Most of us learned to divide fractions. We wrote the problem as it was presented in our math books:
3/4 ÷ 1/2
Then we were instructed to rewrite the problem changing the division to multiplication and flipping the second fraction:
3/4 x 2/1
At this point we could cancel, or we could multiply and reduce later. Let’s multiply:
We can reduce to by dividing the numerator and denominator by 2:
And if necessary, we can change this to a mixed number:
Does this answer make sense? It’s hard to tell. We’ve followed a procedure, an algorithm, but do we understand what just happened? For most of us, understanding the connection between the original division and the answer was missed. Maybe your elementary teacher didn’t explain it. Maybe he did and you didn’t understand or remember.
In Math for the Middle Grades we use a wonderful curriculum called Math Mammoth. Math Mammoth is written by a Maria Miller, a homeschool mom who was born and educated in Finland and now lives in the U.S. According to her website (click here), she was tutoring homeschooled children and saw that there was conceptual understanding missing from the children’s math education. In her books she provides lessons in understanding math concepts, followed by lessons that teach the traditional algorithms for those concepts.
Students who join us for Math for the Middle Grades get a good start on understanding of operations with whole numbers, fractions, decimals, and percents. This understanding provides some great advantages:
- Greater ability to calculate mentally. This is a great time saver when solving long, complicated algebra trigonometry equations.
- Increased recognition of sensible answers. When following an algorithm to divide decimal numbers or add fractions it’s helpful to have a rough estimate of what the answer should be. That estimate can be made quickly by mental calculation when the operation is understood.
- More easily connect real world problems with the math that represents them. Solving real world problems can be difficult to solve when the process starts with picking the right algorithm. Making a connection between the algorithm for multiplying decimal numbers and calculating the sales tax on a particular purchase seems arbitrary. Understanding the concepts of decimal part of a number or percent of a number has a more direct connection to the problem.
Math for the Middle Grades help students in grades five and up with understanding the concepts described in this post and lots more. In this worktext-based class we also study basic math facts, geometry, and graphs. Most weeks also include a game that provides practice of math skills.
Join us! Find more information at WEST.