Algebraic manipulation is usually taught as a list of rules delivered in whatever order the textbook chose. Students collect like terms in September, expand brackets in October, and never find out that these are the same operation wearing different clothes. This is a five-lesson sequence for MYP Years 1 to 3 that builds manipulation on one idea: an expression can be rewritten without changing its value. Each lesson below has an objective, a core activity, a check, and a note on what to cut when the week goes wrong.
Lesson one: equivalence before technique
Objective. Students can decide whether two expressions are equivalent and justify the decision.
Core activity. Sets of expression cards to sort into equivalence families by substituting values. No rules given. Students discover that 2(n + 3) and 2n + 6 agree for every value they try, and that 2n + 3 does not.
Check. Give a pair that agrees at n = 2 but nowhere else. Students who declare them equivalent have learned to test one value, which is the misconception this lesson exists to catch.
If time is short, keep this lesson and cut lesson three. Everything downstream depends on equivalence being the organising idea rather than a procedure.
Lesson two: collecting like terms as counting
Objective. Students simplify sums of unlike terms and can explain why unlike terms cannot be combined.
Core activity. Bar or area representations first, symbols second. Three lengths of a and two lengths of b physically cannot become five of anything, and the picture settles that permanently.
Check. Two items only: 3a + 2b and 3a + 2a + b. The first is the diagnostic; students who write 5ab have not attached the letter to a quantity.
The volume of practice this lesson needs is more than you can write on the board, and it must vary the surface features rather than repeating one form. Algebra Basics – Understanding and Simplifying Algebraic Expressions | Math Resource | GRADE 5–9 is built for exactly this stage, with the differentiated levels that let the group who got it in ten minutes move on while the rest consolidate.
Lesson three: expanding as area
Objective. Students expand a single bracket and can say what the bracket represented.
Core activity. Rectangles partitioned into two parts, area calculated two ways. Students write both expressions and confirm equivalence, which links straight back to lesson one.
Check. Expand 3(2x − 4). The negative is the whole check. Students who write 6x − 4 have treated the multiplier as attaching to the first term only.
If time is short, this is the lesson to compress into half of lesson four, because expanding is easily rehearsed alongside factorising once the area image exists.
Lesson four: factorising as reading the picture backwards
Objective. Students factorise a two-term expression and check by expanding.
Core activity. The same partitioned rectangles, now given the areas and asked for the side lengths. Presenting factorising as the reverse of a known move rather than as new content halves the resistance.
Check. Factorise 12x + 18. Students who write 2(6x + 9) have factorised correctly but not fully, and that distinction is worth naming rather than marking wrong.
Lesson five: manipulation with a purpose
Objective. Students rearrange an expression to answer a question that could not be answered before.
Core activity. A context where simplification pays off: comparing two mobile phone tariffs, two ways of pricing a school trip, two growing patterns. Students simplify because the simplified form answers the question faster, not because they were told to.
Check. One unfamiliar context, worked independently. This is the criterion C evidence for the sequence and it is worth collecting properly.
Contexts involving pricing and comparison need proportional reasoning to be secure, and it often is not. Where that is holding a group back, running Algebra Basics – Ratio, Proportion and Percentage | Math Foundations Workbook | GRADE 5–9 as a parallel homework strand fixes the foundation without spending a lesson on it.
Where the sequence goes next, and what to protect
The natural continuation is equations, and the transition works if students already read the equals sign as a balance. Introduce that in lesson five as a preview rather than waiting, so the next unit starts from something familiar. Algebra Basics – Solving Equations and Understanding Inequalities | Math Foundations Workbook | GRADE 5–9 picks up cleanly from here, keeping the same equivalence logic rather than presenting solving as a fresh set of rules.
If the week collapses and you get three lessons instead of five, run one, two and five. Technique can be rebuilt later. The idea that rewriting preserves value cannot be retrofitted easily, and a student who holds it will teach themselves most of the rest. You will know the sequence has worked when a student, faced with an unfamiliar expression, substitutes a number to check their own rearrangement without being told to.
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