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- Adding and subtracting expressions with indices
- Simplifying algebraic expressions by multiplying indices
- Simplifying algebraic expressions by dividing indices
- Using the addition law for indices
- Using the addition and subtraction law for indices

- Exploring powers of powers

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Indices A self marking exercise on indices (powers or exponents) including evaluating expressions and solving equations.
- Indices Pairs The traditional pairs or pelmanism game adapted to test knowledge of indices.
- Indices Video Indices, exponents and powers can all be used as a short way to describe repeated multiplication.
- Don't Shoot The Square You will need to be quick on the draw to shoot all of the numbers except the square numbers.
- Power Shift Arrange the given numbers as bases and indices in the three-term sum to make the target total.
- Surds A self-marking exercise on calculating, simplifying and manipulating surds (also known as radicals).

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Indices Where do many fish live? Indices (in the seas!) This topic involves the use of the index, power or exponent. The concept is easily misunderstood and a surprisingly large number of pupils will evaluate 62 as 12 and not 36. After having mastered positive integer indices pupils should move on to negative indices and fractional indices. Exploring this topic in both numeric and algebraic ways will provide understanding and competence in this important concept.
- Number Spotting patterns is an important skill in many areas of life. The world of numbers contains many fascinating patterns and understanding them enables better problem solving strategies. From seeing patterns in the multiples of numbers shaded in a hundred square to spotting the recurring sequences of digits in decimal numbers there is a great deal for pupils to be introduced to. This topic includes even, odd, prime, triangular, perfect, abundant, square and cube numbers. It uses factors and multiples to find solutions to real life problems and encourages number connections to be investigated for pleasure. There are a lot of puzzles, challenges and games too. See also the Mental Methods topic and our Number Skills Inventory.
- Roots Pupils should learn how to find real roots associated with integer powers (square root, cube root and higher). They should also learn to distinguish between exact representations of roots and their decimal approximations. Just how do you find the cube root of a number? By trial and improvement, iterative calculations or by learning to use a calculator efficiently?

Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.

Work out the number of stamps needed to post a parcel.

The calculations are obscured by ink blots. What do you think the calculations would look like if there were no blots?

This lesson starter presents a number of statements about indices and pupils are asked if they can spot the mistake.

Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.