PLACE VALUE 49 50 51 52 – TENTHS & HUNDREDTHS (OLD PV20F11 & PV21F12)

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Once students can describe additive place value of two- and three-digit numbers flexibly, there is no new learning in additive Place Value. Students are continually building on this understanding to higher and more complex numbers, including whole numbers with more digits, decimals and fractions, which students begin to investigate multiplicatively.
Multiplicative place value starts with whole numbers, as students demonstrate and explain that we are multiplying and dividing by 10 to get the values of the places to the right and left.
After students have demonstrated and explained multiplicative relationships between fractions, they apply this understanding to divide 1 by 10 to get a tenth. They apply their understanding that fractions are named by their relationship to 1, to divide a tenth by 10 to get a hundredth of 1.
Explicitly teaching and investigating multiplicative place value with metric measurement makes decimals visible.
It makes sense to teach fractions, then fractions in place value, then fractions in metric measurement, because fractions have been around for more than 3000 years, place value for about 1500 years, decimals for about 300 years, and the metric system for about 300 years – and they are all based on the same conceptual understanding!