Year 4 Number Cheatsheet

• Place value to 5 digits: 10,000s (ten-thousands), 1,000s (thousands), 100s (hundreds), 10s (tens), 1s (ones)
• Addition and subtraction with 4-digit numbers can use place value strategy or the standard algorithm
• Multiplication facts extend beyond single digits; know facts up to 12 × 12
• Division with remainders occurs when grouping doesn't divide evenly
• Equivalent fractions are different fractions that represent the same amount (e.g. 1/2 = 2/4)
• Decimals to tenths: 0.1 = 1/10, 0.5 = 5/10, etc.
• Financial maths includes budgeting (planning money) and shopping (adding prices and change)
• Compare and order fractions and decimals by finding common denominators or converting to decimals

Example 1: 4-Digit Addition with Regrouping

Add 2,347 + 1,256

Step 1: Line up by place value:

2,347
+1,256

Step 2: Add ones: 7 + 6 = 13. Write 3, carry 1

Step 3: Add tens: 4 + 5 + 1 (carry) = 10. Write 0, carry 1

Step 4: Add hundreds: 3 + 2 + 1 (carry) = 6. Write 6

Step 5: Add thousands: 2 + 1 = 3. Write 3

Answer: 2,347 + 1,256 = 3,603

Example 2: Division with Remainders

Divide 23 ÷ 4

Step 1: How many 4s fit into 23? 4 × 5 = 20, 4 × 6 = 24 (too much)

Step 2: 4 goes into 23 five times (5 × 4 = 20)

Step 3: Subtract: 23 - 20 = 3 (this is the remainder)

Step 4: Write as 5 R3 (5 remainder 3)

Answer: 23 ÷ 4 = 5 R3

Example 3: Equivalent Fractions and Decimals

Are 0.5 and 1/2 the same?

Step 1: 0.5 = 5 tenths = 5/10

Step 2: Simplify 5/10 by dividing top and bottom by 5: 5÷5 = 1, 10÷5 = 2

Step 3: 5/10 = 1/2

Step 4: So 0.5 = 1/2 ✓

Answer: Yes, 0.5 and 1/2 are equivalent

Example 4: Financial Maths — Shopping

You buy a notebook for $3.50 and a pencil for $1.20. How much do you spend?

Step 1: Add the amounts: $3.50 + $1.20

Step 2: Dollars: $3 + $1 = $4. Cents: 50¢ + 20¢ = 70¢

Answer: Total = $4.70

• Mistake: Forgetting to regroup/carry in addition. Adding 347 + 256, forgetting to carry the 1 from 7+6=13.
  Fix: Underline or mark carried digits. Work column by column, and carry every time.
• Mistake: In division, not checking remainders. If 23 ÷ 4 = 5 R3, verify: 5 × 4 + 3 = 23 ✓
  Fix: Always check: (quotient × divisor) + remainder = original number
• Mistake: Confusing equivalent fractions with different values. Thinking 1/2 ≠ 2/4 because numerators are different.
  Fix: Equivalent fractions represent the same amount. Draw pictures or use a number line to verify.
• Mistake: Not comparing decimals correctly. Thinking 0.3 > 0.25 (wrong!) because 3 < 25 as whole numbers.
  Fix: Compare tenths first: 0.3 = 3 tenths, 0.25 = 2 tenths + 5 hundredths. 3 tenths > 2 tenths, so 0.3 > 0.25.
• Mistake: In shopping, adding $3.50 + $1.20 as 3.50 + 1.20 = 4.60 without labels, then confusion about the result.
  Fix: Always include the dollar sign and decimal point. Add dollars and cents separately if needed.

• Place Value: The value of a digit based on its position (ones to ten-thousands)
• Regroup (or Carry): Moving 10 units from one place value to the next (e.g. 10 ones = 1 ten)
• Remainder: The amount left over after division when it doesn't divide evenly
• Quotient: The result of division (e.g. in 20 ÷ 5 = 4, the quotient is 4)
• Equivalent Fractions: Different fractions that represent the same amount (e.g. 1/2 = 2/4)
• Denominator: The bottom number of a fraction (how many equal parts the whole is divided into)
• Numerator: The top number of a fraction (how many parts you have)
• Decimal: A number with a decimal point, used to show tenths, hundredths, etc.
• Tenths: One of ten equal parts; written as 0.1, 0.2, ... 0.9
• Budget: A plan for spending money that shows how much money you have and how you will use it