Ratio Challenge
This task involves pairs playing two related games. In the first game all the total amounts are equal.
It introduces the students into the rules of the game. In the second game the amounts are varied
and the game requires more complex strategy.
Mathematical Focus
Ratio
MA4-1WM A student communicates and connects mathematical ideas using appropriate
terminology, diagrams and symbols
MA4-2WM A student applies appropriate mathematical techniques to solve problems
MA4-3WM A student recognises and explains mathematical relationships using reasoning
This activity would be sequenced after students have learnt to divide an amount in a given
ratio. In the game each student will have one share of an amount of money. The game aims
to teach students that it is not the size of their number in the ratio that affects their amount,
but the size of their number relative to the other share.
The language of ratio is problematic for many students. Emphasise the terms share, part and
total amount.
Incidental connected content in context:
Chance
Groundwork
Game cards. Students compete in pairs. Each player needs a set of 6 playing cards labelled 1,
1, 2, 2, 3 and 4.
Each pair needs playing board #1 for the task 1, and playing board #2 for the task 2. The
amounts of money are all intentionally multiples of $210. This makes the calculations easier
with all the possible variations of ratios.
10 small balls of Blu-Tack per pair helps in preventing the cards from being knocked off the
playing board.
Timing 60-90 minutes
Task Part 1
Version 1 of the game board lists five amounts of $210. The players decide which order they will play
their game cards. They place them face down with the first card on the top of their pile.
Playing board #1 only requires students to use five of their six cards. They decide which one not to
use, but they are not to tell their opponent.
Each player turns over their top card. Player 1 places their card to the left of the ratio colon in the
top row of playing board #1. Player 2 places their card to the right of the ratio colon in the top row.
Players calculate their share of the $210 and record it on the playing board.
This is repeated for every row. When all five rows are complete the students total their shares.
In the example below Player 2 narrowly wins.
Reflection 1
Questions
Is it possible for a pair to draw?
When the two shares from players 1 and players 2 are added, what is the total? Why does
every pair in the class have the same total of $1050?
What is the minimum amount needed to win?
Once one player has calculated their share, is there an efficient strategy to calculate the
second player’s share? (Subtract the first players total from $1050.)
Did this game rely on strategy or was it just chance?
Task Part 2
Show the students playing board #2. Ask them how the game has been changed. If their only
suggestion is that there are different amounts, ask them what effect this will have.
Set the students to play using playing board #2.
Reflection 2
If the students were finding calculating their shares difficult then this may be a focus for
discussion.
Did some students use a different strategy to the first game? Why?
It would be beneficial for students to explain efficient strategies for playing board #2 using
appropriate mathematical terminology. Have student pairs list successful strategies and
explain why they work. These strategies can then be shared and summarised as a class.
Options
Use different amounts of money or different ratio parts, to make the calculations more difficult and
provide the necessity of rounding. Perhaps expect students round to the nearest five cents.