Using Number Pieces for Work with Decimals

I've written before about Number Pieces - one of my favorite apps!  (It is free - I hope you give it a try!)  While there are obvious connections to the primary grades for this app, how might you use it in the intermediate grades?

One possibility is for addition and subtraction of decimals.  Using base-10 blocks for decimals is a shift for students.  Since early school experiences, many students have thought of the unit (or small cube) as "one".  Before using base-10 blocks with decimals, it is important to give students opportunities to explore changing the meaning of "one".  If "one" is the long/rod, what does the unit cube represent?  If "one" is the flat, what does the long/rod represent?

After students have a chance to explore these relationships, the base-10 blocks can be a useful tool.  For example, in the problem "Mary bought 9 pens.  Each pen cost $0.35.  How much did Mary spend on the pens?" students might use repeated addition to solve the problem.  They might set up the problem to show that the flat will represent $1.00 and 3 tenths and 5 hundredths represent the cost of one pen.

Then students might draw 9 representations of 3 tenths and 5 hundredths to show the 9 pens.  They can show the repeated addition as 0.35 x 9.

If you use the "lasso" tool, you can group all of the blocks together and then click the "join" button.  This will group the tenths into ones, as well as the hundredths into tenths.

Using the "lasso" again, the app will join the tenths into ones.  The student can then see that 0.35 x 9 is equal to 3.15.

This app provides students with a tool to visualize joining situations (and separating situations if you use the different colors) with decimals.  This can be an engaging tool for students and help students create mental representations of the problems they are solving!