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What is division? A first lesson in sharing

The first division sheet in the shop is a lesson, not a drill: the idea in a child’s words, a picture of 12 counters already dealt into 3 rings, the sum worked step by step, and six problems to try with the same picture beside each. Nothing to choose before it prints.

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Division is sharing

NameDate/ 6

Read the box and count the rings. Then try the six below.

Dividing is sharing out fairly

12 ÷ 3 means 12 things shared between 3. The answer is how many each one gets. Think of dealing cards: one for you, one for you, one for you, and round again until they are all gone.

3 rings · 4 in each

12 ÷ 3, step by step

  1. 1.12 candies. 3 children. Draw 3 rings.
  2. 2.Give one to each ring. Again. Again. Again.
  3. 3.Nothing left. Count one ring: 4.
  4. 4.12 shared between 3 is 4 each.
  1. 12 shared between 3 is 4 each
  2. 12 ÷ 3 =4
  3. 3 × 4 =12

For the grown-up: get 12 real things out and deal them into 3 piles, one at a time, like cards. When they are gone, count one pile — that is the answer.

  1. 1.20 ÷ 5 =
  2. 2.15 ÷ 3 =
  3. 3.24 ÷ 4 =
  4. 4.12 ÷ 4 =
  5. 5.8 ÷ 2 =
  6. 6.18 ÷ 3 =
Free printables and learning gamesschoolskills.app#1

Division is sharing

NameDate/ 6

Read the box and count the rings. Then try the six below.

Dividing is sharing out fairly

12 ÷ 3 means 12 things shared between 3. The answer is how many each one gets. Think of dealing cards: one for you, one for you, one for you, and round again until they are all gone.

3 rings · 4 in each

12 ÷ 3, step by step

  1. 1.12 candies. 3 children. Draw 3 rings.
  2. 2.Give one to each ring. Again. Again. Again.
  3. 3.Nothing left. Count one ring: 4.
  4. 4.12 shared between 3 is 4 each.
  1. 12 shared between 3 is 4 each
  2. 12 ÷ 3 =4
  3. 3 × 4 =12

For the grown-up: get 12 real things out and deal them into 3 piles, one at a time, like cards. When they are gone, count one pile — that is the answer.

  1. 1.20 ÷ 5 =4
  2. 2.15 ÷ 3 =5
  3. 3.24 ÷ 4 =6
  4. 4.12 ÷ 4 =3
  5. 5.8 ÷ 2 =4
  6. 6.18 ÷ 3 =6
Free printables and learning gamesAnswer keyschoolskills.app#1

What is on this sheet

Sharing comes first because it is the meaning of division children arrive at school already holding: a five-year-old can deal candies out fairly long before anyone shows them a ÷ sign, and the research this page follows found sharing to be the one model of division most children carry all the way into middle school. So the page starts there — one for you, one for you, one for you — and the counters are drawn already dealt into as many rings as there are children, because that is the picture children read most easily: the rings are the children, and the count in one ring is the answer.

The sentence is written three ways under the picture — 12 shared between 3 is 4 each, 12 ÷ 3 = 4, 3 × 4 = 12 — so the sign is tied to the story and to the times table from the first page, and the total is always the first number written. The next lesson, division as making groups, uses the same 12 ÷ 3 to tell the other story; the two pages are meant to be read a day or two apart, and the drill sheets after them are for the week the picture is no longer needed.

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 deals division as a deck of its own, for later: once a child no longer needs the rings, the same facts are there to race.

Every table this sheet uses

One page each, with the full table on it and something true about that number rather than filler.

Every math sheet

42 topics, each one a page like this one — the sheet, its answer key, and no account to print either.

Adding and taking away

The facts underneath everything else, and the columns after them.

Times tables

Multiplication and division, from the twelve tables to the bracket.

Parts of a number

Fractions, decimals, percentages and money — one idea, four ways.

Measuring the world

Clocks, units and shapes: the math that is about something.

Numbers, algebra and data

Signs, letters standing for numbers, and what a set is doing.