Primary 6 Mathematics

P6 Maths: Percentages, Ratio, Circle, Speed, 3D Shapes, Probability, Decimals, Statistics, Simple Equations

The order below is the recommended shallow-to-deep path.

Units 單元

Tap a unit name to jump to its topics.

百分數 Percentages5/5 live

  1. 1Lesson 1: What is Percentage?Basic
  2. 2Lesson 2: Converting Between Percentage, Fraction & DecimalBasic
  3. 3Lesson 3: Percentage in Real LifeBasic
  4. 4Lesson 4: Growth and DepreciationAdvanced
  5. 5Lesson 5: Advanced PercentageAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1What is the denominator of a percentage?

Q2What is 75% as a decimal?

Q3A shirt costs $120, 20% off. Sale price?

Q4Population grows from 50,000 to 60,000. Growth rate?

Q5Price $300, tax 5%. Total with tax?

比與比例 Ratio & rate4/4 live

  1. 6Lesson 6: What is Ratio?Basic
  2. 7Lesson 7: Proportion and ApplicationsBasic
  3. 8Lesson 8: Direct and Inverse ProportionAdvanced
  4. 9Lesson 9: Map ScaleBasic
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q115 boys, 25 girls. Ratio of boys to girls? (simplest form)

Q2Solve: 2:5 = x:20, x = ?

Q34 pens cost $20. How much for 7 pens?

Q4Scale 1:100000, 1 cm on map = ? km real

Q5Simplify 18:27

圓 Circle3/3 live

  1. 10Lesson 10: Introduction to CirclesBasic
  2. 11Lesson 11: Circumference of a CircleBasic
  3. 12Lesson 12: Area of a CircleAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Radius 8 cm. Diameter?

Q2Diameter 10 cm. Circumference? (π = 3.14)

Q3Radius 5 cm. Circle area? (π = 3.14)

Q4Diameter 14 cm. Radius?

Q5Radius 7 cm. Circumference? (π = 3.14)

速率 Speed3/3 live

  1. 13Lesson 13: Introduction to SpeedBasic
  2. 14Lesson 14: Distance and Time CalculationsBasic
  3. 15Lesson 15: Average SpeedAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q180 km in 2 hours. Speed?

Q260 km/h for 3 hours. Distance?

Q3First 2 h: 60 km, next 3 h: 90 km. Average speed?

Q4Speed 50 km/h, 4 hours. Distance?

Q5150 km at 50 km/h. Time?

立體圖形 3D shapes3/3 live

  1. 16Lesson 16: Introduction to 3D ShapesBasic
  2. 17Lesson 17: Volume CalculationsBasic
  3. 18Lesson 18: Surface AreaAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Cube has how many faces?

Q210 × 4 × 2 cm. Volume?

Q35 × 4 × 2 cm. Surface area?

Q4Cuboid has how many vertices?

Q5Cube side 5 cm. Volume?

概率初步 Probability2/2 live

  1. 19Lesson 19: What is Probability?Basic
  2. 20Lesson 20: Probability ApplicationsAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Fair coin, probability of heads?

Q2Roll die 60 times, expected 3s?

Q3Die, probability of 6?

Q4P(red) = 25, pick 100 times, expected red?

Q5Bag: 3 red, 2 blue. Probability of blue?

小數與四則 Decimals & operations4/4 live

  1. 21Lesson 21: Decimals: Introduction and Addition/SubtractionBasic
  2. 22Lesson 22: Decimal MultiplicationBasic
  3. 23Lesson 23: Decimal DivisionAdvanced
  4. 24Lesson 24: Decimal Word ProblemsAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q12.5 + 1.23 = ?

Q22.5 × 4 = ?

Q38.4 ÷ 4 = ?

Q4Buy $28.5, pay $50, change?

Q55 - 2.34 = ?

統計與數據 Statistics & data4/4 live

  1. 25Lesson 25: Data Collection and OrganisationBasic
  2. 26Lesson 26: Mean, Median, ModeBasic
  3. 27Lesson 27: Pie Charts and Bar ChartsBasic
  4. 28Lesson 28: Statistics ApplicationsAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1What does frequency mean?

Q21, 2, 3, 4, 5. Mean?

Q3Pie chart total angle?

Q4First step to read a chart?

Q5Survey 20 people, Maths 5, what %?

簡易方程 Simple equations3/3 live

  1. 29Lesson 29: What is an Equation?Basic
  2. 30Lesson 30: Solving Equations PracticeBasic
  3. 31Lesson 31: Equation Word ProblemsAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1What is an equation?

Q2x + 5 = 12, x = ?

Q3First step of word problem?

Q4x + 3 = 8, x = ?

Q5x - 8 = 3, x = ?

Vocabulary book 生字簿

All terms, bilingual (printable).

p
percentage名詞

A number expressed as a fraction of 100

p
percent sign名詞

The symbol %

p
per cent片語

Out of every 100

f
fraction名詞

A fraction, e.g. 12

d
decimal名詞

A decimal, e.g. 0.5

d
denominator名詞

The bottom number in a fraction

n
numerator名詞

The top number in a fraction

o
out of片語

From a total of

c
convert動詞

To change from one form to another

d
divide by片語

To divide by

m
multiply by片語

To multiply by

s
simplify動詞

To reduce a fraction to its simplest form

e
equivalent形容詞

Equal in value

d
denominator名詞

The bottom number in a fraction

n
numerator名詞

The top number in a fraction

p
percentage名詞

A number out of 100

d
discount名詞

Reduction in price, e.g. 20% off

o
original price名詞

Price before discount

s
sale price名詞

Actual price paid

p
principal名詞

Money deposited in the bank

i
interest名詞

Money the bank pays you for using your money

a
annual rate名詞

Interest rate per year

p
percentage increase名詞

How much something grows, as a percentage

p
percentage decrease名詞

How much something drops, as a percentage

g
growth rate名詞

How much something grows, as a percentage

d
depreciation名詞

Value going down, e.g. car depreciation

m
multiplier名詞

The number you multiply by, e.g. 1.25 means +25%

c
compound growth名詞

Growth calculated on the new value each year

o
original value名詞

The original amount

n
new value名詞

The amount after growth or depreciation

p
percent increase名詞

How much something goes up, in percent

p
percent decrease名詞

How much something goes down, in percent

t
tax名詞

Money paid to the government

s
sales tax名詞

Tax when you buy things

c
cost price名詞

What you paid to buy it

s
selling price名詞

What you sell it for

p
profit名詞

Money you made

l
loss名詞

Money you lost

s
simple interest名詞

Interest on original principal only

c
compound interest名詞

Interest compounds, based on new principal

r
ratio名詞

Comparing two quantities

f
first term名詞

Number before the ratio sign

s
second term名詞

Number after the ratio sign

s
simplify動詞

Reduce to simplest form

r
ratio value名詞

First term divided by second term

e
equivalent ratio名詞

Equal ratios, e.g. 2:3 = 4:6

p
proportion名詞

Two ratios are equal

p
part-to-part片語

Ratio of one part to another part

p
proportion名詞

Two equal ratios

c
cross multiplication名詞

Method to solve proportion

s
share by ratio片語

Divide by ratio

t
total parts名詞

Sum of all ratio terms

m
map scale名詞

Scale on a map

e
equivalent ratio名詞

Equal ratios

u
unknown名詞

Unknown number, usually x

r
ratio problem名詞

Word problem on ratio

d
direct proportion名詞

One goes up, other goes up too

i
inverse proportion名詞

One up, other down

c
constant名詞

Fixed number

q
quotient名詞

Result of division

p
product名詞

Result of multiplication

s
speed名詞

How fast

t
time名詞

How long

d
distance名詞

How far

m
map scale名詞

Scale on a map

m
map distance名詞

Distance on the map

r
real distance名詞

Real distance

s
scale denominator名詞

The number after the colon

k
kilometre名詞

Kilometre, 1 km = 1000 m

c
centimetre名詞

Centimetre, 1 m = 100 cm

l
linear scale名詞

Scale shown as a line

r
ratio scale名詞

Scale written as 1:xxxxx

c
circle名詞

Round shape

c
centre名詞

Middle point

r
radius名詞

Distance from centre to edge

d
diameter名詞

Through centre, edge to edge

c
circumference名詞

Perimeter of circle

c
compass名詞

Tool for drawing circles

c
chord名詞

Line between two points on circle

a
axis of symmetry名詞

Line of symmetry

p
pi名詞

The ratio C/d ≈ 3.14

c
circumference名詞

Distance around the circle

d
diameter名詞

Through centre, edge to edge

r
radius名詞

Centre to edge

s
semicircle名詞

Half a circle

p
perimeter名詞

Total distance around

w
wheel名詞

Wheel

c
constant名詞

Fixed number

a
area名詞

Surface size

r
radius squared名詞

Radius × radius

s
semicircle名詞

Half circle

q
quarter circle名詞

Quarter circle

s
sector名詞

Slice of circle

s
square metre名詞

Square metre, m²

s
square centimetre名詞

Square centimetre, cm²

p
pi名詞

π ≈ 3.14

s
speed名詞

How fast

d
distance名詞

How far

t
time名詞

How long

k
km/h名詞

Kilometres per hour

m
m/s名詞

Metres per second

a
average speed名詞

Average speed over whole journey

f
formula名詞

Math rule

u
unit名詞

Measurement unit

d
distance名詞

How far

t
time名詞

How long

d
departure time名詞

When it leaves

a
arrival time名詞

When it arrives

t
timetable名詞

Schedule

h
half hour名詞

30 minutes

q
quarter hour名詞

15 minutes

r
remaining distance名詞

Distance left

a
average speed名詞

Overall speed for whole journey

t
total distance名詞

Whole distance

t
total time名詞

Whole time

g
going名詞

Travelling to

r
returning名詞

Coming back

t
trap名詞

Trick question

h
harmonic mean名詞

Type of average for speeds

j
journey名詞

Whole trip

3
3D shape名詞

Three-dimensional shape

f
face名詞

Flat surface

e
edge名詞

Where two faces meet

v
vertex名詞

Corner point

c
cuboid名詞

Box shape

c
cube名詞

Equal-sided box

c
cylinder名詞

Can shape

c
cone名詞

Ice cream cone shape

s
sphere名詞

Ball shape

v
volume名詞

Space taken up

c
cubic centimetre名詞

cm³

c
cubic metre名詞

m³

l
litre名詞

Litre, L

m
millilitre名詞

Millilitre, mL

c
capacity名詞

How much it can hold

l
length名詞

How long

w
width名詞

How wide

h
height名詞

How tall

s
surface area名詞

All outer faces added up

f
face名詞

Flat surface

w
wrapping paper名詞

Wrapping paper

p
paint動詞

Paint

w
wall名詞

Wall

c
ceiling名詞

Ceiling

f
floor名詞

Floor

s
square centimetre名詞

cm²

p
probability名詞

How likely something happens

e
event名詞

Something that happens

f
fair形容詞

Equal chance

d
die名詞

Singular of dice

c
coin名詞

Coin

o
outcome名詞

Result

i
impossible形容詞

Cannot happen

c
certain形容詞

Must happen

e
expected frequency名詞

Expected number of times

t
trial名詞

Number of times you try

w
with replacement片語

Put back after each pick

w
without replacement片語

Don't put back

m
mutually exclusive形容詞

Can't happen at same time

p
predict動詞

Guess what will happen

w
weather forecast名詞

Weather forecast

l
lucky draw名詞

Lucky draw

d
decimal名詞

Decimal number

d
decimal point名詞

The dot .

t
tenths名詞

110 place

h
hundredths名詞

1100 place

t
thousandths名詞

11000 place

a
add動詞

Add

s
subtract動詞

Subtract

m
multiply動詞

Multiply

d
divide動詞

Divide

d
decimal places名詞

dp

f
factor名詞

Number being multiplied

p
product名詞

Answer of multiplication

p
pad with zeros片語

Add zeros

m
mental math名詞

Mental math

d
decimal point名詞

The dot in a decimal, e.g. in 0.64; its position depends on counting decimal places

w
whole number名詞

A number with no decimal part, e.g. 32; first multiply as whole numbers: 32 × 2 = 64

e
estimate動詞

To roughly check an answer, e.g. 2.4 × 0.15 is about 2 × 0.15 = 0.3

d
divisor名詞

Number you divide by

d
dividend名詞

Number being divided

q
quotient名詞

Answer of division

r
remainder名詞

Remainder

l
long division名詞

Long division

d
decimal point名詞

The dot; the quotient's decimal point aligns with the dividend's, e.g. 6.4 ÷ 2 = 3.2

s
shift the decimal point片語

Multiply both divisor and dividend by 10 or 100 so the divisor becomes whole, e.g. 7.2 ÷ 0.4 = 72 ÷ 4

d
divide evenly片語

To divide exactly with no remainder, e.g. 72 ÷ 4 = 18

w
word problem名詞

Word problem

c
change名詞

Change (money back)

u
unit conversion名詞

Unit conversion

m
metre名詞

Metre, m

c
centimetre名詞

Centimetre, cm

k
kilogram名詞

Kilogram, kg

g
gram名詞

Gram, g

c
concentration名詞

Concentration

s
statistics名詞

Statistics

d
data名詞

Data

f
frequency名詞

How many times

f
frequency table名詞

Frequency table

s
survey名詞

Survey

c
category名詞

Category

p
pie chart名詞

Pie chart

b
bar chart名詞

Bar chart

t
tally mark名詞

Tally mark

m
mean名詞

Average (sum ÷ count)

m
median名詞

Middle value

m
mode名詞

Most frequent

a
average名詞

Average

s
sum名詞

Total

e
extreme value名詞

Outlier

s
sort動詞

Arrange in order

f
frequency名詞

How many times

p
pie chart名詞

Pie chart

b
bar chart名詞

Bar chart

s
sector名詞

Sector

p
proportion名詞

Proportion

a
angle名詞

Angle

p
protractor名詞

Protractor

s
scale名詞

Scale

c
compare動詞

Compare

a
analysis名詞

Analysis

c
conclusion名詞

Conclusion

s
survey名詞

Survey

d
data名詞

Data

p
popular形容詞

Popular

m
misleading形容詞

Misleading

d
decision名詞

Decision

c
compare動詞

Compare

e
equation名詞

Equation

u
unknown名詞

Unknown

s
solve動詞

Solve

v
variable名詞

Variable

b
balance名詞

Balance

b
both sides名詞

Both sides

e
equal形容詞

Equal

s
solution名詞

Solution

s
solve動詞

Solve

i
isolate動詞

Isolate

s
substitute動詞

Substitute

c
check動詞

Check

u
unknown名詞

Unknown

e
equation名詞

Equation

b
both sides名詞

Both sides

o
operation名詞

Operation

w
word problem名詞

Word problem

t
translate動詞

Translate

u
unknown名詞

Unknown

a
age名詞

Age

g
gift名詞

Gift

b
book名詞

Book

c
check動詞

Check

s
solve動詞

Solve

More units rolling out in batches — same illustrated format.