Integers and Patterns

Integers are all the whole numbers and their opposites. This means integers include positive numbers (like 1, 2, 3...), negative numbers (like -1, -2, -3...), and zero. Zero is an integer, but it is neither positive nor negative. We use integers to count, measure, and describe quantities that can be above or below zero.

Negative numbers are numbers less than zero. They are written with a minus sign (-) in front of them, like -5. We use negative numbers in everyday life for things like: \n- Temperatures below zero (e.g., -10°C).\n- Depths below sea level (e.g., -50 metres).\n- Money owed or debt (e.g., owing $20 can be thought of as -$20).\n- Floors below ground level in a building (e.g., parking level -1).

A number line is a straight line with numbers placed at equal intervals or distances along it. It helps us visualize and compare numbers. \n- Zero is usually in the middle.\n- Positive numbers are to the right of zero.\n- Negative numbers are to the left of zero.\n- The further a number is to the right, the greater its value. The further a number is to the left, the smaller its value. For example, -2 is greater than -5 because -2 is to the right of -5 on the number line.

A pattern is a sequence of numbers, shapes, or objects that follows a specific rule. When working with integer patterns, we look for how the numbers change from one term to the next. This change is the 'rule' of the pattern. The rule often involves adding or subtracting a constant integer.

A pattern rule describes how to get from one term to the next in a sequence. To find a pattern rule:\n1. Look at the first two numbers. How do you get from the first to the second? (e.g., add 3, subtract 2).\n2. Check if this same operation works for the next pair of numbers (from the second to the third, and so on).\n3. Once you find the consistent operation, that's your rule! For example, 'Start at 5 and add 2 each time' or 'Start at 10 and subtract 3 each time'.