Indices/ Fractional Indices/ Surds

This is a set of 3 lessons looking at all aspects of Indices, from the 3 basic rules, through to differentiation.

Calculating using the 3 rules of Indices Lesson 1
The power and root starter can be projected onto the board and printed out so the students can fill in the sheet and spot the problem that they have no solution for.
Then the three laws of indices are introduced and each time the students have 7 questions to complete. A power point is also attached with these on.
There are then 6 mixed question which also introduces algebra as well as just numbers.
4 more complex questions will then be tackled as a group.
Plenary – here they need to work out the powers of numbers by using the 3 laws they have learnt

Investigating Fractional Indices Lesson 2
Here the students have a Thunk as a starter.
You will introduce the idea of any number to the power of zero and how to prove it using the powers of indices.
Students will use a calculator to see if they can work out what the fractional indices ate doing to the number, make sure they write the questions down and keep the solutions as fractions, or they will struggle to spot what’s going on. Then negative powers are introduced and again the students need to decide what’s going on.
There is a worksheet embedded, a power point to use as an extension where 5 out of 10 questions are correct, the students have to decide which.
There is a plenary flipchart embedded with a set of questions where the students have multiple choice answers that you can use an activote pod, or ABCD cards etc, or get them to do it as a quiz.

Converting between Indices and Surds (A/A*) Lesson 3
There are starter questions which look at simplifying surds.
Then you look at how to convert from fractional powers to surds and visa versa.
You can then look at fractions and how to combine them with indices,
The last two slides are to do with differentiations, if you haven’t covered this you can just change the 2nd slide from surd form into indices.