I had so much fun watching the "lightbulbs" turn on in math today. When I was a kid, I would never have believed that fractions could be fun, but it was a blast today! The children worked diligently and enthusiastically figuring out how mixed numbers and improper fractions work.
Yesterday we learned that if we share 7 brownies with 4 people that each person would get 1 3/4 brownies. 1 3/4 is called a mixed fraction. It's a whole with a fraction left over.
Today, I asked third grade mathematicians to compare fractions to a whole. I asked if a fraction was more than a whole, same as a whole or less than 1 (a whole). We noticed that fractions like 2/3, 3/4, 1/2 are all less than 1. We noticed that fractions like 5/5, 8/8, 6/6 are equal to 1. (Any time the numerator and denominator are the same, the fraction is equal to 1. Finally we learned about fractions that are more than a whole - 9/4, 8/6 etc... We made the generalization that if the numerator is larger than the denominator, the fraction is automatically larger than
1. Ask your third grade mathematician to draw you a picture proving these ideas.
Next, I challenged the students to turn 17/4 into a mixed number. I reminded them that a mixed number had some wholes and some fraction of the whole. Most students solved the problem by drawing out squares split into fourths, but several children made the connection to division and were able to solve it mentally!
Finally, I assigned the mixed number 3 2/5 and asked third graders to find the equivalent improper fraction. Most problem solved the problem by drawing 3 rectangles divided into fifths, but even more of them used multiplication and addition to solve this problem.
I was very proud of our mathematical minds today. Challenge your child to convert mixed numbers to improper fractions and improper fractions to mixed numbers. At the third grade level it is very appropriate for them to draw pictures to help them solve the problem.
Have fun! :o)
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