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Learning inverse
operations through
mapping diagrams

Inverse operations are opposite operations that undo each other. Before undoing an operation, it is important that students are able to describe in words a mathematical expression with at
least two operations such as 2a + 1. This is to ensure that they know ‘what happens to a first?’. In
this case, a is multiplied by two first, and then one is added to it. If we show ‘what happens to a’ in
2a + 1 in a mapping diagram, it will look like this:

And the idea of inverse operations is that whatever you do last must get ‘undone’ first. Hence the
diagram below

When students are comfortable with using the mapping diagram to explain and work with
inverses, they may then proceed to solving algebraic problems which largely incorporates the idea
of undoing a series of operations to solve for the unknown.

The following video on Inverse Operations shows how this concept of undoing operations
are used to solve equations.
Video: Algebra: Inverse Operations

Component: Algebra
Topic: Inverse operations This video will cover the following areas:
1. Definition of inverse operations
2. Inverse operations in algebra
Post-Video Activity:
A. Try using the mapping diagram to solve Po’s problem in the video.
B. Partner up!
Draw a mapping diagram each for an expression with at least two operations (such as 2a + 1).
Exchange your diagrams. Now create a story for the mapping diagram and explain the inverse
operations involved.

binomials via the
F.O.I.L method

Multiplying binomials can be done in two ways:
1. The distributive law method
2. The F.O.I.L method
((Mindy, there is a gap between the writing above and below here. As a reader, I would expect to
see some explanations or elaboration on the two ways before the examples))
Let’s take an example of an expression that consists of two binomials: (y + 3)(y + 2). Using the
distributive law method by letting A = y + 3, the equivalent form becomes:

(y + 3)(y + 2)
[let A = y + 3]

= A (y + 2)
[expand the brackets]

= Ay + 2A
[substituting A]

= (y + 3)y + 2(y + 3)
[expand the brackets]

= y2 + 3y + 2y + 6
[collect like terms/simplify]

= y2 + 5y + 6
The F.O.I.L method can be a great alternative strategy for expanding brackets. Watch the following
video that explains how this method can be used to multiply binomials in algebra.
Video: Algebra: The F.O.I.L method

Component: Algebra
Topic: The F.O.I.L method
This video will cover the following areas:
1. Recap on addition and multiplication of variables
2. Using the F.O.I.L method to expand binomials in algebra
Multiplying out the brackets in binomials is an essential skill that supports other algebraic activities
such as finding a solution for the variable (unknown) or rewriting the expression in its equivalent
form. Hence, it is important to practice expanding binomials using either the good old distributive law
method or the infallible F.O.I.L method. Click on the link in the following section to put those skills to
Post-Video Activity:
Try the FOIL Cruncher game on http://www.coolmath.com/crunchers/algebra-problems-multiplyingpolynomials-FOIL-1
Have fun!

expressions made

The first step towards solving any algebraic problem is knowing how to simplify an expression.
However, this can be intimidating if students are not familiar with the common terminologies used
in its context. This video captures a great way to introduce many algebraic nomenclatures before
explaining what are like and unlike terms. The difference between them is explained through
comparisons between terms with different variables and exponents, which are commonly confused
by many algebra novices.
When simplifying an algebraic expression, one common misconception stems from conjoining
algebraic terms as such: a + b = ab and x + y + z = xyz. This is due to the expectation that the sum
of two or more quantities must result in one value - from conjoining terms through arithmetic addition
and subtraction, such as 5 + 8 = 13 and 7 - 3 - 1 = 3.

One effective way to address this is to make clear to students the difference between a like term
and an unlike term. Students must also have a clear understanding on the concept of equality to
comprehend that conjoining algebraic terms may result in one or more terms. That is, it is valid and
justifiable if the collection of sums and/or differences in algebra result in expressions such as a + b,
or even a2 - a + b.
Check out the video below on combining like terms in algebra.

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