The gap between Ivy and Ben never closes. It grows every year.
The big ideaA year of waiting leaves a gap that never closes, because it is the biggest year.
How it works
Ivy planted 100 pretend coins today. Ben waited one year, then planted his 100, exactly one year behind.
Both gardens follow the same rule, so Ben's garden is always where Ivy's was a year before.
Ivy always holds one extra year of growth, and the last year is the biggest year. So the gap keeps growing.
Ivy plants now. Ben plants a year later.In year ten, Ivy leads by 23 coins.
Example 1: Ben is always one year behind
After one year, Ivy has 110 and Ben plants his 100.
Both gardens follow one rule.
So Ben's garden is always where Ivy's was a year before.
Example 2: The gap in year five
Ivy holds 160 and Ben holds 146.
160 − 146 = 14
The gap is 14 coins.
Example 3: The gap in year ten
Ivy holds 256 and Ben holds 233.
256 − 233 = 23
The gap grew from ten coins in year one to 23 in year ten.
Example 4: Catching up
Ben could plant 110 coins instead of 100.
110 − 100 = 10
That one year cost ten coins, and then the gardens match every year.
Words to know
gap
How many coins one garden is ahead of the other.
behind
Starting one year later than the other garden.
growth
The new coins a garden adds in a year.
Watch out
The gap does not close by itself. It only grows.
The last year is the biggest year of growth, so being a year behind costs the most.
A year late is not too late. The garden still grows, and starting now beats starting next year.
These gardens are made up. Real ones pay different amounts, and nothing is promised.
Try it
Year 2: Ivy has 121 and Ben has 110. What is the gap?
Year 5: Ivy has 160 and Ben has 146. What is the gap?
Does the gap close by itself if Ben waits?
Ben plants 110 a year late. How do the gardens compare?
Answers: 1. 11 coins · 2. 14 coins · 3. No · 4. The same from then on
Try at homeWith a grown-up, talk about something where starting one year earlier would have mattered, like a skill, a hobby or a habit. Why did that year matter?
For grown-upsTalk about something where starting one year earlier would have mattered, like a skill, a hobby or a habit. Why did that year matter? The numbers here come from a made-up garden, and nothing is promised for any real money.
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