Indices and roots
Term 3 starting in week 11 :: Estimated time: 2 weeks
- Square and Cube numbers (review)
- Calculate higher powers and roots
- Powers of ten and standard form (review)
- The addition and subtraction rules for indices (review)
- Understand and use the power zero and negative indices
- Work with powers of powers
- Calculate with numbers in standard form (review)
For higher-attaining pupils:
- Understand and use fractional indices
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Activities for pupils
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.
Standard Form Test your understanding of standard form (scientific notation) with this self-marking quiz.
Standard Form Video Learn how to write and calculate with numbers in standard form - sometimes called scientific notation.
Standard Order Arrange the numbers given in standard form with the smallest at the top and the largest at the bottom.
Indices True False Arrange the given statements involving indices to show whether they are true or false.
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).
Here are some exam-style questions on this topic:
- "(a) Write 0.0000657 in standard form." ... more
- "The number 1.25 × 10n is a cube number." ... more
- "The difference between the areas of the two squares is 51 cm2." ... more
- "Without using a calculator, show clearly that \(27^{\frac23}\) is equal to \(9\)." ... more
- "At a particular time the distance between Earth and Mercury was \(7.7 \times 10^7\) km." ... more
- "There's an old Elvish wives tale that roughly translated reads:" ... more
- "Work out the exact value of \(n\)." ... more
- "Without using a calculator find the values of the following:" ... more
- "If a, b and c are positive integers use the following statements to find the values of a, b and c." ... more
- "\(y = a \times b^{x – 2}\) where \(a\) and \(b\) are numbers." ... more
Here is an Advanced Starter on this statement:
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?
Lesson Starters
Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.
1st Lesson
Square Sequence
Write out as many square numbers as possible in 4 minutes.
2nd Lesson
Square and Even
Arrange the numbers on the cards so that each of the three digit numbers formed horizontally are square numbers and each of the three digit numbers formed vertically are even.
3rd Lesson
Squigits
A challenge to find numbers which have each of their digits as square numbers.
4th Lesson
Exponential Error
This lesson starter presents a number of statements about indices and pupils are asked if they can spot the mistake.
5th Lesson
Absolutely Everyone
A choice of questions about the current world population which is constantly changing.
6th Lesson
Refreshing Revision
It is called Refreshing Revision because every time you refresh the page you get different revision questions.
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.
