This lesson introduces multiplication as scaling. Students already know that multiplying a number by 1 results in the original number. Now they learn that multiplying a number by a whole number greater than 1 results in a product greater than the original number, and multiplying a number by a fraction less than 1 results in a product less than the original number.
One goal of the Common Core is to develop a deeper understanding of fractions by using a progression of concepts from simple to complex. This lesson prepares students for the conceptual shift involved in progressing from adding and subtracting whole numbers to adding and subtracting fractions.
In this lesson, students apply their understanding of fractions to compare two fractions. They use fraction models and number lines to help them reason about the size of unit fractions.
Can you cut a hole in a piece of paper large enough to walk through? You can, and if you use a map of the world you have an incredible lesson on not wasting our worlds resources.
Can you tie a knot in a piece of rope without letting go of the two ends?