Teaching Indices
Thursday, September 5, 2019
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| Source: dotmaths.com |
I know I tin strength out programme a sequence of lessons on indices for whatever historic menses grouping (Year 8 correct through to Year 12) together with I'll live able to notice expert character engaging resources. Later inwards this shipping I'll characteristic some of my favourites.
Concepts
Concepts
The concepts relating to indices are relatively slow to explicate from kickoff principles. The reasoning behind the index laws is straightforward. We tin strength out encounter that b2 x b5 = b7 exactly past times writing out the expressions inwards total (ie b x b x b x b x b x b x b). Students volition chop-chop location the patterns. The 'anything to the ability of null equals one' dominion is also fairly unproblematic to explicate using the logic shown below.
Negative powers tin strength out live explained past times extending the partitioning constabulary (ie what happens when nosotros dissever b2 past times b7?), or past times considering patterns (see Gems 8 for to a greater extent than on this).
Fractional powers tin strength out live explained using the multiplication law.
And together with hence it's exactly a instance of students remembering the laws together with practising them until they learn fluent. Mim Gosling (@mimgosling) created the moving-picture present below to aid students recollect how fractional powers locomote -"Fractional indices are similar a bloom - the bottom's the root, the top's the power!". So if yous receive got a educatee who gets confused past times fractional indices, exactly remind them that the root is at the bottom (like inwards a tree).
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| Source: @StIvoMaths |
A lesson on index laws I taught an introductory lesson on index laws latterly - I wrote these slides to construction the degree news together with activities. After nosotros established each index law, the degree did 3 quick exercise questions earlier moving on to the adjacent law. Once we'd covered all 3 laws, the students completed this 'Powers of y eliminator' from Teachit Maths, which was fantastic. It had exactly the correct combination of independent practice, stretch together with 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 costless to borrow bits, though some formatting may live lost when yous download it (the PDF version is much prettier!).
Card Sorts
It's a dandy thought to receive got a well-organised provide of sorting activities (eg Tarsia puzzles) inwards your maths department. Find a clever agency to shop them (eg inwards stackable plastic takeaway boxes) together with label the boxes clearly. It takes a flake of fourth dimension to laid upward the bill of fare sorts. If you've got the budget, it's ever best to learn them laminated. Print each assault a dissimilar coloring (eg if in that location are 10 groups inwards the class, impress the bill of fare sets on 10 dissimilar colours) - this stops the sets getting mixed up. Use expert character elastic bands - inexpensive ones degrade chop-chop - or perish on each laid inwards an envelope.
My subdivision has a collection of 56 bill of fare sorts create for purpose inwards lessons (sadly, I spent many many hours sitting at the guillotine during my summertime holidays!). We telephone weep upward them our 'Black Box Resources' because nosotros perish on them inwards dark CD boxes from Ikea. Two of my favourite bill of fare sorts are for indices. The first is Indices Dominoes by Teachit Maths - a genuinely dainty activity, amongst the added bonus that the answer is written backwards hence students can't cheat past times guessing the words. I also like Using Indices from the Standards Unit. Card laid H5N1 (pairs activity) is genuinely useful when you've taught fractional together with 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 dandy worksheets together with 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 3 index laws:
Homeworks
I've made ii Pret homeworks for this topic, both are available here.
Enrichment
There's loads of dandy extension questions for this topic. I beloved these mega quadratic equations from Don Steward.
together with these mega difficult powers questions, also from Don Steward
That's it from me - if yous know of whatever other fantastic indices resources, delight comment below or tweet me.
Card Sorts
It's a dandy thought to receive got a well-organised provide of sorting activities (eg Tarsia puzzles) inwards your maths department. Find a clever agency to shop them (eg inwards stackable plastic takeaway boxes) together with label the boxes clearly. It takes a flake of fourth dimension to laid upward the bill of fare sorts. If you've got the budget, it's ever best to learn them laminated. Print each assault a dissimilar coloring (eg if in that location are 10 groups inwards the class, impress the bill of fare sets on 10 dissimilar colours) - this stops the sets getting mixed up. Use expert character elastic bands - inexpensive ones degrade chop-chop - or perish on each laid inwards an envelope.My subdivision has a collection of 56 bill of fare sorts create for purpose inwards lessons (sadly, I spent many many hours sitting at the guillotine during my summertime holidays!). We telephone weep upward them our 'Black Box Resources' because nosotros perish on them inwards dark CD boxes from Ikea. Two of my favourite bill of fare sorts are for indices. The first is Indices Dominoes by Teachit Maths - a genuinely dainty activity, amongst the added bonus that the answer is written backwards hence students can't cheat past times guessing the words. I also like Using Indices from the Standards Unit. Card laid H5N1 (pairs activity) is genuinely useful when you've taught fractional together with 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 dandy worksheets together with 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 3 index laws:
- Simplifying Indices Code Breaker - Teachit Maths
- Collect a Joke - Number Loving
Once you've moved onto fractional together with 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 disceptation to mean value close together with explicate to the class.
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| Extract from 'Why does?' past times Susan Wall |
There's also a truthful or imitation activity which is designed to address mutual misconceptions.
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| Extract from 'True or False' past times Susan Wall |
Blanks
I featured a 'blanks' draw of piece of occupation thought inwards Gems 17. Make upward some questions similar those shown below together with seat them upward to a greater extent than or less the room. Provide post-it notes hence students tin strength out propose values that fit.
I've made ii Pret homeworks for this topic, both are available here.
There's loads of dandy extension questions for this topic. I beloved these mega quadratic equations 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, together with mayhap equally extension inwards Year 11, I similar to produce some locomote on comparison indices amongst dissimilar bases. For example, I similar this ordering starter.
And my worksheet exponential equations has been useful. It ends amongst this lovely question.
Finally, I desire to part ii questions that I've been using for years amongst GCSE students, either when I learn indices or when I learn algebraic fractions. My students are ever horrified past times how complex these questions look, but if they're confident amongst indices together with hence both equations are genuinely surprisingly slow to solve. I'm non certain where these questions originated hence apologies to the creator for non giving credit.
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| How v squared looks inwards nightmares. |