We were given a picture of two boxes of chocolates(like below) and asked which one was more nutty?
These two activities really helped me to come to understand the importance of proportional sense. My future students will likely be making similar mistakes, but having a discussion on these ideas and working through proportions without numbers will be helpful. Introducing students first to proportions and making sense of the relationships between them will get students asking important questions:
- What quantities are being compared?
- What other factors do I have to consider?
- What roles do these variables play/what's their relationship?
- How is it affecting the goal(if it's nuttier or more blue)?
Through this, students can begin to develop a sense of how to compare proportions and what to take into account. Then, when dealing with the numbers and fractions they should to able to reason if the answer they arrive at is a logical one or not. They can rely on asking questions to led them to the correct calculations and hopefully dealing with fractions will not seem as daunting.