Remember: A small fee every year eats more than it looks, because the coins taken stop growing. Ask three things about a fee: how much, how often, and for what.
Read and answer
Read the story first, then answer.
A keeper with a feeOmar and Tess each planted one hundred pretend coins, and both gardens grew the same way, with one new coin for every ten. But Tess's garden had a keeper who charged a fee. A fee is a price for a service, like tending the garden. Each year, the keeper took one coin for every fifty inside. In year one both grew to 110, before the keeper took two, leaving Tess with 108, while Omar had 110. Two coins sounded tiny, but the keeper came back every year. By year five, Omar had 160 and Tess had 146. By year ten it was 256 against 211. By year twenty, Omar had 655 and Tess had 447. Look at the growth alone: Omar's garden grew by 555 coins and Tess's by 347, so the fee ate 208, more than a third of all the growth. The keeper took only 89 coins in all, yet Tess was 208 behind, because coins taken stop growing too.
1
A keeper takes 1 coin for every 50 inside. From a garden of 200 coins, the keeper takes coins.
2
From a garden of 300 coins, the keeper takes coins.
3
In year one both gardens grow to 110. The keeper takes 2 coins from Tess. How many coins does Tess have left?
112108110
4
A fee is a price for a service.
TrueFalse
5
Look at the table. After 10 years, Omar is ahead of Tess by coins.
6
After 20 years, Omar is ahead of Tess by coins.
7
The keeper took only 89 coins in all, yet Tess is 208 behind. Why?
Omar planted more coinsThe keeper took the rest laterCoins taken as a fee stop growing too
8
The keeper takes the fee only once, in the first year.
TrueFalse
Order, match and fix
9
Number the story.
Year twenty: 655 against 447
Year ten: 256 against 211
The keeper takes 2 coins in year one
Omar and Tess plant 100 coins each
10
Join each one to its number.
1Omar's growth in 20 years
2Tess's growth in 20 years
3What the fee ate
4What the keeper took
A89 coins in all
B555 coins
C208 coins
D347 coins
11
Tess says: two coins a year is tiny, so the fee barely matters over twenty years. Is Tess right?
YesNo
12
Circle each question worth asking about a fee.
How much?How often?What color is the keeper's hat?For what?How tall is the garden?
13
Stretch: a smaller fee takes 1 coin for every hundred, and after 20 years that garden holds 547. Where does 547 sit?
Below Tess's 447Above Omar's 655Between Tess's 447 and Omar's 655
14
Write three questions you could ask about any fee.
15
Draw a rabbit nibbling a tree, one bite for each year, to show how a small fee adds up.
Scan the code at the top to mark this sheet on screenTake a photo of your answers or type them. It is marked for you automatically, and your score is kept.
Answer key · Set A
Fees that eat your growth
14 200 holds four fifties, so the keeper takes four coins.
26 300 holds six fifties, so the keeper takes six coins.
3108 110 − 2 = 108. Omar, with no fee, keeps 110.
4True The keeper tends the garden, and the fee is the price for that work.
545 256 − 211 = 45.
6208 655 − 447 = 208.
7Coins taken as a fee stop growing too A coin taken stops growing, so the gap is bigger than the fees.
8False The keeper came back every year, every single year.
94, 3, 2, 1 They plant first, then the keeper takes the first fee, and the years go by: year ten, then year twenty.
101-B, 2-D, 3-C, 4-A 555 − 347 = 208, and the keeper took only 89 coins.
11No Twenty years of bites are not small: the fee ate more than a third of the growth.
12How much?, How often?, For what? Grown-ups ask three things about a fee: how much, how often, and for what.
13Between Tess's 447 and Omar's 655 A smaller fee bites less, so the garden ends in between the two.
14Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.