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?

Factorising Quadratics

I am looking at factorising with year 9 after half term and I have been thinking about starting the lesson with the following task. I know they have looked at rectangles regularly at KS2 and KS3 and our next unit after the current one is on 2D shapes. I thought this activity would give them a good starting point to start factorising quadratic by inspection.

Surface Area of Triangular Prisms

I have been looking at triangular prisms and in particular ones that had integer lengths. I wanted to look at some triangular prisms with right-angled triangle cross-section, isosceles and scalene.

I wanted students to think about what the nets would look like and how we find the surface area.

I have picked some shapes that would have the same VOLUME so we can discuss how the surface area is different and why.

I have picked some shapes that have surface areas that are close in value.

Here is the handout:

some screens shots from the lesson

It went really well (as well as expected and as well as I hoped) The biggest issues I could see was using the correct lengths for the surface area. I made a match up activity for next lesson to see if this could help

Graphs: Distance/Time

We have been looking at graphs and spent a lot of time looking at gradient and y-intercept and now we are moving onto distance-time graphs. I thought we could start at looking at some gradients and the connection to speed and next lesson we will look at starting later or at a different distance from home. I would like students to connect back to the work with gradients and y-intercepts.

Gradient

I have been looking at Linear Graphs with year 10 and we started looking at problems that I might plot on a graph. We also looked at the connection and patterns between groups of co-ordinates.

We looked at this problem early on and discussed how we knew which lines were equal in length

We then looked at a grouped of lines we had plotted and looked at the connection between the line and equation that matched it. We noticed all the lines were parallel and increased by the same “step” each time.

We also looked at what happened if the y-intercept was the same but the gradient different.

We looked at some DESMOS activities and then we looked at different problems related to parallel lines