One of the most significant shifts I have observed when tutoring Year 7 mathematics is the transition from intuitively finding an unknown number to formally solving an algebraic equation. While these skills are fundamentally connected, algebra required students to approach familiar mathematical ideas in a more structured and abstract way. I have found that this transition is often where students begin to rely heavily on memorised procedures rather than developing a genuine understanding of what they are doing.
A student may have no difficulty answering a question such as, "What number added to 5 gives 12?" They can often recognise the answer immediately. However, when this familiar problem is represented algebraically, students are expected to move beyond simply identifying the unknown. They must manipulate the equation systematically, use inverse operations and maintain equality throughout each step.
When introducing this process, I find it more effective to focus on the reasoning behind each operation rather than teaching students to "move" numbers from one side to the other. For example, when solving an equation such as 2x + 5 = 13, I encourage students to consider what has to be done to isolate the unknown and how each operation can be undone in reverse order. This reinforces the idea that an equation represents a relationship that must remain balanced, rather than a set of sumbols that can be rearranged according to a collection of rules.
I also encourage students to verbalise their reasoning as they work. Asking, "Why did you subtract 5?" or "What are you trying to undo?" can reveal whether a student genuinely understands the process or is simply following a memorised sequence of steps. It also encourages students to become more conscious of their own mathematical thinking which further increases their own confidence in answering more difficult questions in class.
Teaching algebra is not simply about finding the unknown. It is about developing logical, systematic reasoning and understanding the purpose behind each step, rather than memorising procedures.
