ArticlePDF Available

Investigations: Treehouse Series

Authors:
INVESTIGATIONS
THE MATHEMATICAL
ASSOCIATION OF VICTORIA
PRIME NUMBER: VOLUME 35, NUMBER 4. 2020
© The Mathematical Association of Victoria
$QG\*ULI¿WKVDQG7HUU\'HQWRQV7UHHKRXVHVHULHVLVSRSXODUZLWKSULPDU\VFKRROFKLOGUHQ7KHIROORZLQJLQYHVWLJDWLRQVGUDZ
IURPWKH¿UVWERRNThe 13-Storey Treehouse.
TREEHOUSE SERIES MATHS PROBLEMS
James Russo, Monash University and Toby Russo, Spensley Street Primary School
,I\RX¶UHDIDQRIWKH7UHHKRXVHVHULHVWKLQNDERXWVRPHRWKHUPDWKVSUREOHPVIDFLQJ$QG\7HUU\DQG-LOORQWKHLUDGYHQWXUHV
+RZPDQ\FRPELQDWLRQVRIÀDYRXUVFRXOGWKHUHEHDWWKHLFHFUHDPSDUORXUZLWKÀDYRXUV":KDWDERXW$QG\¶V9HU\%DG
7HDFKHUZKRGLGQ¶WNQRZKRZWRFRXQW"<RXPD\ZDQWWRVKDUH\RXULGHDVZLWKXVDWSULPHQXPEHU#PDYYLFHGXDX
In the secret
underground
laboratory,
7HUU\XVHV
his enlarger
RQDEDQDQD
Imagine it’s
just a regular
VL]HEDQDQD
to begin with,
but ends up the
same height
DV7HUU\+RZ
many times
bigger did the enlarger make the banana?
<RXZLOOQHHGWRHVWLPDWHWKHOHQJWKRI
DQDYHUDJHEDQDQDDQG7HUU\¶VKHLJKWWR
ZRUNRXWWKHSRZHURIWKHUD\
Hint: Use your handspan to estimate
WKHOHQJWKRIDEDQDQD0HDVXUH\RXU
outstretched hand from the tip of your
¿QJHUWRWKHWLSRI\RXUWKXPE1RZ
DVVXPH7HUU\LVDERXW\RXUKHLJKW+RZ
much has the banana grown?
EXTENSION
+RZPXFKPRUHEDQDQDLVWKHUHQRZ"
,ILWZHLJKHGJUDPVEHIRUHLWZDV
enlarged, how much does it weigh now
DQGKRZPDQ\NLGVFRXOGKDYHLWIRUD
snack?
THE GIANT
BANANA
GROWING
SEA MONKEY
Once the sea monkey had eaten all the
VHDPRQNH\JURZWKIRRGDQGDOOWKH
RWKHUVHDPRQNH\VLWEHJDQWRJURZ
TXLFNO\:LWKLQDIHZVHFRQGVLWGRXEOHG
LQVL]H7KHQLWGRXEOHGDJDLQ7REHJLQ
WKHVHDPRQNH\ZDVWHHQ\RQO\FP
ZLGH+RZORQJGLGLWWDNHWR¿OOXSWKH
jar? Growing at this rate, how long until
LWZDVDKXPDQVL]HGPHUPDLGFDOOHG
0HUPDLGLD"
Hint:,PDJLQHLWGRXEOHGLQVL]HHYHU\
VHFRQGV'UDZDWDEOHWRVKRZKRZELJLW
ZDVDIWHUVHFRQGVDQGVHFRQGV
EXTENSION
Imagine the sea-monkey didn’t stop
JURZLQJ«KRZORQJXQWLOLWZDVWKHVL]H
RIDQHOHSKDQW"+RZORQJXQWLOLWZDVDV
ELJDV
THOUSAND-STOREY TREEHOUSE
$QG\DQG7HUU\VWDUWHGZLWK7KH6WRUH\7UHHKRXVHIROORZHGE\7KH6WRUH\
7UHHKRXVHDQGLQUHOHDVHG7KH6WRUH\7UHHKRXVH:KLFKERRNQXPEHU
are they up to? What do you think the title of their next book will be? What about
WKHWKERRNLQWKHLUVHULHV",PDJLQH$QG\DQG7HUU\FRQWLQXHWRUHOHDVHERRNV
XQWLOWKH\DUHVRROGWKHLUEUDLQVDUHOLYLQJLQVLGHURERWVZKDWERRNGR\RXWKLQN
WKH\ZRXOGUHOHDVHLQ"
MERMAIDIA THE
SEA MONSTER
/XFNLO\7HUU\SXWKLVHQODUJHULQUHYHUVH
DQGEODVWHG0HUPDLGLDWKHVHDPRQVWHU
6KHEHJDQWRVKULQNXQWLOVKHZDVMXVW
WKHVL]HRIDMHOO\EHDQ,IWKHIHURFLRXV
0HUPDLGLDZDVPORQJKRZSRZHUIXO
was the ray when in shrink mode?
Hint:0HUPDLGLDLVWKHVL]HRIDMHOO\
EHDQDIWHUEHLQJ]DSSHG/HW¶VVD\DMHOO\
EHDQLVFPORQJ
EXTENSION
,PDJLQH\RXXVHG7HUU\VUD\RQGLIIHUHQW
WKLQJVDWVFKRRO:KDWLVWKHODUJHVWWKLQJ
you could shrink at school that would be
VPDOOHQRXJKWR¿WLQ\RXUSRFNHWDIWHU
\RX]DSSHGLW":KDWLVWKHVPDOOHVWWKLQJ
you could shrink at school that would
still be big enough to see with the naked
eye afterwards?
ResearchGate has not been able to resolve any citations for this publication.
ResearchGate has not been able to resolve any references for this publication.