Fractions block 3rd and 4th grade- December

After returning from Thanksgiving break, the third and fourth grade class began our second math block of the year. With a solid preparation in arithmetic skills from earlier in the fall, we were ready to introduce the idea of fracturing whole numbers into smaller pieces. We wait to work on this concept until students are developmentally able to understand how a whole object can be made up of infinitely smaller parts. To keep fractions from becoming too abstract, too quickly, we spent the majority of this first block using our hands to divide real objects into smaller and smaller pieces.

I began with a dramatic demonstration of fracturing, by channeling my inner ‘Thor’ and smashing some ice cubes with a hammer. Each student took their turn, and as we cleaned up the bits, we took note of the wide range of sizes of the pieces. Though it was a dramatic and entertaining method of breaking something, we all agreed that when you are put in charge of splitting objects in real life, you often want them to be evenly divided. After the ice, we progressed to splitting an orange, and discussing many hypothetical pizzas, pies, and cakes until our mouths watered. In addition to many food examples, one of our class parents lent us some of her home school fraction tools. These provided us with great new options for hands-on building and rearranging of fractions. The combination of food and tools allowed us to introduce many different ways of dividing shapes, and practice identifying halves, thirds, fourths, eighths, etc.

To further aid in this process, we began a new main lesson book for Fractions. Each student received 10 paper circles at the beginning of the block. Since I lead most of our watercolor painting, I decided to provide the students this chance to choose their own color combinations for each paper circle. They loved it and were pleased with the outcome. Once the circles were beautifully painted, we began with a page dedicated to “One Whole” with a simple full circle. From there, we progressed incrementally up to sixteenths with the appropriate slices cut from the paper circles. It is amazing to watch how much better the students are able to conceptually understand dividing a circle, when they do it with their own hands. Through drawing the lines, splitting the wedges in half, and cutting on their own, it began to sink in. Labeling the slices with the proper notation allowed the students to learn the written form through their recognition of the corresponding illustration. The different sized wedges also provided a basic visual understanding of equivalent fractions before I ever formally introduced it in class.

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Whole

 

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Halves and Fourths

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Sixths

To encourage a flexible understanding of notation, I progressed from asking math questions orally to writing them on the board as well. I wanted to cement the connection between the visual shape of a fraction, its written name in notation, and its oral name. As we worked on this, we transitioned into identifying other real-life scenarios that incorporate fractions. Our list was a great review of their measurement blocks from last year including time, length, weight, liquid volume, distances, money, etc. This allowed us to move from merely dividing shapes to considering fractions of groups of things, as well as other numbers. For example: How many years are in ½ of a decade? Or how many minutes are in ¼ of an hour? Or simply what is ¼ of 20?

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Rectangle Fractions

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Time Fractions

Seeing these problems written out helps us transition from thinking through the concrete act of cutting something into pieces, to carrying out the mathematical operations of multiplication, division, addition and subtraction on fractional numbers. We have just begun simple multiplication of fractions such as ½ x 2= 1 and ¼ x 24= 6. The students are noticing how helpful knowing their multiplication tables is for working with fractions! We will continue in the next block to manipulate increasingly complex fractional numbers, as well as to work towards a real understanding of what you are doing to a number when you multiply versus divide it by a fraction.

For reading work during this block, students read any time they finished their work or were waiting for me. They have independent silent reading during our extra time at the end of the day, at least once a week. Tuesdays, we have reading group all together. I have been very pleased to watch as group reading helps the class work on patience and cooperation with each other.  Our current book is “Abel’s Island” by William Steig. It is not a long book, but it is demonstrating an impressive range of vocabulary and keeping all of us on our toes! We revisit many of these words on our weekly spelling lists and quizzes.

For our class stories at the end of each main lesson, I continued reading “The Magician’s Nephew” by C.S. Lewis. We were all captivated, and it was a great change of pace from our math work. We managed to finish the book for a satisfying end to the block, just in time for winter break!

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