Year 3 Number Cheatsheet

• Numbers can be split into place value: thousands, hundreds, tens and ones
• Even numbers end in 0, 2, 4, 6, 8 — odd numbers end in 1, 3, 5, 7, 9
• Multiplication is repeated addition; division is sharing or grouping into equal parts
• Unit fractions like 1/2 (one half), 1/3 (one third), 1/4 (one quarter) represent one equal part
• Money is counted in cents (1c to 99c) and dollars (add dollars, add cents separately)
• Rounding to the nearest 5 cents helps with money: 1c and 2c round down to 0c; 3c and 4c round up to 5c; 6c and 7c round down to 5c; 8c and 9c round up to 10c

Example 1: Place Value and Addition

Write 2364 in expanded form, then add 1000.

Step 1: Break 2364 into place value parts: 2000 + 300 + 60 + 4

Step 2: Add 1000 to the thousands: 2000 + 1000 = 3000

Step 3: Write the full number: 3000 + 300 + 60 + 4 = 3364

Answer: 3364

Example 2: Multiplication as Repeated Addition

Sam buys 4 packets of stickers. Each packet has 5 stickers. How many stickers does Sam have?

Step 1: Recognise this is 4 groups of 5: 4 × 5

Step 2: Add them up: 5 + 5 + 5 + 5 = 20

Step 3: Or use the 5 times table: 5, 10, 15, 20 (the 4th number)

Answer: 20 stickers

Example 3: Unit Fractions and Money

A packet of lollies costs $2. If you buy 1/2 of the packet (you share with a friend), what do you pay for your half?

Step 1: Understand 1/2 means one of two equal parts

Step 2: Split $2 into two equal parts: $2 ÷ 2 = $1

Answer: $1

• Mistake: Confusing place value. Writing 342 as "3, 4, 2" instead of "3 hundreds, 4 tens, 2 ones".
  Fix: Always label each digit with its place value (Th, H, T, O) first.
• Mistake: Forgetting to carry when the ones add to more than 9. E.g. 27 + 16 = 33 (wrong).
  Fix: Line up numbers by place value: 7 + 6 = 13, write 3 ones and carry 1 ten, so 27 + 16 = 43.
• Mistake: Thinking 1/3 is bigger than 1/2.
  Fix: More pieces = smaller pieces. 1/2 (split in 2) is bigger than 1/3 (split in 3).
• Mistake: Adding money: 65c + 38c = 93c, but not rounding. If rounding to nearest 5c: 93c → 95c (rounds up).
  Fix: When adding cents, check if you need to round afterwards.

• Place Value: The value of a digit based on its position (ones, tens, hundreds, thousands)
• Even Number: A whole number that can be split into two equal groups (ends in 0, 2, 4, 6, 8)
• Odd Number: A whole number that cannot be split into two equal groups (ends in 1, 3, 5, 7, 9)
• Multiplication: Repeated addition; the number of groups × the amount in each group
• Division: Sharing objects into equal groups, or grouping objects into sets
• Unit Fraction: A fraction with numerator 1, showing one equal part (1/2, 1/3, 1/4)
• Numerator: The top number in a fraction (how many parts you have)
• Denominator: The bottom number in a fraction (how many equal parts the whole is split into)
• Rounding: Changing a number to the nearest 5 cents or 10 cents for easier calculation