Divide, multiply, subtract, bring down — the four words a child meets at school, each printed beside what it means. The worked example is 657 ÷ 3 in the bracket with the shaded squares filled in, the steps under it say what every digit is worth, and six three-digit divisions follow: four with the squares shaded, two with the shape of the working drawn and the squares left plain.
Read the worked example and the steps under it. Then try the six below: the shaded squares show where each number goes.
Divide one column at a time, biggest first
657 ÷ 3. Share the hundreds first, then the tens, then the ones. Whatever is left over in one column joins the next — like changing a leftover note into coins. Four steps, the same in every column: divide, multiply, subtract, bring down.
2193657−605−327−27R0
657 ÷ 3 = 219, step by step
1.Divide. How many 3s in 6 hundreds? 2 hundreds. Write 2 above the 6.
2.Multiply. 2 × 3 = 6. Write 6 under the 6.
3.Subtract. 6 − 6 = 0. Nothing left in the hundreds.
4.Bring down. Bring the 5 down: 5 tens. How many 3s in 5? 1. Write 1 above the 5. 1 × 3 = 3. 5 − 3 = 2 tens left.
5.Bring the 7 down beside the 2: 27 ones. How many 3s in 27? 9. Write 9 above the 7. 9 × 3 = 27. 27 − 27 = 0. Nothing left.
6.Read the top: 219. Check: 219 × 3 = 657.
For the grown-up: make them say what each digit is worth — ‘6 hundreds shared by 3 is 2 hundreds’ — and the steps are the same in every column.
Long division, step by step
NameDate/ 6
Read the worked example and the steps under it. Then try the six below: the shaded squares show where each number goes.
1.4528−−−R
2.5735−−−R
3.4848−−−R
4.4936−−−R
5.7861−−−
6.3975−−−
Long division, step by step
NameDate/ 6
Read the worked example and the steps under it. Then try the six below: the shaded squares show where each number goes.
1.1324528−412−1208−8R0
2.1475735−523−2035−35R0
3.2124848−804−408−8R0
4.2344936−813−1216−16R0
5.1237861−716−1421−210
6.3253975−907−615−150
What is on this sheet
The words are the abbreviation, and the page’s job is the thing abbreviated. A child chanting the four steps can carry them out with no idea that the 2 they wrote is two hundreds, and that child brings the next digit down into the wrong column, which is the commonest long-division error there is. So every step here is said in place-value language — how many 3s in 6 hundreds? — and the grid under the bracket gives every digit a column of its own. Read the chunking page first if the bracket is new: this is the same method, written shorter.
The six to try are chosen so the method is met clean: three digits by one, the first digit at least the divisor, no remainder and no zero in the answer. Four are guided, with the squares that get written in shaded and the last row marked R; two show only the minus signs and the rules, for a child who no longer needs to be shown which square. The problems run on to a second page. The long-division drill pages carry on from here, with the grid, the zeros and the two-digit divisors.
The answers were worked out when the problems were, so the key is the same page with the answers drawn in rather than a second attempt at the same questions — there is no way for the two to disagree. The number in the footer is the seed the sheet was built from: it is printed so that the identical sheet can be had again next week, rather than one that merely looks like it.
Change what is on it
This page is one sheet out of a family that can print thousands, and the settings behind it — how many problems, how big the numbers get, how they are laid out, whether there is room to work — are all switches. The builder link at the top of the page carries this sheet’s own settings, so the bench opens on exactly the sheet here rather than on a blank one.
The configuration travels in the address bar rather than on a server, so the link can be bookmarked or sent to somebody as it stands — and what they open is this sheet, down to the seed, rather than another one like it.
The same facts, on screen
Every subtraction under the bar and every fact over it is in The Grid; the bracket itself is paper's.
