Teaching Indices

Source: dotmaths.com

I've mentioned earlier that I dear educational activity indices, in addition to that's because a) there's loads of bright resources available b) the concepts are tardily to explicate c) there's some lovely extension problems in addition to d) this is of import mathematics! You can't produce calculus without agreement indices.

I know I tin displace programme a sequence of lessons on indices for whatever historic menstruum grouping (Year 8 correct through to Year 12) in addition to I'll live able to abide by skillful lineament engaging resources. Later inwards this shipping service I'll characteristic some of my favourites.

Concepts

The concepts relating to indices are relatively tardily to explicate from kickoff principles. The reasoning behind the index laws is straightforward. We tin displace encounter that b² x b⁵ = b⁷ precisely past times writing out the expressions inwards total (ie b x b x b x b x b x b x b). Students volition rapidly spot the patterns. The 'anything to the ability of null equals one' dominion is also fairly elementary to explicate using the logic shown below.

Negative powers tin displace live explained past times extending the partitioning police pull (ie what happens when nosotros split b² past times b⁷?), or past times considering patterns (see Gems 8 for to a greater extent than on this).

Fractional powers tin displace live explained using the multiplication law.

And thence it's precisely a instance of students remembering the laws in addition to practising them until they perish fluent. Mim Gosling (@mimgosling) created the painting demonstrate below to tending students recollect how fractional powers piece of occupation -"Fractional indices are similar a blossom - the bottom's the root, the top's the power!". So if you lot receive got a pupil who gets confused past times fractional indices, precisely remind them that the root is at the bottom (like inwards a tree).

Source: @StIvoMaths

A lesson on index laws

I taught an introductory lesson on index laws lately - I wrote these slides to construction the shape give-and-take in addition to activities. After nosotros established each index law, the shape did iii quick exercise questions earlier moving on to the side past times side law. Once we'd covered all iii laws, the students completed this 'Powers of y eliminator' from Teachit Maths, which was fantastic. It had precisely the correct combination of independent practice, stretch in addition to engagement. These were the questions that most students got stuck on:

I was quite proud of the slides I made for this lesson - there's an editable version here so experience gratis to borrow bits, though some formatting may live lost when you lot download it (the PDF version is much prettier!).

Card Sorts
It's a peachy thought to receive got a well-organised furnish of sorting activities (eg Tarsia puzzles) inwards your maths department. Find a clever agency to shop them (eg inwards stackable plastic takeaway boxes) in addition to label the boxes clearly. It takes a flake of fourth dimension to educate the carte du jour sorts. If you've got the budget, it's e'er best to learn them laminated. Print each assail a dissimilar colouring cloth (eg if at that topographic point are 10 groups inwards the class, impress the carte du jour sets on 10 dissimilar colours) - this stops the sets getting mixed up. Use skillful lineament elastic bands - inexpensive ones degrade rapidly - or proceed each laid inwards an envelope.

My subdivision has a collection of 56 carte du jour sorts educate for run inwards lessons (sadly, I spent many many hours sitting at the guillotine during my summertime holidays!). We telephone outcry upwards them our 'Black Box Resources' because nosotros proceed them inwards dark CD boxes from Ikea. Two of my favourite carte du jour sorts are for indices. The first is Indices Dominoes by Teachit Maths - a truly prissy activity, alongside the added bonus that the answer is written backwards thence students can't cheat past times guessing the words. I also like Using Indices from the Standards Unit. Card laid H5N1 (pairs activity) is truly useful when you've taught fractional in addition to negative indices.

You powerfulness also similar these treasure hunts: simple index laws and negative & fractional indices, both from Teachit Maths.

Worksheets
There's loads of peachy worksheets in addition to activities for independent practice. I've already mentioned the Powers of y eliminator from Teachit Maths. Here's ii to a greater extent than first-class resources that are suitable for practising the iii index laws:

• Simplifying Indices Code Breaker - Teachit Maths 
• Collect a Joke - Number Loving

Once you've moved onto fractional in addition to negative indices, there's loads to a greater extent than first-class resources (these powerfulness live useful inwards Year 12 too):

• Mental Powers Code Breaker -Teachit Maths 
• Ever wondered why? - JustMaths 
• Indices activity - SRWhitehouse on TES

STEM Centre provides some fantastic indices activities from Susan Wall. For example, I similar 'Why does?' (extract below) inwards which students are allocated a tilt to intend virtually in addition to explicate to the class.

Extract from 'Why does?' past times Susan Wall

There's also a truthful or faux activity which is designed to address mutual misconceptions.

Extract from 'True or False' past times Susan Wall

Blanks

I featured a 'blanks' business thought inwards Gems 17. Make upwards some questions similar those shown below in addition to seat them upwards to a greater extent than or less the room. Provide post-it notes thence students tin displace advise values that fit.

Homeworks
I've made ii Pret homeworks for this topic, both are available here.

Enrichment
There's loads of peachy extension questions for this topic. I dear these mega quadratic equations from Don Steward.

in addition to these mega difficult powers questions, also from Don Steward

And ii to a greater extent than fantastic rich tasks from Don Steward: Power Sums and Find the Power. 

At H5N1 level, in addition to peradventure every bit extension inwards Year 11, I similar to produce some piece of occupation on comparison indices alongside dissimilar bases. For example, I similar this ordering starter.

And my worksheet exponential equations has been useful. It ends alongside this lovely question. 

Finally, I desire to portion ii questions that I've been using for years alongside GCSE students, either when I learn indices or when I learn algebraic fractions. My students are e'er horrified past times how complex these questions look, but if they're confident alongside indices thence both equations are truly surprisingly tardily to solve. I'm non certain where these questions originated thence apologies to the creator for non giving credit.

That's it from me - if you lot know of whatever other fantastic indices resources, delight comment below or tweet me.

How v squared looks inwards nightmares.