Factors and Factorising

Year 9 have been looking at simplifying algebraic fractions. They have spent the last half term looking at Fractions, Decimals and Percentages and the last few weeks expanding and factorising expressions so I thought I showed them the following and then next lesson the series of TRUE or FALSE statements. I thought that this would be a good idea to help students understand why some fractions can be simplified and others can’t. I have wondered if it might be a good idea to use the “factors” slides in my next lesson on factors as and extension of the basic idea of 7 is a factor of 35 etc.

Surface Area and Volume of Cylinders

I have been thinking a lot about a recent interaction on Twitter and how teachers calculate the surface area of a prism. I really liked the idea of looking at the areas of the cross sections (especially as it linked to volume of a prism) and adding the area of the net of the “tube” so, multiplying the perimeter of the cross section by the length. I have played around with a similar format I used for surface area recently and it worked well but I think I like to now move the students to using this approach. Plus I’d like them to practice volume alongside surface area so they can distinguish the two.

Interaction above

I made this after speaking to @MRSEVCartwright

Thanks to @mathsteacher09 for the suggestion of using circles not side elevation images for the area of the cross section

Number of Factors

I have been thinking about Prime Factors again and more precisely how many factors a number has. I was thinking about the smallest number with just 1 factor and then the smallest with 2 factors and so on. I liked the reminder that the odd number of factors belonged to square numbers. There was so much to notice as I complied a list of the first 12 smallest numbers that had just 1 factor, 2 factors etc. I liked thinking of the combinations that give us the factors of a number. I liked thinking about the fact that 60 has 12 factors because 3×2×2=12 (1 more than 2 × by 1 more than 1 × by 1 more than 1) and that 25 × 3 is also a number with 12 factors. The issue I have now, is which slide below will I show my class when I use it… do I want them to write each number as a product of prime factors and then notice the number of factors are increasing? or start with the number of factors and ask them the to find the smallest number that it works for or do I give them a mix of all different columns filled in?