Primary 4 Maths | Mixed Operations and Brackets Lesson-Prep Guide (for tutors) | 45-minute flow, teaching script, common errors

2026-11-15

Tutor lesson-prep guides · Primary Maths

Pupils work left to right not from carelessness but because nobody told them operations have ranks. This lesson sets three rules and demands a circled first step before any writing.

Objectives — By the end of the lesson the pupil can: (1) state the three rules — brackets first, multiply and divide before adding and subtracting, same level left to right; (2) circle the next part to work out before writing anything; (3) complete a mixed expression with one pair of brackets; (4) use a rough size check to judge whether an answer is plausible.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Adding and subtracting	works out 47 plus 28	answers 75
Times tables	says what 9 times 7 is	answers 63
Meaning of brackets	writes an expression that multiplies the whole sum by 5	answers with brackets around the sum

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Entry check	asks adding, times tables and brackets, writes answers on the right of the board	answers aloud and writes one expression with brackets
6-14 min	Set the three rules	writes brackets, multiply and divide, add and subtract as three ranks on the board	copies the rules and circles the first step in 8 plus 4 times 5
14-23 min	One pair of brackets	demonstrates 8 plus 4 in brackets times 5 and stresses finishing inside first	gets 60 and explains why it is not 28
23-32 min	Operations inside brackets	demonstrates 50 minus 2 times the sum of 3 and 7, asking for the order	gets 30 and circles both priority moves
32-41 min	Independent practice	reads questions only and walks the room checking circled steps	works three items, circling before each calculation
41-45 min	Exit check	marks at once and names the rule that broke	says whether the error was order or arithmetic

03 Teaching script (read it out)

Scene 1: Act 1: operations have ranks, they do not queue

An expression is not a queue. Brackets are rank one, multiply and divide rank two, add and subtract rank three. So in 8 plus 4 times 5 you do not start with 8 plus 4. Ask which operator is highest: it is the times. So 4 times 5 is 20, then add 8, and the answer is 28.

When you meet a mixed expression, what is the first question you ask yourself?

Scene 2: Act 2: brackets mean do this first

Brackets are an instruction: finish what is inside. 8 plus 4 times 5 is 28, but 8 plus 4 in brackets times 5 is 60. One pair of brackets changes everything. Work inside first: the sum becomes 12, then times 5. Until the bracket is finished nothing outside it may move.

Before the bracket is finished, may the number outside it move? Why not?

Scene 3: Act 3: same level goes left to right

Within one rank you start from the left. In 100 divided by 5 times 2, divide and multiply share a rank, so 100 divided by 5 is 20, then times 2 is 40. Multiplying 5 by 2 first gives 10, which is wrong. Adding and subtracting behave the same way: 20 minus 8 plus 3 goes 12, then 15.

When two signs are in the same rank, which one goes first?

04 Question types and worked steps

Type	Example	Steps	Answer
Only adding and subtracting, or only multiplying and dividing	20 minus 8 plus 3	same rank, left to right, one line at a time	15
Adding mixed with multiplying	8 plus 4 times 5	circle the times, get 20, then add 8	28
One pair of brackets	8 plus 4 in brackets times 5	finish inside for 12, then times 5	60
Operations inside brackets	50 minus 2 times the sum of 3 and 7	bracket gives 10, times 2 gives 20, then 50 minus 20	30

Sanity check (teach this): Three checks: is there a circle on the page, since a page with no circled step means guessing; is the size of the answer plausible, because 8 plus 4 times 5 must be bigger than 8 while 60 means the multiply was skipped; and does a bracketed version come out larger, since a bracketed question with a smaller answer usually means the brackets were dropped.

05 Independent practice (3 questions)

Question	Answer	What to watch
What is 6 plus 3 times 9?	33	whether the multiply was circled first
What is 6 plus 3 in brackets times 9?	81	whether the bracket was finished first
What is 45 divided by the difference of 9 and 4?	9	whether the bracket gave 5 before dividing

06 Common mistakes and what to say

Mistake	Student writes	Say this
Working left to right throughout	8 plus 4 times 5 answered as 60	The 4 in front of the plus still has to be multiplied by 5; you added before multiplying.
Leaving the bracket half done	5 times the difference of 9 and 4 answered as 41	The bracket is not finished, so the 5 outside has not earned the right to come in.
Dropping the brackets that were meant	writing 8 plus 4 times 5 when the whole sum should be multiplied by 5	If the whole sum is multiplied by 5, put brackets round it, or the 5 only touches the last number.
Starting a same-rank pair from the right	100 divided by 5 times 2 answered as 10	Divide and multiply share a rank, so whichever is written first goes first.

07 Homework (paper, section and question numbers)

Primary 4 maths paper 1: four operations section — Section A, questions 1 to 4

08 Exit check (last 5 minutes)

Question	Answer	Decision
What is 9 plus 2 times 7?	23	wrong: reteach Act 1, multiply before adding
What is 9 plus 2 in brackets times 7?	77	wrong: reteach Act 2, brackets first
What is 60 minus 3 times the sum of 4 and 6?	30	wrong: reteach the three moves, bracket then multiply then subtract

09 Tutor FAQ

Which year group is this for?

Hong Kong primary schools make mixed operations and brackets a computing focus in Primary 4, after earlier years of single-step work. Fraction and decimal work in Primary 5 and 6 reuses the same order, so this chapter should be settled once.

Is 45 minutes enough?

Yes, but Act 3 needs its full time. Pupils struggle to accept that left to right and multiply first can both be true, so contrast 100 divided by 5 times 2 with 100 divided by the product of 5 and 2 on the spot.

Is there a practice paper?

Yes. The homework line links to the Primary 4 paper with the section and question numbers, and the page carries an answer version.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.