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Written multiplication – long method
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Foundational skills
Multiply by a multiple of 10
\[ \text{Calculate } 34 \times 20 \]
Multiply a number by a multiple of ten using place value.
Set up long multiplication
\[ \text{Set up } 234 \times 56 \]
Write a long multiplication in the correct column format.
Place the second partial product
\[ \text{Where does 2nd part go?} \]
Understand the offset or placeholder zero for the second partial product.
2-digit × 2-digit
No exchanges required
\[ \text{Calculate } 12 \times 13 \]
Multiply two 2-digit numbers where no carrying is needed.
Exchanges in partial products only
\[ \text{Calculate } 34 \times 23 \]
Multiply where carrying occurs within partial products.
Exchanges when adding
\[ \text{Calculate } 45 \times 36 \]
Multiply where carrying is required when adding partial products.
High complexity
\[ \text{Calculate } 78 \times 69 \]
Multiply with carrying in multiple steps throughout.
3-digit × 2-digit
Minimal exchanges
\[ \text{Calculate } 123 \times 12 \]
Multiply a 3-digit by 2-digit number with few carries.
Moderate exchanges
\[ \text{Calculate } 245 \times 34 \]
Multiply with carrying in several columns.
Exchanges in most columns
\[ \text{Calculate } 456 \times 67 \]
Multiply with carrying occurring in most steps.
High complexity
\[ \text{Calculate } 789 \times 89 \]
Multiply with maximum carrying throughout all steps.
4-digit × 2-digit
Moderate complexity
\[ \text{Calculate } 1234 \times 23 \]
Multiply a 4-digit by 2-digit number with some carrying.
High complexity
\[ \text{Calculate } 3456 \times 47 \]
Multiply with carrying in many columns.
Very high complexity
\[ \text{Calculate } 6789 \times 78 \]
Multiply with extensive carrying throughout all steps.
Zeros in the calculation
Multiplier ends in zero
\[ \text{Calculate } 234 \times 30 \]
Multiply when the multiplier ends in zero.
Multiplicand ends in zero
\[ \text{Calculate } 340 \times 26 \]
Multiply when the multiplicand ends in zero.
Multiplicand internal zero
\[ \text{Calculate } 304 \times 26 \]
Multiply when the multiplicand contains an internal zero.
Both numbers contain zeros
\[ \text{Calculate } 340 \times 30 \]
Multiply when both multiplicand and multiplier contain zeros.
Special cases
Missing digit: Multiplier
\[ 234 \times 2? = 5382 \]
Work out a missing digit in the 2-digit multiplier.
Missing digit: Multiplicand
\[ 2?4 \times 23 = 5382 \]
Work out a missing digit in the multiplicand.
Missing digit: Partial product
\[ \text{First PP: } 20? \]
Work out a missing digit in one of the partial products.
Missing digit: Answer
\[ 234 \times 56 = 1310? \]
Work out a missing digit in the final answer.
Timer (Optional)
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Question