A Close Game


The purpose of this activity is to engage students in using operations on whole numbers to investigate a given context.

Achievement Objectives
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
NA3-7: Generalise the properties of addition and subtraction with whole numbers.
Description of Mathematics

The background knowledge and skills that should be established before and/or during this activity are outlined in the diagram below:

Click to show example questions for each heading

This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.


In the third Bledisloe Cup match between Australia and the All Blacks, in 2014, the game was won by just one point.

  1. The table below shows the number of tries, conversions and penalties each team scored and the number of points each is worth. Use the table to work out which team won the game.
  2. Before 1992, a try was only worth 4 points. If the value of a try was never changed to 5 points, would the same team have won the game?
  3. The earliest scoring system for rugby was just 1 point for a try, 2 for a conversion and 3 for a penalty. If rugby scoring had remained as this original system, who would have won the game?
  Tries Conversions Penalties
Points for each 5 2 3
Australia 3 2 3
New Zealand 4 3 1

The procedural approach  (show more)

  • The student is able to use operations on whole numbers, to find an unknown.

The conceptual approach  (show more)

  • The student is able to use mathematical strategies to find an unknown.
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Level Three