How to make it
- Set dividend and divisorPick a dividend of 2 to 5 digits and a divisor of 1 or 2 digits; one-digit divisors run from 2 to 9.
- Exact or with remaindersLeave With remainders off for problems that divide evenly, or tick it to let the key show answers like 218 R 3.
- Print with working spaceTwelve problems fill a page in rows of three with room underneath; change the count, then print or save a PDF.
Divide, multiply, subtract, bring down
Work through 875 ÷ 4 with the class. Divide: how many 4s in 8? Two, so write 2 above the 8. Multiply: 2 × 4 = 8, written under the 8. Subtract: 8 − 8 = 0. Bring down the next digit, 7. Now repeat: 7 ÷ 4 is 1, 1 × 4 = 4, 7 − 4 = 3, and bring down the 5 to make 35. Once more: 35 ÷ 4 is 8, 8 × 4 = 32, 35 − 32 = 3. No digits are left, so the answer is 218 R 3.
Many teachers give children a memory aid for the four steps and write it on a card beside the sheet; any phrase whose words start with D, M, S and B will do. The final check is to multiply back: 218 × 4 = 872, plus the remainder 3, is 875. If that works, the problem is right without looking at the key.
Each problem on the sheet sits under the bracket with the divisor outside, and a generous block of empty space beneath it for those multiply and subtract rows. Three problems fit across a page, and twelve, the starting count, fill it.
Zeros in the answer, and two-digit divisors
The step that catches most children is a zero in the quotient. In 824 ÷ 4, the 8 gives 2 and the 2 that comes next is smaller than 4. The temptation is to skip it and bring down the 4 straight away, giving 26. Instead, write 0 above the 2, because there are zero 4s in 2, then bring down the 4 to make 24, which gives 6. The answer is 206, and 206 × 4 = 824 confirms it.
Two-digit divisors add estimation. For 744 ÷ 24, ask how many 24s are in 74. Rounding helps: about 70 ÷ 20, so try 3. Then 3 × 24 = 72 and 74 − 72 = 2. Bring down the 4 to make 24, which goes once, and the answer is 31. When an estimate is too big, the multiplication gives more than you have; when it is too small, the subtraction leaves a number as large as the divisor. Either signal means adjust the digit by one.
A helpful habit for two-digit divisors is to write the first few multiples of the divisor down the margin before starting: 24, 48, 72, 96 and so on. It turns each guess into a lookup, and it shows plainly when a remainder is too big, because the remainder must be smaller than the first multiple on the list.
What grade is long division taught?
In the US, long division usually starts in fourth grade with one-digit divisors and dividends up to four digits, and US and Canadian sheets (those that open on Letter) with a one-digit divisor carry CCSS 4.NBT.B.6 in the footer, a code that stays on five-digit dividends too, although the standard itself stops at four digits. Fifth grade moves to two-digit divisors, shown as CCSS 5.NBT.B.6. By sixth grade students are expected to divide multi-digit numbers fluently with the standard algorithm, CCSS 6.NS.B.2, and five-digit dividends with two-digit divisors make good review; the footer still shows the fifth-grade code for those settings.
In England, pupils usually learn short division in Year 5 and formal long division by two-digit numbers in Year 6. In Australia, written division with one-digit divisors tends to come in Years 5 and 6. A good sequence for any of these: two-digit dividends exact, three-digit exact, three-digit with remainders, four digits, then two-digit divisors.
| Dividend and divisor | Remainders | Footer code | Typical US grade |
|---|---|---|---|
| 2 or 3 digits ÷ 1 digit | Off, then on | CCSS 4.NBT.B.6 | Grade 4 |
| 4 digits ÷ 1 digit | On | CCSS 4.NBT.B.6 | Grade 4 to grade 5 |
| 3 or 4 digits ÷ 2 digits | Off, then on | CCSS 5.NBT.B.6 | Grade 5 |
| 5 digits ÷ 2 digits | On | CCSS 5.NBT.B.6 | Grade 5 to grade 6 |
Long division or bus stop short division
The bracket on these sheets is the same shape UK schools call the bus stop. With a one-digit divisor, children can use either method on the same problems. In short division, the multiply and subtract steps happen in the head and only the remainder is written, as a small digit tucked in front of the next one. In long division, every step is written below. Short division is quicker; long division leaves a trail that makes errors easy to find.
A sensible plan is to teach the long version first so every step is visible, then let confident children switch to short division with one-digit divisors and keep the long form for two-digit divisors. Children who still need the basic facts first will get more from a page of division facts worksheets than from a bracket they cannot fill.
Typical mistakes, and how to use the key
Besides the skipped zero, watch for bringing down two digits at once, subtraction errors inside the working, a quotient digit that is too small (the subtraction leaves a remainder bigger than the divisor), and digits written in the wrong column so the answer ends up with a digit too many. Squared paper keeps each digit in its own column; a page of quarter-inch graph paper for working out is worth having on hand.
The key prints the quotient and remainder in pink above each bracket, in the position of the problem on the sheet. It does not show the working, so when an answer differs, go through the child's rows to find the first step that went wrong. Asking children to check by multiplying back connects this skill to multi-digit multiplication, and the check often finds the error before you do.
How many problems to print
Long division is slow, so fewer problems is usually better. When the method is new, four to six problems done together on the board, then a few alone. For practice, eight to twelve, which is one page. For a check at the end of a unit, ten to twelve with remainders on, mixing three and four digits by printing two short sheets if needed. Five-digit dividends with two-digit divisors take a long time each; six is a solid homework.
Tick Bigger print if handwriting is large and the working space looks tight; each row then holds fewer problems with more room around them.
A tutor with a fourth grader who keeps losing track of the steps might print six exact problems with three-digit dividends, work the first one aloud, and ask the student to talk through the second while the tutor writes. The last four are done alone, then checked by multiplying back before the key comes out. When a session like that goes smoothly twice in a row, add remainders.
Questions
How do you teach long division step by step?
Teach the four repeating steps: divide, multiply, subtract, bring down. Start with a two- or three-digit dividend and a one-digit divisor that divides evenly, model the first few problems aloud, and have children check each answer by multiplying back. Add remainders, then zeros in the quotient, then two-digit divisors.
Can I make long division worksheets with remainders?
Yes. Tick With remainders and the dividends are chosen freely, so most problems leave a remainder and some divide exactly. The key writes answers like 218 R 3. Without the box ticked, every dividend is a multiple of its divisor, which suits the first lessons.
Does the answer key show the working?
No. The key shows the final quotient and remainder above each bracket, in the same layout as the worksheet. That keeps marking fast and works with long or short division. To find where a wrong answer went astray, follow the child's subtraction rows and check each against the divisor.
Can the divisor have two digits?
Yes. Choose 2 digits under Divisor and problems use divisors from 10 to 99, with the dividend at least as large as the divisor. Two-digit divisors call for estimating each quotient digit, so start with three-digit dividends and no remainders, and expect fewer problems per lesson.
What is the difference between long division and short division?
Both use the same bracket. Long division writes every multiplication and subtraction under the dividend; short division, often called the bus stop method in the UK, does those steps mentally and writes only small carried remainders. Short division is usual for one-digit divisors and long division for two.
Why does my child get answers that are too small?
The most common cause is skipping a zero in the quotient: in 824 ÷ 4, writing 26 instead of 206. Each time a digit is brought down and the number is still smaller than the divisor, a 0 must go in the answer before the next digit comes down.
Common Core State Standards: © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.