One of the biggest challenges many students face is that mathematics often appears to be hundreds of unrelated concepts, rules, and procedures. As students move from Kindergarten through to Grade 12, basic number operations, fractions, integer operations, algebra, percentages, probability, measurement, graphing, and functions can seem like completely different topics with little connection between them.
Let’s Count On Math™ begins with one simple question:
What are we counting?
Mathematics is the study of quantities, how we work with those quantities, and how they relate to one another. When students first identify the quantities involved, many problems become easier to understand because they have a logical place to begin.
Sometimes the answer is obvious:
• We count apples.
• We count dollars.
• We count metres.
• We count square units.
• We count groups.
As mathematics becomes more sophisticated, the quantities become more abstract:
• We count tenths, hundredths, and fifths.
• We count positive and negative quantities.
• We count different numbers, e.g., 3 + 4 x 5 + 2(5 – 2)
• We count algebraic terms such as xs and x2s.
• We count possible outcomes in probability.
• We compare counts such as rise and run, distance and time, or favourable outcomes and total outcomes.
Often, however, we cannot count immediately. Before unlike quantities can be combined, they must first be expressed in compatible forms.
For example:
• Fractions often require a common denominator before they can be added.
• Measurements may need to be converted to the same units.
• Currencies may need to be exchanged to a similar type
• In Order of Operations (BEDMAS) quantities are converted to ones so they can be counted/added together.
• Regrouping in whole-number arithmetic changes one ten into ten ones.
• Like terms in algebra can only be combined after they represent the same kind of quantity.
In Let’s Count On Math™, we call this "making change"—rewriting a quantity into an equivalent form that makes the mathematics easier to understand and work with.
This does not mean every mathematics lesson is simply “counting.” Some lessons are about grouping quantities, some are about comparing quantities, some are about finding relationships between quantities, and others are about rewriting quantities into equivalent forms.
But asking “What are we counting?” provides students with a powerful first step when they are unsure how to begin. It helps them identify the quantities involved before deciding how those quantities should be grouped, changed, compared, or related. Rather than seeing mathematics as hundreds of disconnected ideas, students begin to recognize a smaller set of recurring mathematical actions that connect topics across the curriculum.
That is the goal of Let’s Count On Math™: helping students find and see the structure that gives mathematics meaning.
