To strengthen and deepen knowledge and understanding of arithmetic, how it is used to solve a wide variety of problems,
and how it leads to algebra. In particular, to strengthen the understanding of and the ability to explain why various
procedures from arithmetic work. 
To strengthen the ability to communicate clearly about mathematics, both orally and in writing. 
To promote the exploration and explanation of mathematical phenomena. 
To show that many problems can be solved in a variety of ways.

Problem-solving: Polya's principles.
Numbers: The natural numbers, the whole numbers, the rational numbers, and the real numbers. The decimal system and place value. Scientific notation and powers. Why the standard algorithms for adding and subtracting whole numbers work. Fractions. Percent. Properties of arithmetic. Use of properties in mental arithmetic.
Multiplication: The meaning of multiplication. The grouping, array, area, and tree diagram models for multiplication,
including an introduction to applications in probability. The distributive property, the commutative and associative
properties of multiplication, and their relationships to areas of rectangles and volumes of boxes. Why the standard procedure for multiplying whole numbers works. Why the procedure for multiplying fractions works.
Division: The meaning of division. Why dividing by zero is undefined. Understanding measurement conversions. Why the
standard longhand procedure for dividing whole numbers works. Why the procedure for dividing fractions works. Ratio and proportion and applications, including the Consumer Price Index. Divisibility tests.
How arithmetic leads to algebra.