The ‘product’ maths workshop has recently been learning about place value, number sequencing and investigating patterns within the number system. Students have been applying themselves and enjoying the challenges.
Here are some of the problems that have been investigated:
Week 5 – Factor investigation
Can you identify and describe factors and multiples of whole numbers and use them to solve problems?
After some work on their times tables (click here for strategies you can use at home for this), students learnt about multiples and factors. We then gave them a challenge around numbers that are ‘deficient’, ‘abundant’ or ‘perfect’. (Deficient numbers are a composite number in which the sum of its factors is less than the given number. An abundant number is a composite number whose factors, without the number itself, have a sum greater than the number. A perfect number is one whose factors are equal to a given number).
The problem was to work out which numbers are ‘perfect’ from between 1 and 100. See below for some examples of answers presented:
‘This was a fun, hard and long task! It really tested your brain power and took a lot of concentration. The patterns I discovered were – each prime was a deficient number between 2 and 12 and between 12 and 20 there were more deficient numbers.’ (Ted)
Week 7 – Prime Numbers and Goldbach’s Conjecture
We began this session (as we always do!) with the phrase ‘I’ve got a challenge for you’. This week, the SNC mathematicians were investigating prime numbers. After working out what a prime actually is, they were then introduced to these sums:
8 = 5 + 3 and 10 = 7 + 3 and 12 = 7 + 5. What is common to all these additions?
* * *
Students worked out that it is that an even number appears to be the sum of two prime numbers.
This is the conjecture attributed to Goldbach (a Prussian mathematician, 1690 – 1764) and which bears his name. This was then presented as an investigative challenge: Can every even number (greater than 4) be written as the sum of 2 primes? Can you prove this?
As well as a workshop about recognising prime numbers there is much skill practice in addition and multiplication strategies. Students will complete this investigation next week.