Reply To: Lesson 3 – Proportional Reasoning Is Everywhere! – Discussion

[Diane Hamilton]

One more thought: place value itself requires proportional thinking, and so many students don’t understand this basic principle of our number system because the multiplicative thinking underlying it escapes them. With my grade 3 and 4 students I have them compare objects, to find an object 10 times bigger and another 10 times smaller (What is 10 times smaller than a fridge? Maybe a kitty litter box?). They also measured their height and then shifted over the numbers in the place value boxes (aka moved the decimal point) to find a tenth of their height, then made little cardboard figures we called “tenth of me” figures. All this to help them develop a visceral, embodied understanding of 10 times more/10 times less.

[Diane Hamilton]

One more thought: place value itself requires proportional thinking, and so many students don’t understand this basic principle of our number system because the multiplicative thinking underlying it escapes them. With my grade 3 and 4 students I have them compare objects, to find an object 10 times bigger and another 10 times smaller (What is 10 times smaller than a fridge? Maybe a kitty litter box?). They also measured their height and then shifted over the numbers in the place value boxes (aka moved the decimal point) to find a tenth of their height, then made little cardboard figures we called “tenth of me” figures. All this to help them develop a visceral, embodied understanding of 10 times more/10 times less.