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Students use place value to multiply and divide by decimal numbers and round a number to a given significant figure. As learning progresses they apply this knowledge to evaluate numbers written using standard index form.

This unit takes place in Year 8 Term 1, and follows on from fractions, decimals and percentages.

- 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 =, ≠, <, >, ≤, ≥

- 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}× n^{b}= n^{(a+b)}. The division rule is defined as n^{a}÷ 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 for the priority of 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≤A<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<x≤b
- Use a calculator and other technologies to calculate results accurately and then interpret them appropriately

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