The same sum as the sharing lesson told the other way round: 12 ÷ 3 as how many 3s make 12. Counters in a row ringed three at a time, a number line from 0 to 12 with four jumps back of 3, the steps written out, and six problems to ring or jump through.
Read the box, then ring the groups or jump back along the line. Try the six below.
Dividing is also asking how many groups
12 ÷ 3 can also mean: how many 3s make 12? Think of packing bags: put 3 in every bag, and count the bags you fill. It is the same sum as the sharing page, but a different story. Both are dividing.
groups of 3 · 4 groups
12 ÷ 3, step by step
1.12 candies. Bags hold 3.
2.Ring 3. Ring 3. Ring 3. Ring 3.
3.Count the rings: 4.
4.Start at 12 on the line. Jump back 3 at a time. Four jumps reach 0.
12 ÷ 3 =4
How many 3s in 12? 4
For the grown-up: say it as a question — how many 3s in 12? — and let them make the groups. Then count groups, not candies.
1.18 ÷ 6 =
2.12 ÷ 4 =
3.21 ÷ 3 =
4.15 ÷ 5 =
5.10 ÷ 2 =
6.16 ÷ 4 =
Division is making groups
NameDate/ 6
Read the box, then ring the groups or jump back along the line. Try the six below.
Dividing is also asking how many groups
12 ÷ 3 can also mean: how many 3s make 12? Think of packing bags: put 3 in every bag, and count the bags you fill. It is the same sum as the sharing page, but a different story. Both are dividing.
groups of 3 · 4 groups
12 ÷ 3, step by step
1.12 candies. Bags hold 3.
2.Ring 3. Ring 3. Ring 3. Ring 3.
3.Count the rings: 4.
4.Start at 12 on the line. Jump back 3 at a time. Four jumps reach 0.
12 ÷ 3 =4
How many 3s in 12? 4
For the grown-up: say it as a question — how many 3s in 12? — and let them make the groups. Then count groups, not candies.
1.18 ÷ 6 =3
2.12 ÷ 4 =3
3.21 ÷ 3 =7
4.15 ÷ 5 =3
5.10 ÷ 2 =5
6.16 ÷ 4 =4
What is on this sheet
A child who only ever meets division as sharing gets stuck the day the divisor stops being a number of people — you cannot share between 0.2 of a person, but you can ask how many 0.2s fit in 8.4. That second meaning is what every later sheet leans on: chunking is repeated subtraction, the number line’s jumps are the same thing drawn, and dividing by a decimal is a grouping question or it is nothing. So this page names the second story with the same numbers as the first, and says out loud that both are dividing.
Four of the six problems are counters in a plain row with no rings drawn, because drawing the rings is the exercise; the last two are a blank number line, for a child to jump back along in the divisor. The answer key gives the number of groups. The lesson before this one is the sharing page, and the one after is the array, which holds both stories in one picture and the two multiplications besides.
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 fact on this page is in The Grid’s division deck, for the week the picture is no longer needed.
