# Indices and Surds

### Indices

This resource from Susan Wall contains five activities designed to enable students to explore indices both numerically and algebraically. The resource features a number of activities dealing with negative indices and fractional indices.

Starter activities: contains two starter activities. In the first activity students have to represent an integer value in as many ways as they can, each way to include an index value. The second activity, ‘Why does?’ students have to explain mathematical statements involving indices.

Matching pairs game: Students are required to match a number in index form with its integer value.

Ordering indices: Students compare the values written in index form and place the cards in numerical order.

Odd one out: Given three cards, students find the odd one out and make up their own card to match the odd one.

True or false: Aimed at addressing common misconceptions, in this activity students discuss whether the statements given are true or false.

### Using Indices N12

In this resource from the DfE Standards Unit students are introduced to fractional and negative indices to enable them to evaluate numerical expressions using negative and fractional

indices and use the rules of indices with integer and fractional powers of variables. Students should have some knowledge of the rules of indices for multiplying and dividing numbers in index form

### Further Indices

Following on from the resource ‘Indices’, this resource from Susan Wall contains four activities designed to explore the rules of indices as well as differentiating and integrating functions containing indices.

The rules of indices with algebraic expressions: This activity is a matching exercise with algebraic statements involving negative indices and fractional indices.

Dominoes: is a loop card activity involving negative indices and fractional indices.

Differentiation and integration involving indices: A large, multi-tiered activity matching equivalent functions, differentials and integrals.

Marking: In this activity, students are given questions and solutions to a number of differentiation and integration questions. Students are required to mark the work. The solutions contain many common errors that are made. Students should mark the work for accuracy, correct solutions where necessary and give advice to help the candidate therefore explain what the error was and how to correct it.

### Manipulating Surds N11

In this resource from the DfE Standards Unit students identify equivalent surds and develop their ability to simplify expressions involving surds. Students should understand what a square root is and be able to remove brackets correctly.

### Indices and Surds

This RISP activity from can be used when either consolidating or revising ideas of curve-sketching and indices. The numbers phi, e and pi are used in this investigation where students are asked to estimate the size numbers generated when raising these numbers to different powers. It is suggested that a graphing package would prove useful wihen investigating the set problem.

### Arithmetic

Mathcentre provide these resources which cover aspects of arithmetic, often used in the field of engineering. They include fractions and their associated arithmetic, calculations involving surds, using standard form, as well as understanding and drawing the graph of a function.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of arithmetic will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided