Division arrays worksheets: one picture, four facts
An array of 12 dots, three rows of four, with its four facts beside it and the picture read four ways step by step. Then five arrays to try — none of them square — each with two ruled lines for the two divisions it holds, and one fact with no picture at all.
Read the box and the picture. Then write the two divisions each array holds.
One picture, four facts
If you know 3 × 4 = 12, you already know 12 ÷ 4 and 12 ÷ 3. Think of an egg box: rows across and columns down.
3 rows of 4
3 × 4 =12
4 × 3 =12
12 ÷ 3 =4
12 ÷ 4 =3
Read the picture four ways
1.3 rows of 4. Count: 12. So 3 × 4 = 12.
2.Turn the page sideways: 4 rows of 3. Still 12. So 4 × 3 = 12.
3.12 in 3 rows: how many in a row? 4. So 12 ÷ 3 = 4.
4.12 in rows of 4: how many rows? 3. So 12 ÷ 4 = 3.
Think multiplication
12 ÷ 4 = ? Ask: 4 × ? = 12. It is 3.
For the grown-up: cover the answer and ask what times 4 makes 12 — that is all division is asking.
One array, four facts
NameDate/ 6
Read the box and the picture. Then write the two divisions each array holds.
1.Write the two divisions.
2.Write the two divisions.
3.18 ÷ 3 = Think: 3 × ? = 18.
4.Write the two divisions.
5.Write the two divisions.
6.Write the two divisions.
One array, four facts
NameDate/ 6
Read the box and the picture. Then write the two divisions each array holds.
1.Write the two divisions.24 ÷ 4 = 624 ÷ 6 = 4
2.Write the two divisions.18 ÷ 3 = 618 ÷ 6 = 3
3.18 ÷ 3 = 6 Think: 3 × ? = 18.
4.Write the two divisions.20 ÷ 4 = 520 ÷ 5 = 4
5.Write the two divisions.10 ÷ 2 = 510 ÷ 5 = 2
6.Write the two divisions.21 ÷ 3 = 721 ÷ 7 = 3
What is on this sheet
The array is the one picture that holds a multiplication and its two divisions at once, and turning the page a quarter turn is the commutative law: 3 rows of 4 is 4 rows of 3 without moving a dot. That is why it comes third — after sharing and grouping have each been met on their own — and why the page ends on a boxed think-multiplication: 12 ÷ 4 = ? is 4 × ? = 12, and a child who can turn one into the other has the reflex every written method later depends on, because a long division is a column of exactly that question.
None of the arrays to try is square. A 4 by 4 holds only one division, and the exercise is writing two; so the five are 2 by 5, 3 by 6, 4 by 5, 3 by 7 and 4 by 6, with the row and column counts printed in the gutters and the total left for the child to find. The problems run on to a second page: five arrays with two lines under each are more than the room left under the lesson, and the lesson is not cut to make them fit — a parent who wants the lesson alone prints page one.
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
The Grid asks these same facts both ways, times and divide, which is the whole of what an array teaches.
