Secondary Maths Collection Topic special: Surds
Collection Author:Dave Gale, Maths Secondary Panel Member
The topic of surds is wonderful as it engages the mystery of irrational numbers with what is quite possibly students’ first sense of how ‘neat’ maths is. Most students are at least a little curious about how √2 ×√18 can be exactly 6 and there can be little doubt that students get a real sense of satisfaction when they realise they can simplify ‘hard looking sums’ to something easy.
The resources below follow each other very nicely and lead from introducing square roots, through different types of numbers, into the ways of manipulating surds, a couple of utility resources and finally two proof activities.
Top 10 Resources
- This is a great little game that gets students very competitive. Good for helping students to understand square roots and leads nicely into the topic of surds.
- A nice resource for introducing the concept of different types of numbers. Let’s not forget that students have rarely even considered the possibility of numbers that can’t be written easily as decimals or fractions. Use this resource to open students’ eyes to how numbers have developed and, in particular, recap that fractions are always recurring or terminating decimals. What sort of decimal numbers does that leave for irrational numbers? The layer of Complex numbers has been included as a teaser for motivated students.
- Once students are aware of the possibility of irrational numbers, this is a good way to introduce multiplying and dividing surds. Plays on the surprise value that √2x√8 = (exactly) 4. This powerpoint has a lovely ‘square roots’ image that I’ll be using from now on!
- Continuing to develop students familiarilty and competence with surds. This is a really well thought out lesson plan with T/F cards and a set of ‘show that’ cards too. I’ve used this resource many times in lessons.
- I always find that jigsaws make a welcome break from text books or worksheets. This set of three jigsaws has students practising the most common ways of simplifying surds.
- A useful power point to have running as a loop in the background once students have started working through some practise questions. (Perhaps have this playing while students are doing the tarsia jigsaw above.)
- It’s bingo with simplification of surds! All set up for you so you just have to print some bingo cards and get on with it. Truly excellent.
- Placemats are used quite a lot in primary schools as a way of having easy access to key facts. This is a surds version which you could print out and maybe get laminated so students can refer to them while working through some questions. Try it: you’ll be surprised how quickly students adapt to not having to ask you for help as their first port of call. You could use this as a poster.
- At some point in the teaching of surds, someone always asks how you can be so sure that irrational numbers never recur or terminate. This is a power point that gives you the structure to prove that√2 is Irrational. You’ll definitely need to talk the students through it and you’ll probably lose some of them but when an opportunity for a mathematical proof presents itself you’ve got to give it a go!
- Once your students are proficient with surds, this is a great little challenge for seeing if they can create a mathematical proof. It’s quite tough but not beyond the realms of possibility!