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Thursday, October 08, 2015

Teaching Place Value

Yesterday as we looked for properties that belong to 0,1,2, and 3, one student said, "They are old numbers."
    I asked, "What do you mean by that?"
    He replied, "You know, they were invented in India a long time ago."
    "You're right," I remarked, "and you're the first person to say that today." He smiled proudly.

Now that the planning for the landmark number early year review unit is complete, I'm beginning to think about the place value unit we'll begin soon.

I'll begin the unit with a bit of history. I'll tell students that since we saw the short movie that introduced the history of the digits, I've read a bit more. I'll tell them that I've learned that 0 is also thought to be invented first by the Mayans, and then again by the Indians, as we learned. I also learned that from India the concept moved to Cambodia and China and can be found in ancient Chinese and Indian documents as a dot.

I'll remind them that the math we know was invented to help us problem solve as well as to describe and identify patterns, relationships, connections, and quantities in our world. It's an amazing system of naming, counting, and comparing.

I'll then ask, "How would you describe our system of counting?"

I expect they'll answer with some or all of the following:
  • a digit system
  • a system that goes to "infinity and beyond"
  • a base ten system
  • a decimal system
Then I'll say, "Does anyone know how our system of numbers work?"

As I listen, I'll chart their words and make sure we cover the following points:
  • Our place value system means that every place has a specific value.
  • The places change by X 10 to the left and X 1/10 or .10 to the right.
  • To the left the numbers become greater and greater, and to the right the numbers become less and less.
  • The decimal point separates whole numbers and fractions or decimals (parts of numbers)
  • All numbers are made with 10 digits: 0,1,2,3,4,5,6,7,8,9
  • It's a positional system.
Then I'll show them the model I made of our base ten system. I'll ask them why they think I made the model to look like this. Then we'll complete and color code the model. 

Following that we'll practice decomposing population numbers that relate to our school, community, state, and world. We'll write those numbers in many ways similar to the chart below:

We'll talk about why it's important to understand how to write a number in many ways.

After that we'll watch the Eames' wonderful Powers of Ten movie and discuss the way numbers move from zero to infinitely large and then from 0 to infinitely small.

Students will complete this worksheet as they watch the film:

Later we'll decompose numbers with decimals related to space, and we'll revisit estimation and rounding, operations and related algorithms, and problem solving.

It's a privilege to share such powerful and wonderful learning with children. Their questions and connections will serve to deepen and inform the learning too. It will be interesting to see where this learning path takes us. 


Scientific America
Introduction and Basic Number Counting Systems