Car number plates


The purpose of this activity is to engage students in applying place value and combinations to work out the number of possible number plates.

Achievement Objectives
NA4-1: Use a range of multiplicative strategies when operating on whole numbers.
NA4-6: Know the relative size and place value structure of positive and negative integers and decimals to three places.
Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.


In New Zealand each car has an individual number plate so it can be identified.

Number plates were first introduced in 1964 using a system with two letters of the alphabet and four digits.

In 2001 Transport New Zealand ran out of combinations when ZZ9999 was issued. A new system began using three letters and three digits.

How many plates were possible under the old system and how many are possible under the new system?

In New Zealand the number of new plates issued each year keeps increasing. Let’s say that about 250 000 new plates are issued each year.

How long will the new system last?

What would be an option for a next "new system"? 

The procedural approach (show more)

  • The student uses a listing system leading to multiplication, to work out how many plates are possible.

The conceptual approach (show more)

  • The student uses multiplication to calculate the number of possible plates without any need for listing.

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