Quantity and Magnitude - Physical reality of the mathematics that we model with symbols and the number line (how much, how far, how big, how bright, etc). What exists in time and space (quantity). Relative Size of the quantity (magnitude). Foundational to every lesson. Essential question teachers should be asking themselves: Am I communicating the quantity and magnitude of the math concept?, Numeration - The connection of the quantity to the number world or symbol. It allows us to allocate words and numerals for numbers and sense making of quantity. A code to be cracked (like reading). We must understand the language of the mathematics and mathematical language groups at a rate of 10 in our numeration system. , Equality - The state of being equal in value, A=B. Children need to connect to equality physically, visually, representationally and eventually symbolically. Permeates all of math. Student need to recognize the many ways we can represent equality and inequality. The identity principle needs to be strongly connected to the idea that we are maintaining equality and not changing the value of a term., Base Ten (Power of Ten) - Our number system. This system defines how we build and construct number. We use 0-9 digits to represent all rational numbers. Base ten does not go away and continues to support our mathematical understanding. We need to have students think beyond units and with powers of ten. , Forms of a Number - We represent equal values in many different forms. As mathematicians, we choose the form that works best for us or describes best for us that part of the story. The concept begins in pre-k and continues through trigonometry, physics, etc. We need to develop in students' minds these different systems for evaluating values are interconnected. Forms of a number represent equal values, numbers and mathematical relationships and information. It connects the idea of composing and decomposing numbers and allows a framework for manipulating numbers without changing values., Proportional Reasoning - Explains the relationships between and within the values in a situation. It involves the comparison of numbers within quantities as well as the comparison of numbers between quantities. Begin early as students begin to understand patterns and cost of items to determine a unit rate. Also consider that a percentage is not really a "number". It tells you a ratio per one hundred. Proportional reasoning has a direct correlation to success in higher math. Diagram literacy is essential when building proportional reasoning concepts., Algebraic and Geometric Thinking - How things are related physically, what information can we derive from patterns, how are the numeric patterns and the physical world related? Once internalized, these concepts can be used to investigate both the physical and theoretical universe. Affected by early understanding and underpinning of ideas of equality, quantity, and magnitude. Algebraic and geometric thinking describes, explains, and predicts quantity and magnitude in the real world.,

Components of Number Sense

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