Hands-on Fractions

In math, the 5th graders recently moved from fraction addition to fraction subtraction, with renaming, mixed numbers, and simplifying fraction sums and differences.  

One day, the students cut ⅙ yard from ⅔ yard strands of ribbon they’d first measured and cut, then worked out how much of the ribbon was left. “This much!” was a great answer, but not to someone who was unable to see the ribbon, so they didn’t get out of the math that easily. This helped the students to see a need for being able to express the difference as a fraction that both ⅔ and ⅙ could convert to: sixths.  Thus lowest/least common denominator, ⅙ of 36”, ⅔ of 36”, and accurate measurement skills were all incorporated into this hands-on fraction subtraction introductory activity.

Another day, the students measured out 7 ¾ yards of “fabric” (they used white paper from a long roll, but visualized it as fabric).  Students then measured 2 ¼ yards of the “fabric,” representing a remnant after making curtains from the original cut.  Since their classroom mat area is not even 7 ¾ yards across, and their yard sticks are 39.37’/100cm rulers, there were many built-in opportunities for critical thinking, creative problem solving, negotiating, and sharing of roles to model and explain the answer to the question, “How much fabric was used to make the curtains?” 

Could the fifth grades have just written out ⅔ – ⅙ = ___ , and 7 ¾ – 2 ¼ = ____? Yes, of course! And that abstract algorithm is where they ended up, but by beginning with the lengthier, more complex task of hands-on modelling and talking about real-world math problems, the students developed conceptual understandings of how the algorithm works and what it represents.

Author: The Saklan School Friday Blog

The Saklan School is a private Pre-K through 8 school located in Moraga, CA. Our mission is to think creatively, act compassionately, and live courageously.

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