BEST MATH TUITION SINGAPORE

Your child can do the times tables. So why is long division still going wrong? If you have watched your Primary 3 child work through a page of long division, you have probably seen the same thing happen more than once. They get the first few right. Then one goes wrong, and when you check the working you cannot tell where it broke. The next day they make a completely different mistake. It is easy to conclude that your child is weak at maths. Usually that is not what is happening. Long division is not one skill. It is four, and they arrive in the same lesson. Your child has to work out how many times the divisor fits, multiply, subtract, and bring the next digit down — while keeping every digit in the right column. Then, before that is secure, the questions turn into word problems, and two more skills arrive on top. Most children do not fail long division because it is hard. They fail because too much arrived at once, and nobody separated it out. Every cycle runs all four steps. Miss one and the answer breaks. Before you start: a 30-second check There is one thing that has to be in place first. Ask your child these three questions. Each answer should come back in about three seconds. What is 7 × 4? How many 4s in 28? What is 52 − 48? The second question is the one that catches people out. It is a multiplication fact read backwards, and long division only ever asks for it backwards. A child who can recite the four times table forwards but has to think about “how many 4s in 28” will lose their place halfway through a column. If any of the three is slow, hesitant or wrong, work on that first. Long division will not fix it. It will hide it. Why more practice usually does not help The instinct, when a child keeps getting long division wrong, is to give them more long division. More worksheets, more questions, more practice. This rarely works, and the reason is simple. A mixed worksheet gives your child twenty questions that each require four skills. When they get one wrong, neither of you learns anything, because you cannot see which of the four broke. You mark it wrong, they try again, and the same thing happens next week. What works is separating the skills, then testing them one at a time. That is what the nine worksheets below do. Each one introduces exactly one new idea and nothing else. When your child gets stuck, you know which rung they are standing on. The nine places it goes wrong The full ladder. Each worksheet adds one new idea and nothing else. 1. Two-digit ÷ one-digit — the four steps, run once The whole method in a single cycle. Divide, multiply, subtract, bring down, and stop. What goes wrong: the answer digit ends up in the wrong column, usually shifted one place left. Every answer digit must sit directly above the digit it came from. Download Worksheet 1 — Two-Digit Division (PDF) ↓ 2. Three-digit ÷ one-digit — repeating the cycle Now the cycle runs three times instead of once, and your child has to hold their place while doing it. What goes wrong: they run the cycle twice, then copy the last digit down instead of dividing it. A three-digit number needs the cycle three times, once for every digit. Download Worksheet 2 — Three-Digit Division (PDF) ↓ 3. When the first digit is too small In 213 ÷ 3, the 2 cannot be divided on its own. It joins the 1, and the answer has two digits instead of three. What goes wrong: they force a digit above the 2 anyway and write 071, or put a 0 there. Nothing goes above that digit at all. Download Worksheet 3 — First Digit Too Small (PDF) ↓ 4. Zero in the answer 408 ÷ 2 = 204. Not 24. What goes wrong: they divide, get nothing, and move straight on without writing the 0. This is the single most common wrong answer in the whole topic, and because it is usually mixed in among other questions, nobody notices it is a specific, fixable error. Download Worksheet 4 — Zero in the Answer (PDF) ↓ The zero is easy to skip because nothing visibly happens at that step. 5. Division with remainder Something is left over, and the answer stops being a single number. What goes wrong: they leave a remainder bigger than the divisor — writing 5 R 6 for a division by 4. That always means the last answer digit was too small. Download Worksheet 5 — Division with Remainder (PDF) ↓ 6. One-step word problems Now they have to read a story and decide what to divide before any of the method matters. What goes wrong: “shared with 3 friends” means four people, not three. They divide by the number of friends and forget to count the child doing the sharing. Download Worksheet 6 — One-Step Word Problems (PDF) ↓ 7. Two-step word problems Add or subtract first, then divide. What goes wrong: they divide the first number they see. Given 246 stamps and 132 more, shared into 3 albums, they divide 246 by 3 and never add the 132. Download Worksheet 7 — Two-Step Word Problems (PDF) ↓ 8. Remainder in context The division is ordinary. The question decides which half of the answer is wanted. What goes wrong: asked how many are left over they give the number of groups, and asked how many groups they give the leftover. Same working, opposite answer. Download Worksheet 8 — Remainder in Context (PDF) ↓ 9. Filling one more group The hardest one, and the one that separates children who understand from children who have memorised. What goes wrong: “packed into 4 bags” and “packed into bags of 4” look almost identical and need different methods. In the