Remember: A year of waiting leaves a gap that never closes, because the last year is the biggest year. Starting now beats starting next year.
Read and answer
Read the story first, then answer.
Ivy and Ben plant a year apartIvy and Ben each had one hundred pretend coins to plant. Ivy planted hers that day, while Ben watched, his coins in a pouch. "I will plant mine next year," Ben shrugged. "What is one year?" A year went by, and Ivy's garden grew to 110. Only then did Ben plant his hundred, exactly one year behind. Both made-up gardens followed the same rule, so Ben's garden was always where Ivy's had been a year before. In year two, Ivy had 121 and Ben 110, so the gap was eleven, then twelve, thirteen, fourteen, and on up. By year ten, Ivy had 256 and Ben 233: twenty-three apart. The gap never closes, because Ivy always holds one extra year of growth, and the last year is the biggest year. To catch up, Ben could have planted ten extra coins, 110, so the gardens would match every year.
1
Ben planted his hundred coins a year after Ivy planted hers.
TrueFalse
2
Year 2: Ivy has 121 and Ben has 110. The gap is coins.
3
Why is Ben's garden always where Ivy's garden was a year before?
Ben's rule is slowerIvy's rule is fasterBen is one year behind and both gardens follow the same rule
4
Look at the table. In year 4 the gap is coins.
5
Year 5: Ivy holds 160 and Ben holds 146. The gap is coins.
6
At year five the gap is 14. At year ten it is 23. What is true about the gap?
It stays at tenIt keeps getting biggerIt shrinks
7
The gap closes by itself if Ben just waits.
TrueFalse
Order, match and fix
8
Number the story.
Ivy plants her hundred coins
The gap grows every year
Ben plants his hundred coins
A year passes and Ivy has 110
9
Join each one to what it means.
1Ivy
2Ben
3The gap
4Ten extra coins
Aplants a year later
Bwould make Ben level
Cgrows every year
Dplants her hundred first
10
To catch up, Ben could plant 110. That is extra coins.
11
Ben says: a year is small, so waiting costs almost nothing. Is Ben right?
YesNo
12
Circle each true sentence about the gap.
It starts at ten coinsIt never closes by itselfIt is always ten coinsThe last year is the biggest year of growthA year late is too late
13
Stretch: year 10, Ivy holds 256 and Ben holds 233. The gap is coins.
14
In your own words, why does a year of waiting leave a gap that never closes?
15
Draw two gardens side by side, Ivy's taller. Mark the gap between them.
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Answer key · Set A
The cost of waiting a year
1True Ivy planted that day, and Ben planted exactly one year behind.
211 121 − 110 = 11.
3Ben is one year behind and both gardens follow the same rule Both gardens follow one rule, and Ben started a year later.
413 The gap grows: ten, eleven, twelve, thirteen.
514 160 − 146 = 14.
6It keeps getting bigger The gap does not close by itself. It only grows.
7False Ivy always holds one extra year of growth, so the gap never closes by itself.
81, 4, 3, 2 Ivy planted first, a year went by, then Ben planted, and the gap kept growing.
91-D, 2-A, 3-C, 4-B Planting 110 instead of 100 would make Ben's garden match Ivy's every year.
1010 110 − 100 = 10, so one year of waiting costs ten coins.
11No The gap starts at ten coins and grows to twenty-three by year ten.
12It starts at ten coins, It never closes by itself, The last year is the biggest year of growth The gap starts at ten and grows, and the last year is the biggest. A year late is not too late: the garden still grows.
1323 256 − 233 = 23.
14Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.