Teaching Tip - Solving Equations Using the Flowchart Method
The flowchart method for solving equations is almost magic! I have seen middle school students solve and questions of similar complexity by the end of a one period lesson. It is a powerful method of solving equations where the variable only appears once.
Order of Operations
Solving equations requires students to first master the order of operations.
PEMDAS causes problems, big problems, because it is not logically consistent. Parentheses do come before exponents, and exponents do come before multiplication. But multiplication doesn’t come before division, and addition doesn’t come before subtraction.
Yes, I know you teach M and D are “equal”, and A and S are “equal”, but once kids learn “Please Excuse My Dear Aunt Sally”, that is forgotten. Trust me.
Instead, I suggest you use PEMA for order of operations:
P arentheses, in reading order
E xponents, in reading order
M ultiplication and Division, in reading order
A ddition and Subtraction, in reading order
The phrase “in reading order” works better than “left to right”. For example, if a child is unsure about 12 – 6 + 5, just say “Read it please” and if further help is needed ask, “Which operation did you say first?” Thanks to Mr Fraticelli at MS57 for this neat tip.
The Flowchart Method
Wrapping a present (put the present in the box, wrap the box, put on the ribbon) and unwrapping it (take off the ribbon, unwrap the box, take the present out of the box) is a suggestive analogy for solving equations by ‘undoing the operations, in reverse order’. Another is putting on your socks and shoes in the morning, and taking them off at night.
If a student knows the order of operations, the flowchart method is an efficient method for solving equations in which the variable appears only once. It also teaches students the correct order of the steps needed to solve an equation using the balance method.
The notation in the Impact Math text is a bit confusing. Students see for example the operation
” –1” and do that operation, rather than the inverse operation.. Here is my preferred format:
Solve: 5y – 6 = 24
I think it is important to write both the original operations and the inverse operations so students can see that they are “undoing” the operations, in reverse order.