Index Laws Homework Online

Negative powers can be explained by extending the division law (ie what happens when we divide b2 by b7?), or by considering patterns (see Gems 8 for more on this).

Fractional powers can be explained using the multiplication law.

And then it's just a case of students remembering the laws and practising them until they become fluent. Mim Gosling (@mimgosling) created the picture below to help students remember how fractional powers work -"Fractional indices are like a flower - the bottom's the root, the top's the power!". So if you have a student who gets confused by fractional indices, just remind them that the root is at the bottom (like in a tree).

I taught an introductory lesson on index laws recently - I wrote these slides to structure the class discussion and activities. After we established each index law, the class did three quick practice questions before moving on to the next law. Once we'd covered all three laws, the students completed this 'Powers of y eliminator' from Teachit Maths, which was fantastic. It had just the right combination of independent practice, stretch and 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 feel free to borrow bits, though some formatting may be lost when you download it (the PDF version is much prettier!).

Card Sorts
It's a great idea to have a well-organised supply of sorting activities (eg Tarsia puzzles) in your maths department. Find a clever way to store them (eg in stackable plastic takeaway boxes) and label the boxes clearly. It takes a bit of time to prepare the card sorts. If you've got the budget, it's always best to get them laminated. Print each set on a different colour (eg if there are 10 groups in the class, print the card sets on 10 different colours) - this stops the sets getting mixed up. Use good quality elastic bands - cheap ones degrade quickly - or keep each set in an envelope.

My department has a collection of 56 card sorts ready for use in lessons (sadly, I spent many many hours sitting at the guillotine during my summer holidays!). We call them our 'Black Box Resources' because we keep them in black CD boxes from Ikea. Two of my favourite card sorts are for indices. The first is Indices Dominoes by Teachit Maths - a really nice activity, with the added bonus that the answer is written backwards so students can't cheat by guessing the words. I also like Using Indices from the Standards Unit. Card set A (pairs activity) is really useful when you've taught fractional and negative indices.

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

There's loads of great worksheets and activities for independent practice. I've already mentioned the Powers of y eliminator from Teachit Maths. Here's two more excellent resources that are suitable for practising the three index laws:

Once you've moved onto fractional and negative indices, there's loads more excellent resources (these might be useful in Year 12 too):

STEM Centre provides some fantastic indices activities from Susan Wall. For example, I like 'Why does?' (extract below) in which students are allocated a statement to think about and explain to the class.

Extract from 'Why does?' by Susan Wall

There's also a true or false activity which is designed to address common misconceptions.

Extract from 'True or False' by Susan Wall


I featured a 'blanks' task idea in Gems 17. Make up some questions like those shown below and put them up around the room. Provide post-it notes so students can suggest values that fit.
I've made two Pret homeworks for this topic, both are available here.
There's loads of great extension questions for this topic. I love these mega quadratic equations from Don Steward.
and these mega hard powers questions, also from Don Steward

And two more fantastic rich tasks from Don Steward: Power Sums and Find the Power. 

At A level, and maybe as extension in Year 11, I like to do some work on comparing indices with different bases. For example, I like this ordering starter.

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

Finally, I want to share two questions that I've been using for years with GCSE students, either when I teach indices or when I teach algebraic fractions. My students are always horrified by how complex these questions look, but if they're confident with indices then both equations are actually surprisingly easy to solve. I'm not sure where these questions originated so apologies to the creator for not giving credit.

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

How five squared looks in nightmares.

Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary:

"I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images.
I rate this site as a 5!"

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

"Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated."

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:

"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy:

"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

"It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages."

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK:

"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School:

"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School:

"This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register."

Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales:

"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access the whole month so I can use favourites with classes I see at different times of the week. Thanks."

Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex:

"This website was brilliant. My class and I really enjoy doing the activites."

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School:

"Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work."

0 Replies to “Index Laws Homework Online”

Lascia un Commento

L'indirizzo email non verrà pubblicato. I campi obbligatori sono contrassegnati *