Math
Developing Number Sense/Place Value
What is number sense?
“…a person’s general understanding of number and operations along with the ability to use this understanding in flexible ways to make mathematical judgments and to develop useful strategies for solving complex problems” (Burton, 1993; Reys, 1991)
—from NCTM’s Illuminations website
Professor Jo Boaler from Stanford University explains number sense well in this video. https://vimeo.com/186323926
Using Concrete Tools to Round Numbers
Convince me that 1 678 rounded to the nearest ten is 1 680. This student built the number and could tell that you would only have to add two more to get to 1 680. It would not round to 1 670 because it is eight away.
Showing 1 678 rounded to the nearest ten is 1 680. This student made a number line with benchmarks.
What is 4 782 rounded to the nearest thousand? This number line uses benchmarks to help place 4 782 between its closest thousands and show that it's closest to 5 000.
IMG_4861.MOVIn this video I use an open number line to prove 4 782 rounded to the nearest ten is 4 780.
678 rounded to the nearest hundred is 700 - an open number line proves this.
These students explain their thinking using an open number line.
5 678 rounded to the nearest ten is 5 680 - proof on an open number line.
Modeling Numbers in Flexible Ways
Click on the screen to open it up. It's printable too for extra practice. There's also a blank one to practice other numbers.
This is a video that goes along with the place mat on the left explaining how to model numbers flexibly. **Note as I explain model #3 I made an error. The model is correct, just not my explanation. Side effect of working late at night!