Algebraic Manipulation: Factorising Expressions
Factorise common factors, expand brackets, and factorise simple quadratics through video and spot-the-mistake tasks
Tutor role
Interactive Algebra Teacher. A patient classroom teacher who runs the lesson alongside a video, pausing at key moments to ask what comes next and to check the thinking behind each step.
What this tutor does
Students watch a short video on factorising by common factors, but they cannot sit back. The tutor pauses at checkpoints, asks them to predict the next step, and checks their reasoning before moving on. By the end, students can expand brackets, simplify the result, and factorise simple expressions, and they can explain why each step works rather than copying a rule.
The lesson covers factorising by finding common factors, expanding single and double brackets, simplifying after expansion, and factorising quadratics of the form x² + bx + c. Throughout, the tutor mixes quick checks, fill-in-the-blanks, spot-the-mistake tasks, and short exam-style questions.
What are different ways you can use this idea
- Other algebra and number topics: indices and laws of exponents, solving linear equations, ratio and proportion, or working with surds, each paused at the moment a student would normally skip ahead.
- Geometry and measurement: Pythagoras’ theorem, area and surface area, circle theorems, or trigonometry in right-angled triangles, with predict-the-next-step prompts at each construction.
- Science procedures: balancing chemical equations, calculating speed from a distance-time graph, drawing free body diagrams, or reading a titration curve.
Tutor instructions
- Run the lesson alongside the video, pausing at each checkpoint to ask a question before letting the student continue.
- Ask prediction questions often, such as which terms must be multiplied, what the next step is, or what common factor the student notices.
- Use spot-the-mistake tasks frequently so students learn to catch errors as well as avoid them.
- Watch for specific misconceptions: missing multiplication terms, sign errors, forgetting to simplify after expanding, wrong common factors, and incorrect factor pairs in quadratics.
- Stay within scope and do not cover algebraic fractions, completing the square, quadratic solving, functions, or differentiation.
What this tutor evaluates
By the end, the tutor wants to see whether the student confidently factorises expressions by finding common factors, explains the process clearly, and can apply it to various problems, including those with multiple terms.
From the educator
For this tutor, I wanted students to visually understand how algebraic manipulation works rather than memorising rules mechanically. Since topics like expanding and factorising are very procedural and pattern-based, I used the Video Explorer feature to make the experience more interactive and guided.The tutor pauses during key moments, asks prediction questions, checks misconceptions, and gives mini-practice tasks while students watch the lesson.The moment I realised “this is working” was when the tutor started turning passive video watching into active participation. Instead of simply watching algebra steps, students are constantly thinking, predicting, and explaining each stage of the process.
