The majority of students can easily spot the four arrangements a+b=c, b+a=c, c-a=b and c-b=a; but we need to be careful not to allow them to see these as a complete set. Inquisitive students in the lesson trials were able to construct formats such as: c=a+b, c-b-a=0 and c-(a+b)=0, along with, for the three parts diagrams: a+b=d-c, d-(a+b)=c and 0=d-(a+c)-b. Each of these remains consistent with the diagrams and helps to reinforce the notion of commutativity (or the lack thereof) introduced in the ‘simple four’. This, along with the vast increase in the number of permutations of the three parts diagrams’ equations, should ensure that the most able students never run out of options for the ‘how many can you write?’ questions.
Please can (d) on the worksheet be corrected – the size of the bars is confusing some students as d < 16 yet the bar for d is longer than the bar for 16. Thank you
Bluecoat Maths 
The majority of students can easily spot the four arrangements a+b=c, b+a=c, c-a=b and c-b=a; but we need to be careful not to allow them to see these as a complete set. Inquisitive students in the lesson trials were able to construct formats such as: c=a+b, c-b-a=0 and c-(a+b)=0, along with, for the three parts diagrams: a+b=d-c, d-(a+b)=c and 0=d-(a+c)-b. Each of these remains consistent with the diagrams and helps to reinforce the notion of commutativity (or the lack thereof) introduced in the ‘simple four’. This, along with the vast increase in the number of permutations of the three parts diagrams’ equations, should ensure that the most able students never run out of options for the ‘how many can you write?’ questions.
Please can (d) on the worksheet be corrected – the size of the bars is confusing some students as d < 16 yet the bar for d is longer than the bar for 16. Thank you
Hi,
I’ve changed the 16 to an 8.