Mathematical Habits of Mind: Generalize
Generalization in math is the process of finding a pattern in a group of numbers and creating a rule or statement based on that pattern that a process or problem works a certain way. Generalization is important for Algebra, leading students to understand math with deeper understanding and efficiency. Generalization also gives students the ability to simplify some of their thinking, allowing them to move on to learning bigger and better things. Note, it is important to be careful when making generalizations because sometimes we might make a rule without enough evidence or experience to know it will always be true. This is called over-generalizing. It's okay to make mistakes when learning to generalize, but it's important to talk about them and continue to learn and practice.
One example of generalization is in grocery shopping. Imagine that you are a parent who is trying to plan your family's meals for the week and create a grocery list. You might start by looking at your family's past meal plans and analyzing what types of food you typically eat and in what quantities. By finding patterns in your family's food consumption over time, you can create a general rule or statement about what types of food you need to buy in the future. For example, you might generalize that your family eats a certain number of servings of fruits and vegetables per week, or that you go through a certain amount of milk and bread each week. By using this generalization, you can more accurately predict what types of food you need to buy and in what quantities, which can help you save money and time at the grocery store. Generalization can be used to make more informed and efficient decisions.