Begin this negative and fractional indices worksheet by looking at integers and proper fractions raised to negative indices (Q1).
Next consider mixed numbers and decimals.
Q3 in this excellent resource covers unit fractional indices to all of these types of numbers, before bringing in non-unit fractional indices in Q4.
We then begin to mix negative and fractional indices across Q5-6. Q6 explictly asks for a surd form.
Next in this negative and fractional indices worksheet there’s some reasoning activities with fill-in-the-blanks style questions (Q7).
The last two questions apply the same ideas to algebraic expressions. In Q8 pupils need to write examples as fractions using only positive rational powers. In Q9 they need to write examples in index form.
Don’t worry – we’ve also included an answer sheet in the download.
Free maths teacher resources
The questions in this worksheet have been designed to allow your students to have a go at all significant aspects of the content, but also to notice something about the structure behind each content area.
Students need to use their powers of reasoning to explain why they’re seeing the results they are.
Worksheets requiring arithmetic have been limited to integer calculation on the whole so you can use them with pupils who aren’t fluent in decimal/fractional arithmetic yet.
Where pupils have these pre-requisite skills, we recommend adapting the questions (where appropriate) to include this content.
Peter Mattock is an assistant headteacher and secondary mastery lead for the East Midlands South Maths Hub. He’s the author of Visible Maths and Conceptual Maths (Crown House Publishing). Follow Peter on Twitter at @MrMattock.
Read advice from maths teacher Jo Morgan about helping secondary students understand indices.
