Thursday, November 3, 2016

Decimals to Fractions!

After working our way through Mystery of the Meter, a Cathy Fosnot context for learning, students are working with base-ten blocks, Cuisenaire rods, and area models to make sense of decimals.

Students were provided with a series of problems and through analysis, problem-solving and talk, were able to further develop their understanding of decimals and multiplication.

Up until now, students have believed that when we "multiply" the numbers get bigger. However, this does not hold true when we multiply decimals.  Another big takeaway is that we can operate with whole numbers and then place the decimals where it would be reasonable.

It was a huge day in math today!

After a variety of "tests" to see if we can multiply decimals like we add decimals, students were able to make some sturdy generalizations. And let me say, we tried many problems when "bringing down the decimal" worked-- just like it did when we were doing addition with decimals. But there were always some counter examples that we had to test, retest, reflect, and analyze with other problems.  

We were able to see that when we multiply a decimal with another decimal, we are creating a smaller value. We observed that there is a relationship with the number of places after the decimal and the place of the value in the product. 

     We continued to work with decimals as fractions. We discovered that, unlike adding fractions, when we multiply fractions we multiply the numerators but have to also multiply the denominators!  Whew! So many great connections today. Too many to jot down here! I can say with joy that many students had many "aha" moments today!