#### PLACE VALUE CONCEPT SEQUENCE

This concept is broken into additive concepts and multiplicative concepts. We start our mathematical reasoning using additive thinking and then develop our understanding and capacity to think multiplicatively.
ADDITIVE PLACE VALUE CONCEPTS (standard and non-standard place value of whole numbers to three-digits, partitioning, friends of 10) ARE THE FOCUS IN KINDERGARTEN (informally), YEAR 1, and YEAR 2. Thinking additively about Place Value means we are adding the values together to get the number.
MULTIPLICATIVE PLACE VALUE CONCEPTS (we continue thinking additively – standard and non-standard place value of whole numbers from four-digits and decimals, and begin to think multiplicatively – multiplicative place value of whole numbers and decimals) ARE THE FOCUS IN YEAR 3, YEAR 4, YEAR 5, and YEAR 6. Thinking multiplicatively about Place Value means we are multiplying or dividing each place by 10 to get the value of the place to left or right.
All sequences at A Learning Place A teaching Place have both an empirical and logical basis. The empirical basis means all later levels are both harder than and also include lower levels. The logical basis means that specific earlier levels are prerequisites for specif later levels. Concepts with a logical basis are in the left hand column to allow for easy differentiation. 