1. Build an Army: Strength in Numbers
Ordering Fractions ©

2. “Build an Army” is a series of strategy games which can help make a wide range of topics in mathematics more engaging and challenging for all ages and ability levels
The activities can be edited and adapted to suit the needs of your students
This document contains a Build an Army activity, full instructions how to run it in the classroom, as well as lots of suggestions for support and extension activities, which allow for effective differentiation amongst your students

3. Build an Army General Rules
Each student is given a set of playing cards to cut out
They use the set of cards to assemble the strongest set of 10 soldiers they can
Each soldier will then be sent to battle against a solider from a rival army
They must decide what order they are playing your soldiers before they enter battle.
Perhaps glue the cards onto paper or your mathematics book
Or copy out your order onto a separate sheet of paper
The soldier with the highest total wins the battle
The army that wins the most battles, wins the war!

4. Suggested Format – Part 1
Once students have assembled their armies, get them to fill out the Build an Army Strategy Sheet – this encourages them to reflect on the strategies they have chosen and the mathematics they have used
Then send them into battle against each other:
They must decide on the order their soldiers will battle before battle commences
They must then compare their soldiers in the predetermined order to see who would win each battle
Whoever wins the most battles, wins the war
If two soldiers have the same value, it is considered a draw
You may wish to have the students working in groups of 3, with two students battling and one students acting as the referee/adjudicator
When they have finished a series of battles, encourage them to reflect again on what they have learnt and what changes they would make in future.

5. Build an Army Strategy Sheet (1)
Before the Battle
Explain step-by-step and in detail everything you did to arrive at each of your soldiers. Think of it as a recipe for someone to follow.
Try to answer questions like:
What were your first thoughts when putting together your army?
What was the most difficult bit?
What changes did you make as you assembled your army?
What was the easier solider to assemble?
How did you decide on your order?
What maths skills did you use?

6. Build an Army Strategy Sheet (2)
After the Battle
How many games did you win and lose?
What did you notice about the games you lost?
How would you modify your army for future battles?
What have you learnt?

7. Suggested Format – Part 2
After they have battled each other, challenge your students to modify their army to defeat as many soldiers as possible from the Army to Defeat Sheet.
Who in the class can defeat the most soldiers?
Is it possible to defeat them all?
Can you students come up with a new army that is impossible to beat?
When they have finished, get them to reflect on their strategy
Then look at the Ideas for Extension that accompany each activity

8. General Ideas for Simplification
All the Build an Army activities in this series can be modified to make them simpler. Here are a few ideas:
Only have 5 soldiers
Reduce the size of the numbers
Reduce the number of operations
Have some cards that are fixed in position
Have a “Calculator Check” token
Have support resources available, such as class notes, times table grids,
Employ one of your students as a “class expert” who can be on hand to offer advice and support to other students

9. General Ideas for Extension
There are specific ideas for Extension for each activity, but here are some general ideas that can be used with all Build an Army activities in this series:
Change the rules so the smallest total wins each battle
Have a “joker” card that can be anything the students like
Allow students to trade cards with each other
Introduce limitations on the soldiers, such as you can’t have more than 3 soldiers who are only made up of even numbers
What is the biggest/smallest overall total you can make from all 10 soldiers?
What is the biggest/smallest individual total you can make for one solider?
Challenge your students to develop their own Build an Army game

10. Build an Army: Strength in Numbers
Ordering Fractions ©

11. The playing cards…

12. 1 2 3 4 5 6 7 8 9 10 -

13. Ordering Fractions Rules
A soldier consists of a numerator, denominator and a line to divide the two
The solider that has the largest fraction wins the battle
Whoever wins the most of the 10 battles wins the war!
Fractions can be compared in size following simplification, or converted to a decimal/percentage for comparison

14. Example
Strength = or 2.5
Strength = or

15. Ideas for Extension
You cannot use any two fractions that are the same following simplification
You cannot create any fraction that will simplify
You cannot use fractions that have a value greater than 2 (or 1)
Change the rules so the lowest scoring soldier wins
Challenge students to make the highest/lowest scoring total army using all 10 soldiers
You can only use fractions that covert to terminating decimals

16. Your Army to beat…

17. Theirs
Mine
Winner
10 3
  9 5
8 1
7 1
6 1
7 2
5 2
3 2
6 5
4 1