1. Understanding
1.1. Make connections
1.1.1. Related concepts
1.1.2. Develop new ideas
1.2. Build robust knowledge
1.2.1. Adaptable mathematical knowledge
1.2.2. Transferable mathematical knowledge
1.3. Develop understanding
1.3.1. Whys
1.3.2. Hows
1.4. Build understanding
1.4.1. Connect related ideas
1.4.2. Represent concepts in different ways
1.4.3. Identify commonalities & differences
1.4.4. Able to describe their thinking mathematically
1.4.5. Able to interpret mathematical information
2. Problem-Solving
2.1. Develop ability
2.1.1. Make choices
2.1.2. Interpret
2.1.3. Formulate
2.1.4. Model
2.1.5. Investigate problem situations
2.1.6. Communicate solutions effectively
2.2. Formulate/solve problems
2.2.1. Use mathematics to represent unfamilar or meaningful situations
2.2.2. Design investigations & plan their approaches
2.2.3. Apply existing strategies to seek solutions
2.2.4. Verify their answers are reasonable
3. Reasoning
3.1. Develop capacity for logical thoughts & actions
3.1.1. By analyzing
3.1.2. By proving
3.1.3. By evaluating
3.1.4. By explaining
3.1.5. By inferring
3.1.6. By justifying
3.1.7. By generalising
3.2. Reason mathematically
3.2.1. Explain their thinking
3.2.2. Deduce/justify strategies used and conclusion reached
3.2.3. Adapt to the known and unknown
3.2.4. Transfer learning from one context to another
3.2.5. Prove something is true or false
3.2.6. Compare/contrast related ideas and explain their reasoning
4. Fluency
4.1. Develop skills
4.1.1. Choosing appropriate procedures
4.1.2. Carrying out procedures
4.1.2.1. Flexibly
4.1.2.2. Accurately
4.1.2.3. Efficiently
4.1.2.4. Appropriately
4.1.3. Recall factual knowledge
4.1.4. Recall concepts
4.2. Students are fluent
4.2.1. Calculate answers efficiently
4.2.2. Recognize ways of answering questions
4.2.3. Choose appropriate methods
4.2.4. Make accurate approximations
4.2.5. Recall definitions
4.2.6. Use facts regularly
4.2.7. Find solutions
4.2.7.1. By manipulating expressions
4.2.7.2. By manipulating equations