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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