Primary 4 Maths — Bar Charts and Composite Bar Charts: a Tutor Lesson-Prep Guide (scale, half squares, mean)

2026-11-10

Tutor lesson-prep guides · Primary maths

A pupil sees three squares and answers three. He never looked at the first number on the vertical axis, and that single omission accounts for most lost marks on bar charts.

Objectives — By the end the pupil can: (1) state whether each square stands for 10, 50 or 100 and show that three squares mean 150; (2) read half a square, knowing that half of 50 is 25, and read three and a half squares as 175; (3) compare the two bars of a composite chart, work out the difference and the total, and divide the total by the number of items to get the mean.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Reading a scale	The axis is marked 0, 10, 20. What is the third line?	20
Multiplication	Six times fifty	300
Meaning of a mean	Four numbers add to 140. What is the mean?	35

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Error diagnosis	Show a chart where each square is 50 and ask what three squares mean	Answers and gives a reason
5-12 min	Read the axis	Cover the bars and ask for the value of each gridline	Says 0, 50, 100, 150
12-22 min	Three-act teaching	Deliver the scripts on the scale, half squares and comparing bars	Repeats: first read what each square stands for
22-32 min	Worked examples	Model one reading, one half square, one difference and one mean	Copies one and writes the working
32-40 min	Independent practice	Hand out four questions and require the scale written first	Works alone and shows the multiplication
40-45 min	Exit check	Collect the work and note whether the scale or the arithmetic failed	States the value of one square

03 Teaching script (read it out)

Scene 1: The first move is always the vertical axis

Point at the axis and ask what the first line after zero says. If it says 5, each square is 5; if 50, each square is 50; if 100, each square is 100. The height of a bar only tells you how many squares. The quantity is the number of squares multiplied by the value of one square. So with each square at 50, a bar reaching the sixth line means six times 50, which is 300. That is why the first sentence of any reading is: each square stands for 50. Require the pupil to point at the axis and say it before counting anything.

Say what one square stands for before counting squares.

Scene 2: Half a square is read by proportion

Bars rarely stop on a line. If each square is 50, half a square is 25, so three and a half squares is 150 plus 25, which is 175. If each square is 100, half is 50 and two and a half squares is 250. The pupil should say: this bar passes the third line but has not reached the fourth, so it is three and a half squares. A pupil who cannot say that sentence is guessing.

Half a square is half of one square, not a whole one.

Scene 3: Composite charts: both bars share one axis

In a composite chart each item has two bars, for example one year and the next. Both bars are read against the same axis, so subtracting them gives the difference directly: class A at four squares is 200, class B at six squares is 300, and B is 100 more. For a total, read every bar and add; never multiply the tallest bar by the number of items. For a mean, divide the total by the number of items: 45 plus 30 plus 25 plus 40 is 140, and with four classes the mean is 35. The usual error is dividing by five, counting the empty column beyond the chart, so make the pupil count the items out loud first.

Both bars share the axis, so subtracting gives the difference.

04 Question types and worked steps

Type	Example	Steps	Answer
One bar	Each square 10, the bar reaches the fourth line	Read the scale, count four squares	40
Half a square	Each square 50, bar at three and a half	Three times 50 is 150, half is 25	175
Comparing two bars	Each square 50, A at four, B at six	A is 200, B is 300, subtract	B is 100 more
Mean	Four classes with 45, 30, 25 and 40 books	Total 140, divide by four items	35 books

Sanity check (teach this): Sense check: with each square at 50, six squares must be 300; answering 6 means the squares were treated as the quantity. Three and a half squares must lie between 150 and 200, so 175 is sensible. A mean must lie between the smallest and largest values, and 35 lies between 25 and 45; a mean of 50 would be impossible because no class reached 45 books. A difference can never exceed the total, and 100 is below 140.

05 Independent practice (3 questions)

Question	Answer	What to watch
Half a square	Each square 100, two and a half squares	Two times 100 is 200, half is 50, so 250
Half a square	Each square 20, four and a half squares	Four times 20 is 80, half is 10, so 90
Difference	Each square 50, bars of 300 and 175	300 minus 175 is 125
Total	45, 30, 25 and 40	Add them to get 140

06 Common mistakes and what to say

Mistake	Student writes	Say this
Counting squares as the quantity	Answers 3 people when each square is 50	You counted squares, not people. Each square is 50, so three squares is 150.
Rounding a half square up	Answers 200 for three and a half squares at 50	It passes the third line but has not reached the fourth, so it is in between. Half of 50 is 25, which makes 175.
Dividing by the wrong count	Divides four classes by five	How many classes are on the chart? Four. The mean is the total divided by four, not by the number of squares.
Taking the tallest bar as the total	Writes 45 as the total	45 is only the biggest class. Add all four to get 140.

07 Homework (paper, section and question numbers)

Primary 4 maths paper, bar chart — Section D, questions 1, 2, 3 and 5: reading, comparing and the total
Primary 4 maths paper, mean — Section D, question 4: total divided by the number of classes
Primary maths chapter index — All chapters in one table

08 Exit check (last 5 minutes)

Question	Answer	Decision
Each square 100, two and a half squares	250	An answer of 200 means the half square was dropped; reteach act two
Each square 50, bars of 300 and 175	125	An answer of 300 means only one bar was read; redo the comparison
Mean of 45, 30, 25 and 40	35 books	An answer of 140 means the total was never divided; reteach the meaning of a mean

09 Tutor FAQ

Why is a Primary 4 bar chart harder than a Primary 2 one?

Because one square no longer stands for one unit. In Primary 2 the count is the quantity; in Primary 4 there is one extra multiplication, and pupils fall back on the old habit.

Must half squares be read?

Yes. Real data seldom lands exactly on a line, and reading half squares is also the groundwork for line graphs in Primary 5.

Is the mean too early here?

Only the meaning total divided by the number of items is taught in Primary 4; no working backwards. Full application comes with the Primary 6 chapter on averages and line graphs.

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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.