Exploring Algebra with a Function Machine
Looking for inspiring, new maths ideas for your classroom? Our CSER/Maths in Schools Project Officer, Celia Coffa showcases a fun and engaging activity from our free Maths in Schools online course for Year 3-6 students that combines storytelling with mathematics concepts. The goal is to help students understand pattern growth and basic algebraic functions. The activity is introduced through a picture book, "Two of Everything: A Chinese Folktale" retold by Lily Toy Hong. Students identify and predict patterns and learn to understand the concept of doubling and halving.
In the story, Mr. Haktak discovers a magic pot that doubles anything placed inside it. When Mr. Haktak drops a purse with 5 coins into the pot, it becomes two purses, each with 5 coins. This is a great opportunity to talk about how the pot acts like an algebraic function machine, doubling everything that goes inside.
Encourage students to think critically and use their knowledge of doubling as they experiment with using the function machine and annotating their results. You can then extend the activity by introducing them to a reverse function machine to work out the input by beginning with the output. Working backwards through the machine employs the inverse operation. For example, if the output is 8, they divide by 4 to find the input, which would be 2. These activities will highlight the relationship between addition, subtraction, and multiplication and how these functions relate to number patterns.
The full activity is described in more detail in the Scaffolding Algebra module in our free Year 3 – 6 online course.
Enrol in our free, online and self-paced Maths in Schools courses for F-2, Year 3-6 and Year 7-10 for more ideas and inspiration for teaching maths in your classroom.
This initiative is funded by the Australian Government Department of Education and is part of the Maths in Schools: Teaching and Learning Resources to Support Mathematics project.