Factors, multiples, primes…oh my!

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.

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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? 

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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:

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‘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)

 

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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?

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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.

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