Partial quotients worksheets: division by chunking, explained
Division by taking away big lumps of the divisor — ten twelves at once, then three more — which is what partial quotients means. The number line shows the two hops, the column is written down the page the way a child writes it, the steps say why each lump was chosen, and six divisions by two-digit numbers follow with blank room under each for the lumps.
Read the box and the line. Then try the six below: write down every lump you take, and add the lumps at the end.
Take away big lumps of the divisor
How many 12s in 156? Take away lumps of 12 until nothing is left, then add up how many lumps you took. Like paying with the big notes first and the coins after: ten 12s at once, then the rest.
Written down the page
156
− 120 (ten 12s)
36
− 36 (three 12s)
0 — lumps taken: 10 + 3 = 13
156 ÷ 12, step by step
1.How many 12s in 156? I don’t know — but I know 10 twelves is 120.
2.Take 120 away: 156 − 120 = 36. Write 10 in the side column.
3.How many 12s in 36? 3. Take 36 away: 36 − 36 = 0. Write 3.
4.Add the side column: 10 + 3 = 13. Check: 13 × 12 = 156.
5.Any lump works. Five 12s at a time gets there too, in more steps. Ten-lumps are fastest.
156 ÷ 12 =13
13 × 12 =156
For the grown-up: ask ‘what’s ten lots?’ first. Write down every lump you take, and add the lumps at the end.
Division by chunking
NameDate/ 6
Read the box and the line. Then try the six below: write down every lump you take, and add the lumps at the end.
1.322 ÷ 14 =
2.195 ÷ 15 =
3.190 ÷ 15 =
4.168 ÷ 14 =
5.144 ÷ 12 =
6.253 ÷ 11 =
Division by chunking
NameDate/ 6
Read the box and the line. Then try the six below: write down every lump you take, and add the lumps at the end.
1.322 ÷ 14 =23
2.195 ÷ 15 =13
3.190 ÷ 15 =12 r 10
4.168 ÷ 14 =12
5.144 ÷ 12 =12
6.253 ÷ 11 =23
What is on this sheet
This page comes before long division, not after it, and that is the research talking. Children who reach the compact algorithm by way of chunking make fewer of the errors that come from following steps without a reason, because every line of a chunked division says what it means: 156 take away 120 is ten twelves gone. Every divisor here has two digits, since a one-digit divisor is a table fact a child can already do in their head and would learn nothing from, and the last one leaves a remainder to show the method survives one.
Any lump works, and the lesson says so: five twelves at a time gets to the same answer in more steps, and ten-lumps are only the fastest. What the child is practicing is writing every lump down and adding them at the end — the side column — which is the habit the long-division page then abbreviates into a digit over each column. The six problems run on to a second page, each with six lines of room, so the working has somewhere to go.
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
Not in the games. The multiples a child reaches for — ten twelves, three twelves — are, in The Grid.
