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Monday, August 19, 2013

Introducing Multi-Digit Whole Numbers in Standard Form, Words, and Expanded Form

Fourth graders usually have some background with writing numbers in standard form, words, and expanded form. To continue toward mastery of 4.NBT.A.2, I like to use dry-erase boards like this one from Really Good Stuff:


When we used these boards today, my students told me they'd used them in second and third grades too. Numbers they had experienced looked similar to the one shown above. Today we moved into the millions (and on their request, the billions!) Later this year we'll use these same boards for decimals.

After a review of how to write numbers in words and expanded form, I had students build numbers as I called out the value of each place. Here's an example:
  • nine hundreds
  • three ten thousands
  • five ones
  • six tens
This left some places blank, and students were again required to hold the place value with a zero. After this, they wrote the number in standard form, words, and expanded form. As students finished each step, they flashed their boards at me for approval. Great formative assessment. What problem areas did we experience?
  1. A few children had difficulty moving the number straight down to the standard form lines. This showed me that these students were not grasping the concept of place value.
  2. Many children forgot to put commas after the period names or hyphens between the tens and ones places. It's typical, and I filed this knowledge away to review over and over this year.
  3. Some students kept the tens and ones places (in one or more periods) together when writing expanded form. I had to remind them that EVERY non-zero digit is translated to a separate number when writing expanded form.
After this activity, each child practiced with traditional worksheets. Although this lesson is procedural, it's also conceptual. Don't underestimate its importance! When students understand and can manipulate place value for multi-digit numbers, they possess a sturdy foundation for the study of mathematics.