
Mathematically proficient students:
 1. make sense
 2. reason
 3. model

CA Mathematics Framework
  number sense
  measurement & geometry
  Algebra & functions
  Stats, data analysis, probability
  Mathematic reasoning

Come up with a question that a child has procedural knowledge but not conceptual knowledge.
 give enough detail to explain why they have procedural but not conceptual
 Find the area of the circle. Radius = 3
 Student understands the equation is pi x r squared. They know that pi represents 3.14 and understand that they must multiply by the radius squared. They do not understand where the numbers are coming from.

Anchoring points
 ideas related to new and old information
 ex. numbers  adresses, weight, height, volume

2 subskills you need to know before counting
 1. each object has a name
 2. names have to occur in a certain order

Methods of teaching multiplication
 repeated addition (6 x 3 = 6 + 6 + 6)
 combinations (there are 2 shirts and 3 ties, how many combinations can you make?)
 area (set out counting chips and multiple across and then down)
 lattice multiplication

Methods of teaching division
 partition (how many elements are in a group?)
 If I have a box of chocolate and want to divide them into 3 groups, how many pieces will be in each group?
 measurement (how many groups are there?)
 If I have a box of chocolate and want each person to get 2 pieces, how many people will get chocolate?

4 steps to teachÂ measurement
  identify the attribute
  make comparisons
  use nonstandard units
  use standard units

7 steps to teach geometry
 1. sort shapes
 2. match shapes
 3. make shapes
 4. provide problem solving activities
 5. analyze properties
 6. explore relationships among shapes
 7. prove theories

Quadrilateral
shape with 4 sides

Trapezoid
a quadrilateral with 1 pair of parallel sides

Parallelogram
a trapezoid with 2 pairs of parallel sides

Rectangle
a parallelogram with 1 right angle

Square
a rectangle with adjacent congruent sides

Rhombus
a parallelogram with adjacent congruent sides

Order of shapes
 quadrilateral
 trapezoid
 parallelogram
 rectangle
 square
 rhombus is a parallelogram but can be a square (not always though)

Earliest skill a child develops
 estimation
  if you break a cookie in half and tell a child to pick one, he will pick the bigger half

