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Tuesday, March 01, 2016

Fraction Action: Floor to Ceiling Exploration and Observation

Later this week students will step back into the fractions unit. We deviated from the unit to take a side path of math review to prepare for the systemwide test which includes a host of math topics, but soon the test will be behind us and we'll get back to our core math study.

Our first step back will include a quick review of the fraction bars students created using Google table and a review of basic fraction concepts and language including the following:
  • A fraction is an equal part of a whole
  • The top number in a fraction is the numerator, and the numerator names the parts considered
  • The bottom number in a fraction is the denominator, and the denominator names the parts in all
  • The fraction bar is a division line. For example 1/2 = 1 divided by 2 = .50
  • A fraction can be written as a decimal (estimate or exact) and a percent
  • Just like we have benchmark numbers, we also have benchmark or landmark fractions
  • We can add, subtract, divide, and multiply fractions
After the quick review, about ten minutes, I'll give students a collection of about 25 same sized paper strips. I'll ask students to complete a "floor to ceiling" exercise which requires them to use folding to make a collection of fraction bars equal to one. The fraction bars I'd like them to make are listed on this guide. Once they've completed folding all the bars, I'll ask them to write as many expressions as they can using combinations of the fractions listed on the guide to make one whole. 

This exploration will give me a chance to observe students' current fraction knowledge. I will look to see how they use their Google fraction tables to inform their work. I'll also observe the different strategies they use to make the bars and the kinds of conversations they have with their friends about the task. The last task will help me to understand how much they understand with regard to adding fractions and visualizing that process.

After the exploration we'll do a similar task with fraction number lines. Then we'll revisit lowest common multiples and greatest common factors, and look at how we can add and subtract fractions with different denominators using a variety of mathematical processes. At that point, we'll be ready for a class assessment, and then we'll move into making models that demonstration multiplication and division of fractions and move on to the related mathematical processes. Finally we'll end with lots of project work that includes fractions and many other math concepts as we move towards the PARCC assessment.