Extending Decimals with a Little Bit of That!

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We are beginning a new study on decimals.  Today, I focused on some misconceptions and wanted to see my student's thinking about decimals.  I found a set of decimal talking points and chose to use a few of them in a Kahoot Discussion.  The points I used were:

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This Kahoot was different from our usual game.  This time, as I posed each talking point, students had to WRITE whether they agreed, disagreed, or were unsure and explain why.  When the time was up, our choices showed up as a graph and we took a few minutes with each point to discuss our thoughts.

The first Talking Point was meant to see if students understood comparing decimals.  I wanted to know if they realized that .35 is actually greater than .345 regardless of the number of digits.

The second Talking Point focused on the place of a digit and its relationship to the digits surrounding it.  This will come in handy as we are writing out numbers using expanded notation.

The final Talking Point helped me to see if students had a grasp on equivalent decimals.  The students disagreed on this point, but it all boiled down to the focus of they type of number.  This point is true when only positive whole numbers are involved, but not true when positive decimal numbers are involved.

When we completed the Kahoot, I asked the kids to reflect on our conversations and to choose one of the prompts:

Next we moved into a brief discussion about writing decimal numbers using expanded notation:

My focus was on the "new" information in black, the writing of decimal numbers in expanded form.  This led to a brief discussion about our place value system and how working to the right on a place value chart you are dividing each place by 10 to get the lower place value.  I needed my classes to "see" why there is not a "oneths" place.  I had to show that 1 divided by 10 = .1 = 1/10 and so on.  Each class had at least one person with an AHA moment!

This is where we stopped in each class, in order to actually finish all of the little things from yesterday.  Students worked through an xtramath.org, then if they were interested in UIL Chess they answered the problems, then they completed their letter to the editor, and finally worked on Khan Academy.