RIC-0563 Developing algebraic thinking

LOCKER NUMBERS
Teachers notes
Locker numbers 2
Problem 1
Problem 2
Problem 3
Problem 4
For Problem 1, if the locker number is xyz, then:
y = 2z
x = 2y = 2(2z) = 4z
Since z ≠ 0 (otherwise x, y = 0), z = 1 or 2.
Other values of z will make x or y a 2-digit number.
If z = 1, then y = 2, and x = 4.
The locker number is 421.
If z = 2, then y = 4 and x = 8.
The locker number is 842.
For Problem 2, if the locker number is xyz, then:
y = x + z
With xyz > 700, x = 7 or 8. If x = 7, then z = 1 and y = 8, or z = 2 and y =
9.
The locker numbers are 781 or 792.
If x = 8, then z = 1 and y = 9.
The locker number is 891.
For Problem 3, if the locker number is xyz, then:
z = 3, 6 or 9 y = x – 6
Since y must be non-negative, the only possible values for x are 6, 7, 8
or 9.
If x = 9, then y = 3 and z = 6.
If x = 8, then y = 2 and z = 6.
If x = 7, then y = 1 and z = 6.
If x = 6, then z = 6.
The locker numbers are 936, 826 and 716.
For Problem 4, if the locker number is xyz, then:
x = y + 3 y = z + 3 so x = y + 3 = z + 3 + 3 = z + 6
Since x + y + z is odd, z = 1 or 3.
If z = 1, then y = 4 and x = 7.
The locker number is 741.
If z = 3, then y = 6 and x = 9.
The locker number is 963.
62 DEVELOPING ALGEBRAIC THINKING www.ricgroup.com.au R.I.C. Publications ®
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