As time marches on, this very idea is somewhat of a struggle with some math students. Studying rate, time, and distance problems can become cumbersome when students have to decide if the question "How long?" is referring to how far did somebody go vs how much time has elapsed. Making mistakes in this type of problem is easily done, and sometimes hard to grasp.

Another concept students are struggling with is Angle-Side-Angle (ASA) vs Angle-Angle-Side (AAS). These geometry concepts are useful when trying to prove that two triangles are congruent (almost the same in every aspect). However, these two can seem so similar that differentiating them can be confusing. So what is my explanation on this? First, I tell them to create an illustration that they can draw on so they have a visual. Second, I tell them to realize that order is incredibly important. For Angle-Side-Angle, the known side is sandwiched between the known angles. Below is an illustration of this:

For Angle-Angle-Side, the known side is not sandwiched between the known angles. Again, the illustration for this is shown below:

Hopefully between the visual they create and the explanation on the differences, they will be able to see which one they are using.

For the middle school, conversions are somewhat of a struggle right now. So converting 2 cubic miles to cubic yards is one example of that. They even need to be able to go from metric to English or vice versa. So converting 30,000,000 square meters to square miles is a question they could run across. There are enough different conversion rates that this could get confusing. However, the kids are doing pretty well at it.

These are just three of the many concepts the middle and high school students here at Kingdom Academy have been dealing with in the past month. They are doing great mastering these concepts, though. They are also learning to think in different ways, to slow down and show your work (even if the problem seems easy), and that hard work pays off. It's great to see these kids grow, and I can't wait to see what this next month holds!