Secondary 1 G1 Mathematics Tutor Bukit Timah. Why does 3 + 4 × 2 equal 11, but (3 + 4) × 2 equals 14? A quick Secondary 1 G1 Maths guide to brackets and signs. This easy-to-read guide explains the first decision behind a Mathematics problem, gives worked examples, and ends with a short parent-student check.
Try reading the explanation first, then cover the solution and ask your child to describe the next step. A short reason is more valuable than a memorised answer.
Did you know? The same digits can give two correct but different answers
Did you know? 3 + 4 × 2 = 11, whereas (3 + 4) × 2 = 14. The digits have not changed. The brackets have. This is why a Secondary 1 G1 Mathematics learner needs to understand the order of operations, not simply calculate whichever symbol appears first.
In the first expression, multiplication happens before addition: 4 × 2 = 8, then 3 + 8 = 11. In the second, the brackets tell us to add 3 + 4 first and multiply the result by 2. Both answers make sense because the expressions mean different things.
Try asking your child to read each expression aloud. If the student says “add three and four, then double” for both, the misunderstanding is about the grouping, not multiplication tables.
The practical order: groups, powers, then operations
Start with a reliable working order. First evaluate brackets and other clearly grouped expressions. Then calculate powers such as squares and cubes. Next do multiplication and division, reading those operations from left to right. Finally do addition and subtraction, also from left to right.
Some pupils use the word BODMAS to remember the stages. The memory aid is helpful only when it is interpreted properly. Multiplication and division have equal priority; subtraction is not automatically delayed until every addition has finished.
For example, 18 ÷ 3 × 2 = 6 × 2 = 12. Working out 3 × 2 first would produce an answer of 3, but the expression does not contain brackets telling us to group the 3 and 2.
Why left-to-right matters when division and multiplication meet
Consider 24 ÷ 6 × 2. Begin on the left: 24 ÷ 6 = 4, then 4 × 2 = 8. A student who multiplies the 6 and 2 first may write 24 ÷ 12 = 2. That has silently changed the grouping.
Now compare 24 ÷ (6 × 2). Here multiplication inside the brackets comes first, giving 24 ÷ 12 = 2. The incorrect answer to the unbracketed question is actually the correct answer to this different question.
Ask a learner to insert an imaginary pause after the first operation. If they can say “twenty-four divided by six, then multiplied by two”, they have identified the intended sequence.
Negative numbers add a second layer of meaning
Try −3 + 2 × (−4). Multiply 2 by −4 first to get −8. Then add −3, giving −11.
Now put a pair of brackets around the first two terms: (−3 + 2) × (−4). The bracket evaluates to −1, and (−1) × (−4) = 4. Again, the expressions look similar but describe different operations.
Notice that the sign on a number is not the same thing as the subtraction operation. When signs become confusing, insert brackets around a negative value and write one operation per line. Good working makes the intended calculation easier to inspect.
Subtraction across brackets: the important sign check
Suppose the question is 10 − (3 − 7). Work out the brackets: 3 − 7 = −4. The expression becomes 10 − (−4), so the result is 14.
Compare that with 10 − 3 − 7, which gives 0. Removing the brackets without accounting for the signs has changed the question. A tutor should help the student see what the minus sign is subtracting: a complete quantity, not just the first number in that group.
A short mental check helps here: subtracting −4 is equivalent to moving four units right on the number line. Starting at 10 should therefore lead to 14.
Squares and negative signs: where the brackets sit matters
For a negative number, (−2)² = 4, because (−2) × (−2) is positive. But −2² = −4 under the conventional order of operations: square 2 first, then apply the leading minus sign.
This is a good example of why a calculator entry needs careful grouping. A pupil may understand squaring perfectly and still obtain the wrong result if the negative base is not placed in brackets.
With a calculator, inspect what has actually been entered on the display. It is not enough to remember where the power button sits; the entered expression must correspond to the written question.
Decimals and fractions obey the same structure
Consider 1/2 + 3/4 × 2. Multiply three quarters by two first, giving one and a half. Add one half, and the final result is 2.
Now compare (1/2 + 3/4) × 2. The bracket is one and one quarter, which doubles to 2.5. The fractions have not changed, but the grouping changes the result.
The same priority rules work for integers, decimals and fractions. That is useful for G1 learners transitioning from familiar arithmetic into longer secondary-school expressions.
How a Bukit Timah tutor finds the first wrong step
One student may ignore brackets entirely. Another may think multiplication always outranks division, even when division comes first. A third may know the order but mishandle subtracting a negative value. All three could lose marks on the same worksheet for different reasons.
The existing eduKateSG Secondary 1 Mathematics tutorial programme near Sixth Avenue MRT is described as three-pupil groups with 1.5-hour weekly sessions and close checking of working. A tutor can ask every learner to mark the operation they would perform first, then compare reasons before calculation.
The aim is not to memorise one more acronym. It is to read a mathematical expression with enough precision to know what it says.
Five-minute home check
A. 8 + 12 ÷ 3. Answer: 12. B. (8 + 12) ÷ 4. Answer: 5. C. 30 ÷ 5 × 2. Answer: 12. D. 7 − (−3). Answer: 10. E. (−3)². Answer: 9.
Before each answer, ask the child to circle the operation that must happen first. If the answers are correct only after a reminder about the rule, repeat a changed example a few days later without prompting.
Frequently asked questions
Are integers, negative numbers and powers part of Secondary 1 G1 Mathematics? Yes. The MOE G1 Secondary 1 syllabus includes integer operations and calculator work with squares, cubes and roots. Accurate order of operations supports those skills.
Does division come before multiplication? Neither always comes first. At the same level of grouping, multiplication and division are carried out from left to right.
Can a child rely on a calculator? A calculator helps with arithmetic, but the learner must first decide what expression to enter and whether the answer is sensible.
Related Secondary 1 G1 Mathematics guides
- Three-Part Ratios: Keeping All Parts in Proportion
- Reflex Angles and Full Turns: Understanding 360 Degrees
- Pictogram Keys and Half Symbols: Reading Data Accurately
- Why Negative Numbers Change the Rules
- Substitution with Negative Numbers and Brackets
For the established teaching approach, read the original eduKateSG Secondary 1 Mathematics small-group tutorial guide. This source is unchanged and describes a three-pupil format near Sixth Avenue MRT with 1.5-hour weekly lessons and focused correction.
For official G1 subject-level content, consult the Ministry of Education Secondary 1 G1 Mathematics syllabus. Under Full Subject-Based Banding, G1 is a subject level and is not the same as Posting Group 1. Schools may teach topics in different sequences.
For Bukit Timah families: Bring a marked Mathematics question to discuss the first unclear step. Enquire with eduKate Singapore about suitable current G1 groups, timetables and availability.