This topic covers the fundamentals of proportions and shows their usage in applications where a percent of a number is needed. The student starts by learning the definition of a proportion. The student then learns how to solve for an unknown when given a proportion. Finally, application problems are introduced to give the student real-world examples which involve proportions.
This lesson starts by showing how to set up a proportion using a multiplication table. The instruction shows the student that proportions have been used previously in their mathematics career, they just haven’t been called proportions. The student also learns how to solve applications which involve proportions by using multiplication families.
This lesson shows the student how to write a proportion problem as an equation. The instruction first shows how to work out a proportion problem. It then shows the student how to view the proportion as an equation. The instruction further shows this idea with a handful of examples and shows how to rewrite the proportion as an equation.
This lesson covers another method to solving proportions, namely that of cross multiplication. The instruction shows the student the idea behind cross multiplication before formally introducing it by first showing a step-by-step solution for a proportion. The instruction then points out how cross multiplication accomplishes the same solution with fewer steps. This method of instruction provides a theoretical understanding of cross multiplication rather then teaching it as a rote rule that is arbitrarily correct.
This lesson continues the usage of cross multiplication to show the solution to applications which involve proportions. Cross multiplication is used to solve these applications.
This lesson shows the use of proportions in applications which involve discounts, interest rates, or tips. The instructions teaches the student how to solve these applications, which provide a real-world example of proportions.
This lesson continues the examples of the previous lesson to show more complex examples of proportions in real-world problems. These examples generally include more than one type of percent change. The instruction shows the student how to solve such problems.