displays get a revamp. I like to do lots of posters and displays anyway, but in the run up to Open Day, I wanted to something a little bit special. And this year I devises a project for my Year 7 class which ran over a couple of weeks on the different types of numbers. We had started by looking at various types of numbers, starting with the usual suspects such as Primes, Factors, Multiples, etc. But we diverged into some other nice types of numbers as well, such as Perfect Numbers and Happy Numbers. I used this PowerPoint (shown below) to deliver the lessons, and talk through the different properties. For the first six boxes they simply had to write yes or no (or some other way to denote this, such as tick and crosses, green and red, smiley faces and sad faces). This in itself required the students to do lots of work on the different types of numbers. We had covered several of them up to 100 in class (square, prime and cube) and looked at other examples of the others. Many of the students immediately set about creating lists of the different types of numbers up to 200 (all except Happy numbers). They then compared these with each other to see if they agreed and used this to fill in their cards. The Happy Numbers were a lesson in their own right (and many of them spotted the patterns and cycles that appear with these numbers, such as any number in a Happy Chain is Happy!) But they could not easily produce a list of these numbers, and they had to work out each individual number (this was the exercise on looking at Happy Numbers). The next few boxes were a little bit different. The "# Factors" was for them to write how many factors that number had. The Perfect box needed to be filled with one of Perfect (factors except itself add to itself), Deficient (factors apart from itself sum to less than itself) or Abundant (factors apart from itself sum to more than itself). They then had to list all the factors, preferably in order, and finally use a factorisation tree to work out the Prime Decomposition of each number. Through doing this activity, the students did a huge amount of work on all these different types of numbers, and most importantly working with prime factorisations. Also, for the few that finished their cards earlier than the others, I had a perfect extension task ready: they had to write up a neat description of one of the types of numbers to go along with the rest of the display. With all the cards finished, we then spent a lesson sticking them all to the display paper ready to put up for Open Day. This was an organisational task in its own right, as 19 students worked out how to sort 200 cards into the correct positions on the various pieces of display paper so that it all made sense. They managed amazingly well, and the final display is shown in the various photos below. It was a fantastic project to get them thinking about the different types of numbers, working on quick ways to work things out, spotting patterns that began to emerge etc. It also had a good mix of individual work and collaboration with others. As it is, the project was great, and had produced a fantastic display, but I decided to go one step further. I have recently become a huge fan of Google forms (see my blog post on them here), and so I decided to get an electronic version of their results as well. I quickly put together a form (shown below) which asked for the number they were recording, and also all the relevant information that they had filled in on their cards. I also added a little bit of code to the spreadsheet which collated the results, which then sent them an email response telling them if they were correct or not for each number they submitted (see an example of one of the responses I got for the number 10 below). It also highlighted any incorrect answers on the spreadsheet, making it very obvious for me to see where mistakes were being made (largely they were due to the class not being able to follow the simple formatting instructions for the prime factorisation) With this full set of results gathered, I corrected the few that needed it, and then we had a searchable database of responses for all the numbers from 1200. In Excel, or Google Drive, this spreadsheet can be filtered to access the properties of different types of numbers. You can access the full Google Drive Sheet here, which gives you the ability to filter results by different number types. For example, you could filter all the responses of "Yes" in the Prime Number column which would show only the prime numbers and their properties. Overall this was a hugely enjoyable task, and it has produced two very pleasing outputs: the display looks fantastic; and the spreadsheet gives me more teaching points (what numbers have odd numbers of factors, for example). The students really engaged with the task, and did a huge amount of maths in preparing the cards. In retrospect, and if I had more time to complete the project, then I would have done the Google Form before filling out the cards, giving them the chance to get their answers checked, and hence correct them before putting them on the final cards. This would give the students a bit more confidence in their answers (as they know they are right), and also allow them to learn from the mistakes in a more thorough way.
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Dan RodriguezClark
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice. Archives
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