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**Scheme of work: Key Stage 3: Year 8: Term 1: Indices and Approximation**

- Understand and use place value for decimals, measures and integers of any size.
- Use the four operations, including formal written methods, applied to integers and decimals.
- Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, < and >

- 2
^{3}, 2 is the base and 3 is the power. A base number is raised to a power. - Students should understand the equivalence between dividing by decimals and multiplying by reciprocals as this leads on to dividing with fractions.
- Any number raised to a power of zero is equal to one. Students should understand this as dividing a number by itself equals one.
- The multiplication rule can be defined as n
^{a}x nb = n(a+b). The division rule is n^{a}Ã· n^{b}= n^{(a-b)}. - The power rule (2
^{3})^{2}= 2^{6}is an extension of the multiplication rule. The power of zero rule is an extension to the division rule. - A number raised to a power of negative one is the reciprocal of that number.
- When rounding 3.5 to one significant figure the 3 is the most significant with the 5 tenths rounding it up to 4.
- When writing numbers in standard index for the number before the decimal point must be between 1 to 9 inclusive.

- Develop fluency
- Select and use appropriate calculation strategies to solve increasingly complex problems.

- Reason mathematically
- Extend and formalise their knowledge of ratio and proportion in working with measures and geometry and in formulating proportional relations algebraically.
- Make and test conjectures about patterns and relationships; look for proofs or counter-examples.

- Solve problems
- Develop their use of formal mathematical knowledge to interpret and solve problems.

- Number
- Use conventional notation to prioritise operations, including brackets, powers, roots and reciprocals.
- Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
- Interpret and compare numbers in standard form A 10
^{n}, where 1<=<10, where n is a positive or negative integer or zero - Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
- Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<a<=b
- Use a calculator and other technologies to calculate results accurately and then interpret them appropriately

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