Remember: Divide 72 by the rate for a quick guess at the years to double. It is a close guess, not a promise.
Read and answer
Read the story first, then answer.
Nico and the shortcutNico had a hundred coins growing in a made-up garden. He wondered how long it would take to have two hundred, but counting every year was slow. A garden's rate says how many coins it adds for every hundred, so six new coins for every hundred is a rate of six percent. At twelve percent, Nico counted year by year: 112, then 125, then 140, until after six years he had about 197, nearly 200. Rosa the gardener showed him a shortcut: divide 72 by the rate. Seventy-two divided by twelve is six, so it takes about six years to double, with no counting! The rule is a close guess, not an exact answer. A good guess with a little error is called an approximation. Far from the middle it drifts: at thirty-six percent the rule says two years, but then the garden holds only 185. These rates are made up. Real ones change, and nothing is promised.
1
Six new coins for every hundred coins is a rate of what?
Sixty percentSix percentSix coins
2
Rosa's shortcut: divide by the rate to guess the years to double.
3
Look at the table. At 12 percent the garden doubles in about years.
4
Look at the bars. As the rate gets bigger, what happens to the years to double?
There are fewer yearsThere are more yearsThe years stay the same
5
At 12 percent, Nico's year-by-year count reached about 197 after six years. That is close to 200, but not exactly 200.
TrueFalse
Match, order and fix
6
Join each rate to the years it takes to double.
14 percent
28 percent
318 percent
436 percent
A9 years
B4 years
C2 years
D18 years
7
Working backwards: to double in 9 years, divide 72 by 9. The rate is percent.
8
Number the steps of Rosa's shortcut.
Divide 72 by the rate: 72 ÷ 12
Find the garden's rate (12 percent)
Read it as about 6 years to double
The answer is 6
9
Mo says: the rule of 72 is exact every single time. Is Mo right?
YesNo
10
Tia says: at 9 percent a garden takes 9 years to double, because the rate is 9. What did Tia mix up?
She should have multiplied 72 by 9She should have used the rate as 90She used the rate as the years: 72 ÷ 9 = 8
11
Circle every true sentence about the rule of 72.
It gives a close guess at the years to doubleIt is exact every timeIt works backwards tooIt promises what a real garden will do72 splits evenly many ways, so it is easy to divide
12
At 36 percent the rule says 2 years, but the garden holds only 185. That is coins short of 200.
13
Pick a rate from the bars. Divide 72 by it and write the years to double.
14
Draw a doubling clock for a garden at 12 percent that rings every six years.
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Answer key · Set A
The rule of 72
1Six percent A rate says how many coins a garden adds for every hundred. Six for every hundred is six percent.
272 Seventy-two divided by the rate is a quick guess at the years to double.
36 72 ÷ 12 = 6, so about 6 years to double.
4There are fewer years A bigger rate doubles faster. At 3 percent it takes 24 years, but at 24 percent only 3.
5True The rule says 6 years and the count gives about 197. Close, not exact: that is an approximation.
78 72 ÷ 9 = 8, so a rate of 8 percent doubles in about 9 years.
82, 1, 4, 3 Start with the rate, divide 72 by it, then read the answer as years.
9No The rule is a close guess. At 36 percent it says 2 years, but the garden holds only 185, not 200.
10She used the rate as the years: 72 ÷ 9 = 8 Nine is the rate, not the years. Dividing 72 by 9 gives 8 years.
11It gives a close guess at the years to double, It works backwards too, 72 splits evenly many ways, so it is easy to divide The rule is a close guess that works backwards too, and 72 is easy to split. It promises nothing about a real garden.
1215 200 − 185 = 15, so the shortcut drifts when the rate is far from the middle.
13Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.