Find your next learning step
Start with the difficulty closest to yours, then work through an example and try the practice independently.
Open the complete guide contents
An algebraic letter stands for a number, not a new kind of object. If a box contains n pencils, n tells us how many pencils are in that box. Expressions then describe relationships without requiring us to know the number immediately.
This guide helps Primary 6 pupils read simple expressions, distinguish adding from multiplying and substitute a given value carefully. It begins with ordinary quantities so the symbols carry meaning. No advanced secondary-school manipulation is needed for these examples.
MOE's 2021 Primary Mathematics syllabus includes P6 simple algebraic expressions. These original activities are a focused starting sequence, not the complete algebra syllabus or a statement that every programme uses identical scope.
Let n be the number of pencils in one box. We do not yet know its value. The letter lets us keep talking about that quantity without inventing a number.
In one problem, the same letter retains the same assigned value unless a change is explicitly defined. If n is 8, every occurrence of n in the expression being evaluated uses 8. Do not silently change it halfway through the calculation.
Write the definition beside the working: “n = number of pencils in one box.” The letter is the number, not the box itself. That distinction helps the child attach sensible units to an answer.
If three extra pencils are added to the box, the new number is n + 3. If two pencils are removed, with at least two originally present, the remaining number is n − 2. The expression describes the change relative to the original quantity.
“Three more than n” means n + 3. “Three less than n” means n − 3. Read the relationship rather than placing symbols in the same order as every word in a sentence.
Use a number check to test the meaning. If the box initially holds eight pencils and three are removed, five remain. The expression n − 3 gives 8 − 3 = 5, which matches the story.
Three boxes each contain n pencils. Their total is n + n + n, written 3 × n or 3n. The short notation means multiplication. It does not mean a two-digit number made by putting 3 beside the value of n.
If n = 8, then n + 3 = 11, while 3n = 24. The first expression adds three pencils to one quantity. The second counts three equal quantities.
Draw one box with three extra loose pencils, then three equal boxes. These pictures show why the expressions differ. A child who treats them as interchangeable needs that relationship made visible before practising symbolic rules.
If n pencils are shared equally among four pupils, each receives n ÷ 4 pencils when the sharing is appropriate to the task. The expression may also be written n/4. Name what is being divided and how many equal groups are made.
For 2n + 5, find two times n and then add five. If n = 6, the value is 2 × 6 + 5 = 17. It is not 2 × 11, because the expression does not say to multiply the entire sum n + 5 by two.
Keep the first practice expressions short. Reading the operations accurately is more useful than introducing complicated brackets before the basic relationships are stable.
To evaluate 3a − 4 when a = 7, replace a with 7: 3 × 7 − 4 = 21 − 4 = 17. Keep the multiplication operation visible in the first line.
Do not write 37 − 4. The adjacent 3 and a represented multiplication, not digit joining. Do not replace the 3 as well; only a has been assigned the value 7.
Substitution is a calculation with a supplied value. It differs from finding an unknown value from an equation. This guide concentrates on expressions, so we do not turn every evaluation exercise into an equation-solving task.
Four identical bags each contain b counters, and two more identical bags are added. The total is 4b + 2b = 6b. Both terms count the same defined quantity b.
However, 4b + 2 is not 6b. The second term is two individual counters, not two bags of b counters. Test b = 5: 4b + 2 gives 22, whereas 6b gives 30. That mismatch shows the proposed simplification is wrong.
A number check can expose an error, but a single successful check is not a general proof that two expressions always agree. Use the meanings of the terms to justify a simplification.
- Let p be the number of stickers in one pack. Write the total in five identical packs.
- Write the number left after four stickers are removed from one pack, assuming it contains at least four.
- Evaluate 2p + 3 when p = 9.
- Simplify 3p + 4p.
- Are p + 5 and 5p always equal?
Answers: 1. 5p. 2. p − 4. 3. 2 × 9 + 3 = 21. 4. 7p. 5. No. For example, if p = 2, they give 7 and 10 respectively.
Explain question 4 through packs or equal quantities. Explain question 5 through the difference between adding five and taking five copies. The symbols should remain attached to their relationships.
Use lengths instead of pencils: one strip is x centimetres long, so three identical strips have total length 3x centimetres. An extra two-centimetre piece gives 3x + 2 centimetres.
If the child reads symbols correctly but struggles to write an expression, practise translating a short story. If an expression is correct but evaluation goes wrong, inspect substitution and operation order. Those require different practice.
Parents can ask, “What does this term count?” A clear answer reveals the structure behind the notation. Algebra begins to feel manageable when the child sees it as familiar number relationships written compactly.