Addition and Subtraction (1) Chapter Notes | Year 6 Mathematics IGCSE (Cambridge) - Class 6 PDF Download

Positive and negative integers

• The objective is to estimate, add, and subtract large integers.
• Add and subtract positive and negative integers.
• Find the difference between two integers.
• Integers:
  • Whole numbers, including positive numbers (1, 2, 3, …), negative numbers (-1, -2, -3, …), and zero (0).
  • Used in real-world contexts, e.g., counting animals in a zoo or measuring diving depths of marine mammals.
• Addition and subtraction with large integers:
  • Addition combines quantities, e.g., total penguins in a zoo: 35 (male) + 38 (female) + 22 (juveniles) = 95.
  • Subtraction finds differences, e.g., difference between adult penguins (35 + 38 = 73) and juveniles (22): 73 - 22 = 51.
  • Estimation helps check calculations, e.g., for 13656 - 2419 (flight distances), estimate 14000 - 2000 = 12000.
• Addition and subtraction with positive and negative integers:
  • Use a number line to visualize operations:
    • Addition moves right, e.g., temperature at -30°C rises by 5°C: -30 + 5 = -25°C.
    • Subtraction moves left, e.g., temperature at -30°C falls by 5°C: -30 - 5 = -35°C.
  • Examples:
    • -7 + 2 = -5 (start at -7, move 2 right).
    • 4 - 8 = -4 (start at 4, move 8 left).
    • -1 + 2 = 1 (start at -1, move 2 right).
  • Temperature changes, e.g., -1°C at 8 a.m. rises by 4°C: -1 + 4 = 3°C.
• Finding the difference:
  • The difference between two numbers is the absolute value of their subtraction, always positive.
  • Example: Diving depth difference between sperm whale (3000 m) and elephant seal (1500 m): 3000 - 1500 = 1500 m.
  • Temperature difference, e.g., London (4°C) and Oslo (-5°C): 4 - (-5) = 4 + 5 = 9°C.
• Applications include comparing distances (e.g., flight distances from Dubai), temperatures (e.g., across cities), or scores in games.

Using letters to represent numbers

• The objective is to find the value of a letter that represents a number.
• Use the idea that an unknown is not necessarily one fixed number but a variable.
• Variables:
  • Letters (e.g., a, b, s, t, x, y) represent unknown numbers.
  • A variable can have multiple possible values, unlike a constant (fixed value).
  • Example: In a shape puzzle, each shape represents a number summing to a total, e.g., ■ + □ + ■ = 45.
• Solving for variables:
  • Use relationships to find values, e.g., for a rectangle with perimeter 20 cm, side lengths s and t satisfy s + t = 10 (half the perimeter), yielding pairs: (1, 9), (2, 8), (3, 7), (4, 6), (5, 5), (6, 4), (7, 3), (8, 2), (9, 1).
  • Example: Strips of card with lengths a and b, where b = a + 3 and a + b = 15, solve: a + (a + 3) = 15, 2a + 3 = 15, 2a = 12, a = 6, b = 6 + 3 = 9.
• Expressions with variables:
  • Represent operations, e.g., in a dice game, d (dice score) with instruction d + 4 means add 4 to the score.
  • Commutative property: d + 4 = 4 + d, 2 + d = d + 2, but subtraction is not commutative, e.g., 5 - d ≠ d - 5.
• Perimeter applications:
  • Square perimeter: p = s + s + s + s = 4s, e.g., if s = 5, p = 4 × 5 = 20 cm; if p = 32, 4s = 32, s = 8 cm.
  • Isosceles triangle with perimeter 15 cm, base y, equal sides x: p = x + x + y = 2x + y, e.g., possible values satisfy 2x + y = 15.
• Applications include solving puzzles, calculating distances in games, or determining side lengths in geometric shapes.