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• Turning symmetry • • • • • • 6-spike numbers .
~:t'I.]:t.1'~ Work with a friend if you can. ~:1'IolS1'~
PAGE 54 . PAGE 55

OJ Use 6 beads, a 6-spike abacus and RM 80.
Find and record a number which is:
Challenge
a a 4-digit number with no zeros in it
b a 5-digit number with a zero in the thousands column
1 2043 21 043 4 1 023
c an even number between 40000 and 50000
d the smallest even number 23041 32041 42031
e the smallest 6-digit number 14023 24013 42013
f the largest 5-digit odd number
24031 34021 43021
g the smallest 5-digit number ending in '000'
h the largest 5-digit number ending in '000'. Notice that, since an
odd number is required,
CHALLENGE
the units spike must
have either 1 or 3
Fit these 4 loose spikes on the abacus
IJJ Create and record your own patterns with turning symmetry. in different ways to find twelve 6-digit odd numbers. beads, there must be at
Choose materials to help you . Draw each abacus and write the number it shows. least 1 bead on the ten
thousands spike and the
digits must add up to 10.

rn rn

Open: creating and a Several possibilities such as 3111, 1221, 1113, 1122, etc. but there must be at least one bead on
recording own each of the four spikes at the right hand end of the abacus.
patterns with turning b Several possibilities such as 20211, 10311, 30111 which have no bead on the thousands spike but
symmetry. at least one bead on each of the other four right hand spikes.
c Several possibilities such as 40002, 40020, 40110 which have 4 beads on the ten thousands
spike and either 0 or 2 beads on the units spike to make an even number.
d 6 beads on the units spike.
e 100005, 1 bead on the hundred thousands spike and 5 beads on the units spike.
f 50001, 5 beads on the ten thousands spike and 1 bead on the units spike.
9 15000, 1 bead on the ten thousands spike and 5 beads on the thousands spike.
h 60000.
Notice that in all cases the digits must add up to 6.