Decomposing Fractions to Multiply

I  have always loved to teach fractions, but this year I have learned so much more about  fractions! Truth be told, I’m not a big fan of  The Story of Units math curriculum (Engage NY) but when I realized that my 4th grade students had to learn how to multiply fractions  by a whole number I was kind of scared because I knew that multiplying fractions had previously been a 7th grade skill. After my initial shock wore off I began to look for material that supported this standard and the way that it was suppose to be taught.  I went to the department of education’s website to look at the released test to see how multiplying fractions was going to be tested. I thought I had seen everything when it came to fractions! The way that the students were going to be tested was bananas! The students were going to have to identify an irregular model that matched the algorithm  4 x 4/3 .  I looked through all the material I had on fractions and I quickly realized that I did not have any resources that matched how the students were supposed to be taught this skill.

So, I decide to get online and look at Module 5 of the Story of Units on the Engage NY website and much to my amazement it had just what I needed! Even though my 4th grade students were supposed to have been taught fractions in 3rd grade they still were struggling with the denominator’s role in fractions. The module began with decomposing fractions using a tape diagram and the number bond. Teaching fractions through decomposing helped my students to understand that the numerator in a fraction is broken into 1 part and then added together. The students understood this concept very well because the tape diagram (bar model) gave them a visual that matched the fraction.
After teaching my students to understand decomposing fractions I wrestled with the idea of teaching 8 and 9 year old children how to multiply a whole number times a fraction. As I began to teach the lesson the way  the Story of Units suggested a light bulb suddenly came on! I had a brilliant idea. I had previously taught my students that when a number repeats it can be multiplied. I noticed that the same concept applied to fractions that repeated, however the only difference was that one number would be a fraction instead of 2 whole numbers.

This made teaching multiplying a fraction times a whole number so much easier for my students to understand because they could connect the repeating  of a fraction to repeated addition and multiplication. After I taught my lesson on multiplying fractions I wrote the algorithm 4 x 4/3 on the board and then asked my students, ” What does this mean?”  One of my students raised her hand and said, ” It means four thirds 4 times.”  This was my confirmation that teaching fractions this way works!  I was so impressed by my students that I created Decomposing Fractions to Multiply and materials that support multiplying fractions by a whole number.