Number Systems and Integer Operations

Number Systems

• Integers: Whole numbers, their opposites (negative integers), and zero. Represented on a number line.
• Rational numbers: Numbers that can be expressed as a fraction (a/b) where 'a' and 'b' are integers and 'b' is not zero. Includes integers.
• Irrational numbers: Numbers that cannot be expressed as a fraction. Examples include π (pi) and the square root of 2.
• Real numbers: The set of all rational and irrational numbers.

Operations with Integers

• Addition: Combining integers on a number line. Rules for adding positive and negative integers.
• Subtraction: Adding the opposite (subtracting a number is equivalent to adding its opposite).
• Multiplication: Repeated addition. Rules for multiplying positive and negative integers; positive times positive = positive, positive times negative = negative, negative times negative = positive.
• Division: Repeated subtraction. Rules for dividing positive and negative integers are similar to multiplication.

Order of Operations (BIDMAS/BODMAS)

• Brackets (parentheses)
• Indices (exponents)
• Division
• Multiplication
• Addition
• Subtraction

Factors and Multiples

• Factors: Numbers that divide exactly into another number.
• Multiples: Numbers that are a product of a given number and another whole number.
• Common factors: Factors shared by two or more numbers.
• Lowest Common Multiple (LCM): The smallest multiple that two or more numbers have in common.

Prime Numbers

• Prime numbers: Whole numbers greater than 1 that are only divisible by 1 and themselves. Examples include 2, 3, 5, 7, 11.

Fractions

• Equivalent fractions: Fractions that represent the same value, e.g., 1/2, 2/4, 3/6
• Simplifying fractions: Expressing a fraction in its simplest form, dividing numerator and denominator by their common factors.
• Adding and subtracting fractions: Requires a common denominator.
• Multiplying and dividing fractions.

Decimals

• Place value: Understanding the value of digits in decimal numbers (e.g., tenths, hundredths, thousandths).
• Converting between decimals and fractions.
• Rounding decimals.

Ratio and Proportion

• Ratio: A comparison of two quantities. Expressed as a fraction, a colon (e.g., 3:4) or 'to'.
• Proportion: An equality of two or more ratios.
• Solving ratio problems using proportions.

Percentages

• Percentage: A fraction or ratio expressed out of 100.
• Converting between percentages, fractions, and decimals.
• Calculating percentages of amounts.
• Finding the original amount given a percentage.

Algebra

• Variables: Symbols (usually letters) that represent unknown values.
• Expressions: Combinations of numbers and variables connected by mathematical operations.
• Equations: Statements that show equality between two expressions.
• Solving simple equations involving addition, subtraction, multiplication, and division.
• Formulae: Equations that represent a relationship between different quantities.

Geometry

• 2D shapes: Understanding properties of different shapes like triangles, quadrilaterals and circles (e.g., angles, sides).
• 3D shapes: Understanding properties of different shapes like cubes, prisms and pyramids (e.g., faces, edges, vertices).
• Perimeter: The total distance around the outside of a shape.
• Area: The amount of space inside a shape.
• Volume: The amount of space taken up by a 3D shape.

Data Handling

• Collecting, organizing, and representing data in tables, charts, and graphs.
• Frequency tables: Summarizing data; counting instances of different values.
• Histograms: Displaying frequency of numerical data in intervals.
• Pie charts: Representing data as portions of a whole, using percentages.
• Mean, median, mode, range: Measures of central tendency and spread of data.