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• Handshakes • • • • •
At o party, each guest shakes hands with everyone else.
If there ore 2 guests, there wilt be one handshake
~ AB
Ao----__, B -
AB means 'A and B shake hands'.
If there ore 3 guests, there will be three handshakes.
~-1 A~C~
Practical: copy and complete the
handshake diagram:
l};I Copy and complete this Decide how to use your calculator to help you complete
B AB handshake diagram these equations without using the II key.
for 4 people. a1f69= b-{289= c-f'41=
AC
A $ C--• AD [3J Drow diagrams to show the number of handshakes for: d ~ = e 1576= f ..JTOOOo =
a 5 people
b 6 people.
BC
BO rIJ • Without drawing diagrams, how many handshakes far: ww@ITJ~g .__I _t6__,9. I II .__I _1__,1.1
a 7 people b 1 O people c 11 people?
D CD • How do you know? @] Make up several more equations like this. -{f6 X -{f6 = 4 X 4 = 16
Use only 2 different numbers
[i) • How many handshakes will each person make if there ore:
for each equation.
a 5 people b 9 people c 32 people?
• Copy and continue this table CHALLENGE
for up to 12 people.
Practical: draw diagrams to show • Write all the numbers to 20 using more than one
square root each time.
similar relationships to [I]. •You con make 5 like this. ,j36 - F + -{4 = 5
Now try RM29.
a B
AB BC CD
A C _ __,•- AC BO CE
AD BE DE
AE
a 21 Open: write about other Open: write about a q b 100 c 81
E D square numbers in other square roots in
b 45
b B c 55 different ways. different ways.
A~~ The number of different ~
AB BC CD DE EF
AC BO CE OF
F~D AD BE CF handshakes is a triangular number, a 13 b 17 c 21 e 24 f 100
AE BF
so for 7 the answer will be
AF 7+6+5+4+3+2+1=21.
E
Open: make up more equations multiplying square roots.

Challenge
a 4 b 8 c 31
Open: write all the numbers to 20 using more than one square root each time.
Number of people 1 2 3 4 5 6 7 8 q 10 11 12 Possible answers:
Number of handshakes 0 1 2 3 4 5 6 7 8 q 10 11 yq - 4 = 1 '136 - \ 16 = 2 ~25 - \14 = 3 '14 + '14 = 4 '14 + '\fq = 5
1
made by each person \ 81- \ q=6 ~ 16+ ~q=7 \ 100 - '14 = 8 ~ 16 + '125 = q '1 16 + \1 16 +.../ 4 = 10
\125 + \136 = 11 \136 + \136 = 12 \125 + \ 64 = 13 .Y 100 + '\/ 16 = 14 '181+ '136=15
Total handshakes 0 1 3 6 10 15 21 28 36 45 55 66
\ 400- \ 16= 16 '181+ \ 64=17 '-1 100 + \ 64 = 18 \ 4q + ~ 144 = 1q '1100 + '1100 = 20