![]() ![]() Then they simplify that answer if necessary to connect their thinking to the model. On the second slide, students will invert and multiply the original problem. They will finish the first slide by finding and circling the number of groups they can find with their new whole. ![]() They then count the number of pieces used to make up their new denominator and numerator. First, students will create the fractional model by dragging and overlaying the two fractional pieces. ![]() In this digital resource, there are two parts. This is the number you find when simplifying your improper fraction found from inverting and multiplying your expression. If you go in and circle the number of groups you can make with your new denominator, 2, from your numerator, 3, you find that you can make 1 group of 2 or one whole and then you are left with 1 of 2 pieces or 1 ½. In this example it is 3, which is why it becomes your numerator. You then count the number of pieces you had originally from the ½. In this case it is 2 which is why when you invert and multiply the 2 becomes your denominator. You then count the number of pieces it takes to make ⅓ which is your new whole. This now allows you to easily see ⅓ of the whole while also making a common denominator. When you are dividing the fraction ½ by ⅓, you take your dividend fraction, or what is being divided, ½, and then split it into thirds horizontally. Understanding the Models to Teach Dividing Fractions In some division of fraction problems you can only make a partial group ⅓ ÷ ½ = ⅔ of a group or I can make ⅔ of a group when ½ is my new whole and ⅓ is what I have. When we are dividing a fraction by a fraction, we are essentially saying I am taking a fraction and creating groups the size of another fraction.įor example ½ ÷ ⅓ is saying how many groups of size ⅓ can I make from ½. Understanding and Using Fractional Models Understanding Division of Fractionsīefore we can help our students understand fractional models, we must understand them ourselves. This may be especially true when dividing fractions by fractions. This kind of math learning leads to real understanding and is less likely to be memorized and then forgotten by our students. Possibly even “discovering” the procedures for themselves. Have you ever heard the phrase “Don’t ask why, just invert and multiply”? Our teachers often taught math this way to us, simple procedures with little to no deeper understanding.įortunately, we have discovered that real learning comes from helping children understand the reason behind procedures. The purpose behind visual models is to help our students understand the why. Then add using models on top of that and it is easy to feel overwhelmed! We so often skim or skip over using and teaching models with our students because they can be confusing to not only our students but to us too! When we teach division of fractions through models, it is a powerful and useful tool that when used correctly can deepen our students’ understanding. Looking for a meaningful way to teach dividing fractions by fractions? This FREE digital activity for google slides uses area models to make sense of dividing fractions so your students understand the standard algorithm.ĭividing fractions is probably one of the trickiest standards to teach in sixth grade.
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