Long Multiplication
This topic covers 5 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Multiply by 10, 100
Understand place value when multiplying by powers of 10 - 2-Digit x 1-Digit
Multiply a 2-digit number by a single digit using partitioning - 2-Digit x 2-Digit
Multiply two 2-digit numbers using the grid or column method - 3-Digit x 2-Digit
Extend long multiplication to larger numbers - Challenge — Multi-Step Multiplication Problems
Complex problems requiring long multiplication
Worked Example
The Blacksmith says:
The Blacksmith orders 100 bags of 23 coal pieces each. How many coal pieces?
- 23 x 100: move digits two places left.
- 23 becomes 2300.
Answer: 2300
Common Mistakes
- Forgetting to add a zero (or use a placeholder) when multiplying by the tens digit (e.g. working out 23 × 14 and not shifting the second row)
When multiplying by the tens digit, the answer goes in the tens column. Remind your child: "The 1 in 14 actually means 10, so the whole answer is 10 times bigger — slide it one place to the left." - Making errors in the addition step after the partial products are written out
Long multiplication has two stages: multiply, then add. Encourage your child to check the addition step separately, or estimate the answer first (20 × 14 = 280, so 23 × 14 should be a bit more).
Tips for Parents
- Start with the grid method (also called the box method) before moving to formal long multiplication — it shows where every number comes from.
- Use squared paper to keep digits aligned. Misaligned columns are the most common source of errors.
- Encourage estimation first: "36 × 15 — that is roughly 40 × 15 = 600, so the answer should be close to 600." This catches big mistakes.
- Break it down together: "36 × 15 = 36 × 10 + 36 × 5." Show how the formal layout does exactly the same thing.
Key Words
- Long multiplication — A written method for multiplying larger numbers by breaking them into parts and adding the results.
- Partial product — One part of the answer in long multiplication — when doing 23 × 14, the partial products are 23 × 4 and 23 × 10.
- Grid method — A way of multiplying using a grid to split numbers into tens and units — also called the box method.
- Placeholder — A zero written to show that you are multiplying by tens (or hundreds), not units.
- Estimate — A rough calculation to check your answer is sensible.
Where This Fits
Before this topic: Children need fluent recall of times tables up to 12 × 12 and an understanding of place value in two- and three-digit numbers.
After this topic: Long multiplication extends to multiplying three-digit by two-digit numbers, and supports division, ratio, and real-world problem-solving in Years 5-6.
How MathCraft Teaches This
In MathCraft, Long Multiplication is taught through the Algebra & Arithmetic adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 5 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Long Multiplication with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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