# Indices and Approximation

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

#### Prerequisite Knowledge

• 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 >

#### Key Concepts

• 23 , 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 na x nb = n(a+b).  The division rule is naÃ· nb = n(a-b).
• The power rule (23)2 = 26 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.

#### Working Mathematically

• 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.

#### Subject Content

• 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 10n, 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

## Indices and Approximation Resources

### Mr Mathematics Blog

#### Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

#### GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

#### Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.