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DIFFICULTY EXPLANATIONS
ALIEN SPEED
Controls how fast the aliens move and attack:
- • SLOW: Slow moving aliens
- • NORMAL: Moderate speed
- • FAST: Fast moving aliens
- • EXTREME: Extremely fast and challenging
ADDITION DIFFICULTY
Problems increase in complexity:
- • EASY: Single-digit numbers with sum up to 12, no carrying required (e.g., 8 + 4 = 12)
- • MEDIUM: One or two-digit numbers, sum up to 40, carrying allowed (e.g., 15 + 25 = 40)
- • HARD: Two-digit numbers, sum up to 200, carrying allowed (e.g., 85 + 97 = 182)
- • EXPERT: Two or three-digit numbers, sum up to 999, carrying allowed (e.g., 345 + 612 = 957)
SUBTRACTION DIFFICULTY
- • EASY: Single-digit numbers only, no borrowing required, result up to 9 (e.g., 8 - 3 = 5)
- • MEDIUM: One or two-digit numbers, result up to 40, No borrowing allowed (e.g., 42 - 11 = 31)
- • HARD: Two-digit numbers, result up to 99, borrowing allowed when needed (e.g., 42 - 16 = 26)
- • EXPERT: Two or three-digit numbers, result up to 999, borrowing allowed when needed (e.g., 345 - 212 = 133)
MULTIPLICATION DIFFICULTY
Problems increase in complexity:
- • EASY: Allowed times tables for 1, 2, 5, 10 - both factors can only be 1, 2, 5, or 10 (e.g., 1 × 5 = 5, 5 × 2 = 10, 10 × 5 = 50)
- • MEDIUM: Allowed factors: {1, 2, 3, 4, 5, 6, 10, 11} - both factors must come from this set (e.g., 3 × 4 = 12, 6 × 5 = 30, 10 × 11 = 110, 11 × 11 = 121)
- • HARD: Covers the entire set from 1 through 12 (e.g., 7 × 10 = 70, 12 × 12 = 144, 9 × 11 = 99)
- • EXPERT: Any two-digit by two-digit multiplication (e.g., 23 × 47 = 1081, 56 × 92 = 5152)
DIVISION DIFFICULTY
All problems have whole number answers:
- • EASY: Divisor and quotient can only be 1, 2, 5, or 10 (e.g., 10 ÷ 2 = 5, 5 ÷ 1 = 5, 2 ÷ 2 = 1)
- • MEDIUM: Divisor and quotient can be 1, 2, 3, 4, 5, 6, 10, or 11 (e.g., 66 ÷ 6 = 11, 10 ÷ 2 = 5, 110 ÷ 11 = 10)
- • HARD: Divisor and quotient can be any integer from 1 through 12 (e.g., 144 ÷ 12 = 12, 60 ÷ 5 = 12, 36 ÷ 9 = 4)
- • EXPERT: Divisor and quotient can be any integer from 10 through 99 (e.g., 9801 ÷ 99 = 99, 3600 ÷ 90 = 40, 484 ÷ 22 = 22)