1. Copyright ©2015 Creating Inspired Learning

2. A justification is not just the answer to a problem but also includes how you can prove that you have made sense of the problem. Not just how you solved the problem but why it makes sense mathematically.

3. Copyright ©2015 Creating Inspired Learning To generalize means to make a general or broad statement by inferring from specific cases. When we generalize in math we form ideas based on facts and sense making and use those ideas to develop our mathematical understanding. Generalizing also means we take what we know and apply it to other problems. A conjecture is just an idea. A conjecture combined with a justification is a generalization. Often times a generalization affirms an idea with several examples justifying why that idea makes sense.

4. Copyright ©2015 Creating Inspired Learning Math should make sense! When we look for regularity or look for patterns we are attempting to make sense. When we make connections, reflect, think about mistakes and persevere, we are making sense of the math. To makes sense you focus on deep understanding, not just getting the right answer.

5. Copyright ©2015 Creating Inspired Learning Metacognition is when you think about your own thinking process and what you are learning. It is a higher level thinking skill that can help you deepen your understanding. To reflect means to think deeply and carefully.

6. Copyright ©2015 Creating Inspired Learning When you notice patterns or ideas that repeat in a predictable way, you are noticing regularity. There are patterns and regularity in math and it is our job to try and find them. There are some things in math that we know to be true always. This is the structure of mathematics. They are ideas that have been tested and proven time and time again by mathematicians. We can use these structures in mathematics to help us to solve problems. The properties of mathematics are examples of math structure.

7. Copyright ©2015 Creating Inspired Learning We know that there is not just one way to come up with a solution to a problem. There may be only one answer but many different pathways for getting to that answer. We can also have multiple representations or ways of making sense of a problem. Being able to make connections with other math ideas that may be different from your own can help you deepen your own mathematical understanding.

8. Copyright ©2015 Creating Inspired Learning Mistakes help us learn. Becoming a mathematician is all about making mistakes and learning from them. In fact making mistakes and learning form them is part of life. We all make mistakes. Any time you are learning something new, you are bound to make mistakes. No one likes that feeling when you feel stuck or you feel like you failed but the fact is that mistakes can help us to grow if we learn from them.

9. Copyright ©2015 Creating Inspired Learning A representation of something is a picture, symbol or illustration that expresses an idea. We can show our math ideas with pictures, numbers, equations, models, number lines and words. Each one of these examples can be a representation of our math idea.

10. Copyright ©2015 Creating Inspired Learning To persevere means to never give up. To seek more means to never be satisfied with just doing the minimum work. It means that even if you have an answer you consider whether or not you have done your best work and you search for deeper understanding. Persevering is a life skill that will help you to be successful in anything you do in life, not just in math. Any time something becomes difficult have the strength of will to not give up. Learning something new takes grit and determination. If school was easy and you never had to perform a difficult task, you wouldn’t grow, develop or get smarter in any way. Learning to persevere even when something is difficult is what learning is all about.