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Think of the equation as an onion to isolate any term that is in the center of it. Math is equitable it won't let you cheat, if you try you will FAIL! Whatever you do to one side of an equation you MUST do the exact same operation to the otherside. As kids we learned how to count picking up our toys, then in grade one we started to add them. Grade two was not as much fun since we had to share and learned to subtract. Grade three multiplication was "taught" followed by division in grade four. A theme appears where once we learn to do something we then learned how to undo it. In math this is seen as isolating a term. An essential use of all our learning from elementary school is applied through the rest of our math lives. Given an equation it is not always in the form we require so we have to unwrap it into what we want. Think of the equation as an onion where each outer layer has to be removed to get to the center (required term). The outermost layer of the onion is the furthest operation to the term we are solving for. Solve for x: Now x is the center of the onion so first let’s determine what is the outermost layer to the innermost. Mathematically it is the reverse of Order of Operations commonly known by the acronym (PEMDAS). In the above equation x is: Operation Opposite operation Being squared Square root Multiplied by 3 Corresponding Division Added to 4t Reverse Subtraction Having 2 subtracted Operation Addition Finally divided by 5 Multiplication Reading this in reverse we see that the outermost layer is division by five and the innermost is squaring. If we perform these exact opposite operations in this order to both sides we will have isolated for x. IMPORTANT: Whatever you do to one side you must do to the entire other side [use of brackets aid in this process]. Now we have the inner onion while preserving equity for all the other terms. No matter what math you try we often have to solve for a term that is buried deep, but this method works everytime.

Carrot for cutting into Conics Conics with Carrots is a funny association, but I believe being part of the experiment opposed to the observer is far more memorable when learning. My first step is to shape two carrots into similiar cones so they can be sliced to reveal the conics: parabola, circle, ellipse, and hyperbola. Below is a short video demonstrating the four slices required.

Unlike Terms don't play well together After learning distributive multiplication new terms are created that aren't alike. Unfortunately they do not mix, so it is important to keep the like terms together. What makes a like term and how do I collect them to "Simplify" my equations students ask. LIKE TERM - same variable to identical exponent, only the coefficient and sign can be different. This is best explained with a few examples below. "SIMPLIFY seems to be a catch all in math the isn't always SIMPLE!" OK, I get it so let me show you a method to aid in collecting the like terms in the short video below. Grouping Like Terms with SHAPES.

While I'm developing this site, I'm conflicted as I believe teaching and learning is best in person. Students since the pandemic have echoed this sentiment. If using technology with this site the "Smart"phone is not the way to go. My students are who convinced me to create this site, so I will end this post with a bit of advice for techology. I do practice what I preach. My students hear from me that if I expect them to write something down or try a problem, then I should as well. The time taken is greatly appreciated by students who have more time to absorb an idea or ask a question. The "Real" world is not made for multiple choice and fill in the blanks. If students have notes they should be personal as it aids in long term recall for later synthesis. Einstein managed to discover the Theory of Relativity with chalk and talk, not a "Smart" device in site. Work in groups, make messy notes and talk to one another (Students, Parents & Teachers).

Not until the end of my first year university did I realize how conventions in math work if explained. Too often we accept or worse yet assume conventions, either way this seriously impedes learning. From my experience not one student could explain this to me just as I couldn't in high school. a,b,c ………………….……m/n………..………x,y,z Constants & Coefficients // Variables The first half of the alphabet is generally used for constants and coefficients while the last half of the alphabet is used for variables. Imagine the first time you read: and understanding what you were looking at. Don't worry these blogs are to enlighten you on what may have been assumed. The rule book needs to be explained to be effective.

UNDER CONSTRUCTION - COME BACK SOON Understanding a definition often prevents you from memorizing (a wasteful use of your intelligence). Examples of two terms I like to use to illustrate this is Commutative and Distributive in the mathematical sense. Commutative = to commute or switch places while not changing the value. A * B = B* A Check 2 * 3 = 3 * 2 6 = 6 Distributive = To give each item/term the same amount. a ( b + c) = ab + ac Check 2(1 + 3) = 2(1) + 2(3) 2(4) = 2 + 6 8 = 8 Attempt to understand a new term when introduced opposed to just accepting it. Ask your teacher for the definition if you don't know. In a later post I put these two specific definitions to work in a comical way to truly remember these definitions.

As the old saying goes pictures are worth a thousand words. The best part of a picture is it tells you a story and jogs your memory of an idea. Have you ever stopped to consider how you can check something you memorized. Much of math can be illustrated into a graph, shape, or be given an analogy to a tangible item. When I'm attempting to teach an idea use of pictures and/or stories are quickly injected often garnering humour. Students please put memorizing aside and learn through visualizations. Here is an example when dealing with Arithmetic or Geometric Sequences. Did you notice there seems to be an (n-1) portion to both equations. Why is this. Well a sequence is like a number line that usually skips numbers by either a difference or ratio. Look at the sequence as a loaf of bread that is cut up. In this picture there are 5 slices, not all even, but it only took 4 cuts. Relating sequences to the loaf (Slices - 1) = Cuts. In a sequence we start with the first term that has no difference or ratio added to it. Using n=1 for term one in the equation (n-1)=(1-1)=0. Zero difference or ratio added to the first term.

Believe it or not one of my students was trying to explain how to use a flowchart to isolate for a term. Ironically they were asking me how this system worked. I was dumbfounded! If you do understand this method there is little opportunity to see if you made a mistake or understand what you are doing to the equation. This is a “New Trend” that has frustrated and confused students from my experience. Below I will demonstrate how this “works” for a simple equation and then demonstrate how it fails quickly. Equation: Isolate for x: Write the operations done to the term being isolated sequentially then work from right to left reversing the operations Now try this method with this equation: Please just use the “Onion” Method I describe in my Blog Post “Get Away from me! – Isolating a Term”