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PEMDAS on the Prairie

In our day to day lives we meet many challenges. Decisions have to be made. Each of us analyzes these challenges, find what we think are the best solutions, and proceed. Many of these challenges are small and are solved with hardly a thought. Sometimes, however, the matter at hand is more complicated and coming up with the correct solution can significantly affect future success. If we get it wrong and miss the mark, we often have to "go back to the drawing board" and start over. We might think, "What happened?"

Here are two simple math problems:

8÷2(2 + 2) = ? and 9 – 3 ÷ 1/3 + 1 = ?

They look easy, but, in a recent study, only 60% of 20 year olds in one country solved them correctly (down from 90% in the 1980's!). Look at them carefully, see what you come up with, then see what the correct answer is for the first one at the end of this short post. The trick, as we shall see, is to proceed in the correct order.

Similarly, in restoring or reconstructing a prairie, timing and proceeding in the correct order is paramount to success. Controlling clonal species like sumac is crucial before introducing fire because the clone will be stimulated by fire producing many more stems. Simply cutting large aspen trees, instead of first carefully girdling them and allowing them to die slowly over a year or two, can stimulate the clone to send up a multitude of seedlings. Mowing periodically after planting a prairie is recommended, but doing it at the wrong times when weedy plants have already set seed can actually be counterproductive. Cutting different invasives for control requires timing to be correct for that specific plant. For instance, garlic mustard, not a common problem on a prairie, would have to be cut very early in the growing season, about late April to early May to help with control, whereas Japanese knotweed would hardly be affected by such an early cutting- it would better to wait until as late as July or August. Similarly, a "double cut" method for controlling sumac without the use of herbicide is gaining popularity, but again timing is of the utmost importance. The first cut should be done around July 1 when the clone has invested a lot of resources into each stem and they have just started to flower. Then the second cut is around August 1. Doing this for 2-3 years in a row can be very effective. Controlling wild parsnip with a Parsnip Predator requires cutting the root at the flowering stage before seeds have set. Cutting and treating or foliar spraying woody plants such as buckthorn too early in the year when sap flow is predominantly going from roots to new growth can also fail, but can be more effective if done in the summer into the fall or winter when flow is going the other way and herbicides are transported into the root system. Dispersing seed too early can be a mistake and decrease the germination rate. The list goes on. So, the correct order and timing of our work on the prairie is important for success and it is wise to take the time to do some research before beginning.

Now, back to the math problems. And what the heck is PEMDAS? Well, it stands for Parenthesis, Exponents, Multiplication-Division, Addition-Subtraction. Applying this order in math problems, then proceeding from left to right, will keep you out of trouble when tackling problems such as those above.

How about that first one, 8÷2(2 + 2) = ? Well, according to PEMDAS we should do the parenthesis first, so it would 8÷2(4) or 8÷2×4. Then left to right it would be 4×4=16. Pretty easy. Apparently, many in the 40% who were incorrect thought that the order should be 8÷2(4) then 8÷8 with an answer of 1.

Now, go ahead and apply PEMDAS to the second problem above: 9 – 3 ÷ 1/3 + 1. What is your answer? If you'd like, put your answer in the comments.

So, as the new year unfolds and you are out on the prairie or doing other conservation work, pause and deliberate, think a little about PEMDAS, then do your best to proceed in the correct order with the right timing.

Zoerb Prairie after significant restoration

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19? I was told "there would be no math". But I figure you wish to add to the sum of my fears. I'd like the option of calling so I can put this issue to rest.

Seriously, thank you for this reminder of the importance of order: "Maturity is the capacity to endure uncertainty" (John Huston Finley, ca 1909)

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