You cannot share between 0.2 of a person, but you can ask how many 0.2s make 8.4 — and that question has the same answer as how many 2s make 84. The lesson scales both numbers by ten, works 84 ÷ 2, checks that 42 × 0.2 is 8.4, and says why the answer came out bigger than the number you started with. Six to try follow, two of them needing a hundred rather than ten.
Read the box. Then try the six below: rewrite each one with a whole-number divisor on the first line, and put the answer on the second.
You can’t share between 0.2 of a person
But you can ask: how many 0.2s make 8.4? Think of ribbon. How many 0.2 m pieces can you cut from 8.4 m? Ask it in centimeters — how many 20 cm pieces from 840 cm — and it is the same question with easier numbers. Scale both numbers up by the same amount until the divisor is whole. The answer does not change.
One piece is 0.2. How many make 1? 5
8.4 ÷ 0.2 =42
8.4 ÷ 0.2, step by step
1.Make the divisor whole: 0.2 × 10 = 2.
2.Do exactly the same to the other number: 8.4 × 10 = 84.
3.Now it is 84 ÷ 2 = 42.
4.Check: 42 × 0.2 = 8.4. And 42 is bigger than 8.4 — dividing by less than one makes the answer bigger, because you are asking how many small pieces fit.
Written in one line
8.4 ÷ 0.2 = 84 ÷ 2 = 42. The same value with easier numbers, the way 1/2 is 5/10.
For the grown-up: say it as ‘how many 0.2s make 8.4?’ It is a grouping question, so a big answer is the right kind of answer.
Dividing by a decimal
NameDate/ 6
Read the box. Then try the six below: rewrite each one with a whole-number divisor on the first line, and put the answer on the second.
1.1.44 ÷ 0.12
2.4.8 ÷ 0.4
3.3.6 ÷ 0.04
4.7.5 ÷ 0.5
5.6.3 ÷ 0.7
6.9.6 ÷ 0.3
Dividing by a decimal
NameDate/ 6
Read the box. Then try the six below: rewrite each one with a whole-number divisor on the first line, and put the answer on the second.
1.1.44 ÷ 0.12× 100 both: 144 ÷ 1212
2.4.8 ÷ 0.4× 10 both: 48 ÷ 412
3.3.6 ÷ 0.04× 100 both: 360 ÷ 490
4.7.5 ÷ 0.5× 10 both: 75 ÷ 515
5.6.3 ÷ 0.7× 10 both: 63 ÷ 79
6.9.6 ÷ 0.3× 10 both: 96 ÷ 332
What is on this sheet
This is the page where division stops making things smaller, and it says so out loud. Every child arrives with the belief that dividing shrinks a number, because it always has; 8.4 ÷ 0.2 = 42 breaks it, and a child who is not told why concludes the sum is wrong. It is a grouping question — how many small pieces fit — so a big answer is the right kind of answer, and the fraction bar at the top shows five 0.2s in a single one before the sum is attempted.
The six to try are written along a line with two ruled lines under each, not in a bracket: the first line is for the rewritten sum, the second for the answer. Scaling only one of the two numbers is the mistake this shape catches, since the rewrite has to be written down before it is divided, and the answer key shows both lines. Four are scaled by ten and two by a hundred, so the multiplier is a thing to decide rather than a number to remember. The problems run on to a second page.
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 whole-number division each one turns into is, in The Grid.
