Finding All Possibilities: 5 Key Skills
In this module we are exploring ways to solve maths problems by finding all possibilities. Below are five key skills that support students to understand and confidently approach such problems. It is important that students can:
- Understand the system and find examples that belong.
- Explain why certain examples don’t belong.
- Explore and develop systems for collecting answers.
- Use criteria to sort and organise examples.
- Complete a set of possibilities and prove why there can be no more.
The Land of Possibilities
For this Maths Quest, students will travel to The Land of Possibilities and visit Ice Cream Island, The Domino District, The Realm of Robots and Tower Territory to discover task cards, digital activities and games, design challenges and extension tasks.
Ice Cream Island is the first stop. Here you and your students will use The Ice Cream Maker to make ice cream and solve problems.
You will use this digital activity in your very first lesson as you try to find how many ice creams you can make with two different flavours. On purpose, you will muddle up your attempt creating duplicate ice creams or ice creams that don’t belong because they don’t have two different flavours. This is the launching point for your students to think about what systems or strategies they can use to systematically find all possibilities.
This destination particularly focuses on understanding systems, finding examples that belong, and exploring and developing systems for collecting answers.
The Domino District is the next destination. If you don’t have sets of dominoes to use, there is a link provided to to pdf to download and print.
The standard set of dominoes goes up to the double six tile. You might like to simplify some of the activities by reducing your set to include dominoes only up to the double four.
This destination includes tasks that particularly focus on finding and explaining why certain examples don’t belong to a set has several introductory activities that require students to complete a set of possibilities and prove why there can be no more.
Some of the later activities are more challenging and might only be appropriate for you more confident and capable students.
The Realm of Robots uses a digital activity called The Robot Workshop. This is an activity where students can build and photograph robots that fit the criteria they have been given.
The introductory challenge is to build as many robots as possible using the given pieces. There are two activity sheets for this task – one with a support guide of a tree diagram and one that is left open for students to design their own system.
The activity can then be adapted to meet different levels of confidence and ability. You can select simple challenges with a smaller number of robot parts and also select more complex challenges where there are prices attached to various parts and students are challenge to create robots worth a particular amount of money, or robots where the heads cost at least $5.
This destination promotes students to understand and use criteria to sort and organise examples that belong to a set.
Tower Territory is the final stop. The is a digital activity here called Block Chooser that supplies students with a selection of three or four blocks, with or without duplicates. There are a range of different challenges for them to complete using the set they are given.
Tower Territory also provides many opportunities for students to design their own problems for partners to solve.
It will be valuable for you students to have access to Unifix Blocks and Snap Blocks as they solve these challenges. The tasks review all of the key skills involved in this module. There are some extension activities, particularly Task 9, for your most capable students.