Why is it possible to invert the divisor and multiply

To see why the IM rule works for sharing, lets first solve a sharing division problem. To find how much of the whole this is, we partition the remaining fourth into halves as well, finding t hat we have created eight equal pieces in our whole. Section 8: Explaining the Invert and Multiply Rule Goal To help students draw pictures to explain why the invert and multiply rule works, and to record their explanations in writing.

Big Ideas Because we have two models of division, we need to d evelop two explanations for why the invert and multiply rule works. The Measurement Perspective There are two parts to explaining why the i nvert and multiply rule works from a measurement perspective: 1. The Sharing Perspective To see why the IM rule works for sharing, lets first solve a sharing division problem. Remember that procedure is only powerful and useful in problem solving when students understand what it means and why the procedure is such.

I suggest you also read my post on what it means to understand fractions and math knowledge needed by teachers to teach fractions and decimals. The above lesson is not just about division of fractions. I made it in such a way that weaved in the lesson are the ideas of equivalent fractions, proportion, the property that when you multiply same number to the numerator or dividend and to the denominator divisor it does not change the value of the quotient, division by 1, etc. The main point is to use the lesson on division of fractions as context to make connections and to teach important ideas in mathematics.

I think this is how we should teach mathematics. View All Posts. Good post. In fact, you CAN divide straight across. How about a simple intuitive approach?

It shows a pattern. I eventually lead students to the steps in the article, but even more meaningful is the more concrete understanding that the Connected Math Program offers by supplying stories that involve the amount of cheese needed to make a pizza. I also have students draw illustrations of these problems using number lines and area models rectangular units are easiest :.

So then what does a problem like 6 divided by 2 really mean? You can think of it this way: Imagine you have 6 apples which you then divide up into groups of 2 apples.

That means you have 3 groups of 2 apples in front of you—so 6 divided by 2 or 6 divided into groups of 2 equals 3. Yes, I know this is an extremely simple example, but having a simple example in mind will help as we move to tougher topics. What is it? That means, rather interestingly, that a problem of dividing integers can be turned into a problem of multiplying fractions. What does that really mean? What fraction? What does it really mean?

Well, this is where things start to get a bit tougher.