Primary 4 Maths | Decimals and the Four Operations: Tutor Prep Guide | 45 minutes from place value to decimal word problems

2026-11-08

Tutor lesson-prep guides · Primary Maths

The difficulty with decimals is not the dot. It is that pupils treat the two sides as separate whole numbers, so 3.6 plus 2.45 becomes 6 plus 45. Teach place value before any method.

Objectives — Pupils can: (1) name the place and value of each digit in a decimal; (2) add and subtract in columns with the decimal points aligned, filling gaps with zeros; (3) state the direction and number of places when multiplying or dividing by 10, 100 or 1000; (4) solve one and two-step decimal word problems with a sensible number of decimal places.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Column addition of whole numbers	245 + 360	605
Idea of a fraction	0.1 is which fraction	One tenth
Whole-number multiplication	25 x 4	100
Writing money	$3.60 means how many ten-cent coins	Thirty-six

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0–9 min	Starter: money in a pocket	Show $3.60 and $2.45, ask for the total, let them write 6.05 naturally	Writes 6.05 and explains the 5 is five cents
9–18 min	Place value table	Draw ones, point, tenths, hundredths and place 2.45 digit by digit	Says the 4 means four tenths
18–26 min	Adding: align the points	Model 3.6 + 2.45 by writing 3.60 first, then adding in columns	Gets 6.05
26–34 min	Subtracting with zeros	Model 5 – 1.28 by writing 5.00 first	Gets 3.72
34–43 min	Multiplying and dividing by 10 and 100	Model 0.35 x 100 = 35 and 4.8 / 10 = 0.48 through place value, not a chant	States direction and number of places
43–45 min	Exit check	Three quick oral questions	Answers independently

03 Teaching script (read it out)

Scene 1: Align the decimal points, not the right-hand edge

Pupils are trained to align whole-number columns on the right, so they put 3.6 under the end of 2.45 and add 36 to 245. Say plainly: only digits in the same place can be added, so the points line up and the places line up.
Do one example in a place value table first, then draw a dotted vertical line through both decimal points in the column sum. That line becomes their seatbelt, and after a few goes they draw it unprompted.

Pupil does: draw a dotted line through the decimal points before calculating.

Scene 2: Fill the gap with a zero, never leave it blank

With 3.6 over 2.45 and a blank underneath, pupils read 6 against 5 and get 0.51. The zero turns “no hundredths” into “zero hundredths”, which can be added.
Ask them to say what each row means after filling: 3.60 is three ones, six tenths, zero hundredths. If they can say it, they are not just copying a gesture.

Pupil says: what the zero in 3.60 stands for.

Scene 3: Times 100 moves two places, it does not add zeros

Pupils carry the whole-number habit across and write 0.35 x 100 = 0.3500. Use the place value table: every digit climbs two columns, so the 3 in 0.35 rises from tenths to tens and the answer is 35.
Self-check: multiplying by a number bigger than one must make the answer bigger. 0.3500 did not grow, so it is wrong. Dividing by 10 must make it smaller.

Pupil says: after multiplying by 100, will the number grow or shrink.

04 Question types and worked steps

Type	Example	Steps	Answer
Reading place value	In 2.45, what place is the 4 and what is it worth	Build the place value table and read digit by digit	Tenths, worth 0.4
Decimal addition	3.6 + 2.45	Align points, fill with a zero, add column by column	6.05
Decimal subtraction	5 – 1.28	Write 5 as 5.00, then subtract with borrowing	3.72
Multiplying and dividing by 10 or 100	0.35 x 100 and 4.8 / 10	Use the table to show direction and places	35 and 0.48

Sanity check (teach this): Reasonableness checks: decimal points sit on one vertical line in any column sum; gaps are always filled with zeros; the number of decimal places in the answer does not appear or vanish from nowhere; multiplying by more than one grows the number, dividing shrinks it; word problem answers fit the context (a toy does not cost $605); every answer carries a unit or a currency sign.

05 Independent practice (3 questions)

Question	Answer	What to watch
5 place value questions	Name the value of a digit, two asking how many tenths there are	Checks place is not confused with value
4 column sums	Two needing zeros filled, two needing borrowing	Checks the points are aligned
4 multiply and divide questions	Two of each, one in a money context	Checks direction and number of places

06 Common mistakes and what to say

Mistake	Student writes	Say this
Right-aligned instead of point-aligned	3.6 written at the right end of 2.45	“Decimals line up on the point, not on the edge. Draw the line through both points first.”
Leaving the gap blank	3.6 + 2.45 gives 0.51	“The 6 is tenths and the 5 is hundredths, so they cannot be added. 3.6 becomes 3.60.”
Adding zeros to multiply by 100	0.35 x 100 = 0.3500	“Multiplying by 100 must make it bigger. Yours did not grow, so it is wrong.”
Absurd number of places	A $3.60 toy answered as $605	“Check the situation: would a toy cost six hundred dollars? Wrong places mean a wrong point.”

07 Homework (paper, section and question numbers)

Primary 1 to 6 Maths test papers with answers — Do the P4 decimal questions, drawing the dotted point line every time
Primary Maths chapter index — All chapters in the subject
Redo this chapter — Redo four multiply and divide questions, stating direction each time

08 Exit check (last 5 minutes)

Question	Answer	Decision
What must line up in a decimal column sum	The decimal points	Saying the right edge means back to the third stage
What does 3.6 become before adding 2.45	3.60	Saying nothing needs adding means back to the fourth stage
What is 0.35 x 100	35	Answering 0.3500 means back to the sixth stage
Does dividing by 10 make a number bigger or smaller	Smaller	Saying bigger means back to the sixth stage

09 Tutor FAQ

Can a pupil who gets the method right but cannot explain place value move on?

No. P4 decimals stand on place value, and pupils who only have a chant collapse when decimal multiplication arrives in P5.

Should a calculator be used?

Only to check an answer they have already worked out. Using it to calculate means the sense of place never forms.

Is money a good context?

Very good, because pupils see $3.60 daily. But money only uses two decimal places, so add three-place examples separately.

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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.