164 Blank page
2B 18 Time
(2)
Quick reference
Core activity 18.1: Converting times (Learner’s Book p70)
Learners convert times in days, hours and minutes into months and into minutes.
Core activity 18.2: Time zones (1) (Learner’s Book p72)
Learners investigate how different times around the world occur because of the m
relation to the sun. They calculate time differences and times around the world u
system.
Prior learning Objectives* – please n
across th
Recognise and use the units for time: seconds,
minutes, hours, days, months and years. 2B: Measure (T
Tell and compare the time using digital and 6Mt1 – Recognise and
analogue clocks using the 24-hour clock.
Read timetables using the 24-hour clock. months, years, d
Calculate time intervals in seconds, minutes 6Mt2 – Tell the time usi
6Mt3 – Compare times
and hours using digital or analogue formats 6Mt5 – Calculate time in
Use a calendar to calculate time intervals in 6Mt6 – Use a calendar
days and weeks using knowledge of days in 6Mt7 – Calculate time in
calendar months. 6Mt8 – Appreciate how
Calculate time intervals in months or years.
2B: Problem so
6Ps4 – Use ordered list
*for NRICH activities mapped to
Vocabulary
time zone universal time
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Calcu lat ing Time Time Zones (1) Vocabulary
Let’s investigate 12 Let’s investigate time zo ne: area of the
T he time differe nce betwee n where M arco a nd Cody world w ith a common
Ran i ne ed s to ge t to a da nce les s o n 9 3 liv e is 3 ho ur s, Marc o ’s tim e is a hea d of Co dy ’s. time.There are 24 time
zones.
to day by 20 :2 5. I f the c lo c k s ho ws T hey ha ve a telep h o ne c on vers atio n
th e time no w, h ow lo ng d oe s s he 6
have u n til her les s o n ? for 1 h o ur a n d 1 8 m in ute s . Cody p uts universal time: the time
th e ph o ne d ow n a t 2 0:4 4. standard, orig ina lly
. There are two answers.. W ha t was the time fo r Marc o measured at Greenwich,
w he n he ra ng ? Eng land, s ometimes
called Greenwich
Mean Time (G MT).
112101 1 2 3554450531052 5 1015 11 12 1 This map sh ows approx imately the time zones around the
98 5 4 2 5 20 10 2 world. It shows how far ahead or be hind the time is in ho urs
76 3 from the Universal Time a t ‘0 ’.
30 9
8 4 01 2 34 5 67
5 8 9 10 11 12
76
1 Write whether each of these statements is tr ue or false.
(a) One week is more tha n 1 00 hours. A n c h or Om
age
(b) There are more weeks in a y ear than day s in two mon ths. sk U la a n ba
Acapu atar
(c) There are more than 85 00 0 sec ond s in one day . lc o New Lisb A n ka
York Ma n
(d) One wee k is les s than 10 00 0 minutes. 72 on ra i la
movement of the Earth in Abu
using the 24-hour clock chapter but P or t
(e) There are more months with 30 day s than 31 day s. N o u a kc h o tt Dhabi M o r e s by
note that listed objectives might only
he book when taken as a whole (f) There are more than 7 50 ho urs in one m onth. Quit Lagos Sy dn
o Colom bo ey
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ay
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45
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be 5 within any are covered fully
partially covered18 19 given
2 0 21
25 26
Time)
understand the units for measuring time: seconds, minutes, hours, days, weeks,
decades and centuries; convert one unit of time into another.
ng digital and analogue clocks using the 24-hour clock system.
on digital and analogue clocks (e.g. realise quarter to four is later than 3:40).
ntervals using digital and analogue times.
to calculate time intervals in days, weeks or months.
ntervals in days, months or years.
the time is different in different time zones around the world.
olving (Using understanding and strategies in solving problems)
ts or tables to help solve problems systematically.
o the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 2B 165
Core activity 18.1: Converting
times
Resources: During 2012 photocopy master (p170). 2012 calendar photocopy mas
internet or books with time facts of events and records.)
Display the During 2012 photocopy master for the class:
During 2012 these ve people were busy circumnavigating the Earth.
Mike Hall took the round-the-world-cycling record, taking 91 days, 18 hours.
Juliana Buhring also cycled around the globe. Her time was 152 days, 1 hour.
Carlo Schmid flew solo around the world in 60 days, 17 hours and 22 minutes.
Erden Eruç travelled around the world using only ‘human power’ in 1026 days.
Loick Peyron and 14 crew sailed around the world in 45 days, 13 hours and 43 sec
Ask pairs of learners to discuss how they could create a graph showing the different
by each person to travel around the world. Discuss as a class whether it is possible to
scale for the graph that will enable them to accurately represent both 45 days and 102
Suggest that they make a large graph in a group, or groups, using strips of paper for t
marking the scale using metre sticks.
Ask learners to convert their graph into a time line by taking the longest bar and marking
the other bars along it. They should mark it with a reasonable scale, e.g. 50 day interval
Pairs of learners should calculate and debate the approximate time in months each pers
travel around the world, to the nearest whole month. They should justify their answers u
they know about the number of days in a month. Ask learners to convert the approximat
amount of time each person took into minutes. They should use their graphs or time line
the reasonableness of their answers, by comparing which should be greater, and how m
shorter or longer the bar is than other known numbers of minutes.
Tell learners that Juliana Buhring started her circumnavigation on 23 July 2012. Ask
the 2012 calendar to work out what day she completed her journey (Answer: 22 Dec
2012.) Mike Hall completed his circumnavigation on 4 June 2012. Ask learners to us
calendar to work out what day he started his journey (Answer: 4 or 5 March 2012).
166 Unit 2B 18 Time
(2)
LB: p70
ster (p171). Metre sticks. Long strips of paper. (Optional: access to
conds. As necessary, remind learners about types of graphs
they might effectively use for this type of data, and to
times taken consider different scales for the axis.
o choose a
26 days. Look out for!
the bars and Learners who are trying to be too accurate with their
estimates. Ensure that learners use short cuts using
g the length of the number of days in weeks and months to make
ls. their working more ef cient than counting every day.
son took to
using what
te
es to check
many times
them to use Opportunities for display!
cember
se the Photograph the graphs and display the pictures
alongside the timelines and learners’ facts.
Ask learners to write facts about one of the circumnavigations, including how lo
journey was, in time, than each of the other circumnavigators. They should prese
length of time meaningfully, and think about how they could justify their choice
line.
Summary
Learners will have converted times in days, hours and minutes into months and i
calculated time differences.
Notes on the Learner’s Book
Calculating time (p70): learners order times by converting between hours, minut
seconds and solve problems involving calculating time.
More activities
How long? (individuals or small groups)
You will need access to internet or books with time facts of events and records
Ask learners to investigate the times taken for other journeys or events and to co
continuous activities.
Around the world (individuals or small groups)
You will need access to internet or books with time facts of events and records
Learners can find out what dates the other circumnavigations finished and work o
How fast? (individuals or pairs)
Learners could be challenged to find an approximate average speed, in kilometre
dividing that by the time in hours.
ong the journey took in different units of time and how much longer or shorter their
ent the time differences in the unit they think most effectively communicates the
e. They could calculate the time differences using written calculations or a time
into minutes and Check up!
tes and
Ask learners to write a fictional news report about
someone travelling from the North Pole to South Pole,
including start date, finish date and the time taken.
They should include some detail about the dates and
length of time of different sections of the journey.
s.
onvert them into different units of time, e.g. space flight, world records for
s.
out the start date.
es per hour, for each person, by finding out the distance around the world and
Core activity 18.1: Converting times 167
Core activity 18.2: Time zones
(1)
Resources: Time around the world photocopy master (p172). A globe. Modelling
Show learners the globe and identify your location on it. Make a small model of a pe
modelling dough and fix it in position on the globe. Use a torch to represent the sun a
globe to show how night and day occur. Make another small person out of the model
and fix it to the other side of the world. Demonstrate how, when one model is facing
the daytime, the other model is facing away from the sun, in the night- time. Ask the
small paper labels with times on the hour from 00:00 to 23:00.
Position the globe so that the model on your location is on the opposite side to the tor
would be at midnight. Place the label ‘00:00’ on the table beneath your model. Place
centre point of where the torch is shining. Ask learners to position the other times eq
along the equator around the globe. Explain that the paper labels show approximately
each zone around the world. Ask some children to look at the globe and labels and sa
time is in different places when it is midnight in your location. Rotate the globe so th
position is at 12:00. Ask some learners to use the labels to estimate the time in locati
world when it is midday at your location.
Give learners the Time around the world sheet. Explain that the times on the sheet are f
minute in many locations around the world. Give pairs of learners a world atlas and ask
locate the cities listed on the sheet. Ask:
“What is the difference in time between San Salvador and Reykjavik?” (Answer: 6 ho
“What is the difference in time between London and Athens?” (Answer: 2 hours)
“What is the difference in time between Moscow and Beijing?” (Answer: 4 hours)
“When it is 8.35 am in Buenos Aires, what time will it be in Islamabad?” (Answer: 4:3
“When it is 7.58 am in Washington DC, what time is it in Tokyo?” (Answer: 8:58 pm)
“When it is 10.30 am in Reykjavik, what time is it in Beijing?” (Answer: 5:30 pm)
“When it is 7.30 am in Lima, what time is it in Bangkok?” (Answer: 7:30 pm)
“When it is 9.45 pm in Canberra, what time is it in Rarotonga?” (Answer: 1:45 am)
Tell pairs of learners to choose four different locations from the Time around the world
them to imagine that they were setting up a video chat with children from these four pla
should investigate what time in their own location, if any, would be best for contacting a
children at the same time.
168 Unit 2B 18 Time
(2)
LB: p72
dough. Torch. World atlases.
erson with the Vocabulary
and turn the
lling dough time zone: area of the world with a common time.
g the sun, in There are 24 time zones.
class to make universal time: the time standard, originally measured
at Greenwich, England, sometimes called Greenwich
rch, as it Mean Time (GMT).
12:00 at the
qually spaced Look out for!
y the time in Learners who don’t know which sides to put their
ay what the
hat your times on. Show them that the globe turns to the
ions around the east, so their location would move towards the sun.
So, 00:01 should be east of their position.
for a single Opportunities for display!
them to
Ask groups of learners to create a poster showing what
ours) activities might be happening at the same instant
around the world at a particular time at your location.
35 pm) They should annotate the poster with the time in those
) places in the world.
sheet. Ask
aces. Pairs
all of these
Summary
Learners have investigated how different times around the world occur becaus
movement of the Earth in relation to the sun.
They have calculated time differences and times around the world, reading ana
using the 24-hour clock system.
Notes on the Learner’s Book
Time zones (1) (p72): learners solve problems involving approximately calculati
differences around the world.
More activities
What’s the time? (individuals or pairs)
Ask learners to investigate countries that have more than one time zone. Learner
Games Book (ISBN 9781107667815)
The time zone game (p71) is a game for two players. Players move their counters
se of the Check up!
alogue clocks and
Ask learners to write an explanation, with diagrams, of
ing time how and why time zones around the Earth have been
created.
rs should calculate the time differences in different cities in that country.
s through different time zones and calculate the time in each.
Core activity 18.2: Time zones (1) 169
During
During 2012 these five people were busy circumnavigating
Mike Hall took the round-the-world-cycling record, takin
Juliana Buhring also cycled around the globe. Her time w
Carlo Schmid flew solo around the world in 60 days, 17
Erden Eruç travelled around the world using only ‘huma
Loick Peyron and 14 crew sailed around the world in 45
Instructions on page 166
2012
g the Earth.
ng 91 days, 18 hours.
was 152 days, 1 hour.
hours and 22 minutes.
an power’ in 1026 days.
days, 13 hours and 43 seconds.
Original Material © Cambridge University Press, 2014
2012 C
January February
S MTWT F S SMTWT F S
1234567
8 9 10 11 12 13 14 1234
15 16 17 18 19 20 21 5 6 7 8 9 10 11
22 23 24 25 26 27 28 12 13 14 15 16 17 18
29 30 31 19 20 21 22 23 24 25
26 27 28 29
May June
S MTWT F S SMTWT F S
12345 12
6 7 8 9 10 11 12 3456789
13 14 15 16 17 18 19 10 11 12 13 14 15 16
20 21 22 23 24 25 26 17 18 19 20 21 22 23
27 28 29 30 31 24 25 26 27 28 29 30
September October
S MTWT F S SMTWT F S
1 123456
2345678 7 8 9 10 11 12 13
9 10 11 12 13 14 15 14 15 16 17 18 19 20
16 17 18 19 20 21 22 21 22 23 24 25 26 27
23 24 25 26 27 28 29 28 29 30 31
30
Instructions on page 166
Calendar 2012
y March April
S MTWT F S SMTWT F S
123 1234567
8 9 10 11 12 13 14
1 4 5 6 7 8 9 10 15 16 17 18 19 20 21
8 11 12 13 14 15 16 17 22 23 24 25 26 27 28
5 18 19 20 21 22 23 24 29 30
25 26 27 28 29 30 31
e July August
S MTWT F S SMTWT F S
1234567 1234
8 9 10 11 12 13 14 5 6 7 8 9 10 11
6 15 16 17 18 19 20 21 12 13 14 15 16 17 18
3 22 23 24 25 26 27 28 19 20 21 22 23 24 25
0 29 30 31 26 27 28 29 30 31
r November December
S MTWT F S SMTWT F S
123 1
3 4 5 6 7 8 9 10 2 3 4 5 6 7 8
0 11 12 13 14 15 16 17 9 10 11 12 13 14 15
7 18 19 20 21 22 23 24 16 17 18 19 20 21 22
25 26 27 28 29 30 23 24 25 26 27 28 29
30 31
Original Material © Cambridge University Press, 2014
Instructions on page 168
Original Material © Cambridge University Press, 2014
2B 19 Area and perimeter (2)
Quick reference
Core activity 19.1: Calculating area and perimeter (Learner’s Book p74)
Learners will practise and re ne their methods of estimating the area of an irreg
measure and calculate the perimeter and area of rectilinear and compound shape
Prior learning Objectives* – please note that listed objectives
fully across the book when taken
Measure and calculate the
perimeter of regular and 2B: Measure (Area and perimeter)
irregular polygons. 6Ma1 – Measure and calculate the perimete
6Ma2 – Estimate the area of an irregular sh
Understand area measured 6Ma3 – Calculate perimeter and area of sim
in square centimetres (cm²).
Use the formula for the area 2B: Problem solving (Using under
of a rectangle to calculate 6Ps1 – Explain why they chose a particular
the rectangle’s area. 6Ps2 – Deduce new information from existi
information has on another.
*for NRICH activities mapped to the Cambridge Primary
Vocabulary
No new vocabulary.
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
gular shape by counting squares. They will Area and perimet er (2)
es that can be split into rectangles.
Let’s investigate
s might only be partially covered within any given chapter but are covered this red and y ellow tile is 36 cm2. W at is htahteis
n as a whole area of the red part of the tile?
You c ou ld vis ua lise c uttin g the red
par ts off the tile an d p lac in g the m o n
th e y ello w
sq uare to com pare th e red an d y ello w area s.
1 At a community p icnic each family needs to lay down p icn ic blan kets
big eno ugh for all of their family to sit o n. The Veselova family needs
19 00 0 cm 2 . 2. You c o uld w or k o u t the aera
The Whitmore family needs 1 4 80 0 cm a of each b lan ket r s t atnhde n
en a d d toge ther
The Shah family need s 15 900 cm2. The com b ina tio n s of
Juwe family needs 15 3 00 cm2.
The Tharmarajah family needs 13 6 00 cm2. tw o b lan kets to ma ke the to tals
each f amily need s.
Each family will use two p icnic blan kets. Which blan kets sh ou ld they put
together to m a ke the correct area?BOl9an0lnyckmoenetl oCfanmgily can use each blan ket.
Bl a nk et A Blank et E
90cm long 90cm wide Blank et D
110cm wide
80cm wide Blank et B 90cm long 1m long
1m long 1m wide
70cm wide
Blank et F Blank et J
1m long
1m long
80c m
Bl a nk Blank et H Blank et I
110c m
80cm wideet G 120c m long
60c m wide long
80c l ong
60c m wide
m wide
7 0 cw i de
m
74
er and area of rectilinear shapes.
hape by counting squares.
mple compound shapes that can be split into rectangles.
rstanding and strategies in solving problems)
r method to perform a calculation and show working.
ing information and realise the effect that one piece of
objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 2B 173
Core activity 19.1: Calculating area and perimeter
Resources: Estimating area by counting squares photocopy master (p176). Makin
area of compound shapes photocopy master (p178). Scissors. Sticky tape
Give each group of learners a copy of the Estimating area by counting squares sheet
that some sort of food has been spilt on the T-shirt in the picture. The groups’ challen
to estimate the size of area that has been stained by the food. Tell them that, fortunate
design printed on the T-shirt was a grid of 1 cm squares!
Groups should discuss their method of counting the squares. They might ask different
of the group to count them in different ways to compare the solutions. Once they have
solution they should check that it is written in units of area and explain their reasons to t
about why they think their estimate is close to the actual area covered in food. (The area
food is approximately 16 cm2).
Remind learners of the model house rooms they made and the calculations they carri
out the area and perimeter of floor, windows, door and walls.
Show learners the Making compound shapes sheet. Ask learners to describe how the
nd the area of shape ‘A’. Demonstrate measuring the length and width of rectangle
nearest centimetre, then multiplying to find the area (15 cm2). Ask the learners to nd
rectangle ‘B’ in the same way (16 cm2). Cut out rectangles A and B and place them n
other, with sides touching, so that they create one shape. Secure the pieces together w
Ask learners what area the new shape has (31 cm2), and to explain how they know.
Give learners a copy of the ‘Making Compound Shapes Resource Sheet’. Challenge the
out the rectangles and combine them in different ways to make shapes with areas of:
28 cm2 (Answer: rectangles B & C or F & H)
34 cm2 (Answer: rectangles D & F)
27 cm2 (Answer: rectangles E & G)
Ask learners to discuss in pairs what are the largest and smallest areas they can make b
combining two of the rectangles on the Resource Sheet (Answer: 54 cm2 and 10 cm2).
learners can now investigate which areas can and cannot be made between 10 cm2 and
combining two of the rectangles on the resource sheet.
174 Unit 2B 19 Area and perimeter (2)
LB: p74
ng compound shapes photocopy master (p177). Finding the
t’. Tell them Look out for!
nge is Learners who are unsure of how many squares to
ely, the count. Remind learners that they can count whole or
part covered squares, and that they can count the
members squares more quickly in rows.
agreed a
the class Look out for!
a covered in Learners who are unsure what area is. As necessary,
remind learners that area is a measure of surface
ied out to work or coverage in two directions. Area is measured in
squares. The area of the rectangles on the resource
ey would sheet could be measured using one centimetre
‘A’ to the squares. The number of centimetre squares that
d the area of would cover the same area as the rectangle is the
next to each number of centimetres in each row multiplied by
with sticky tape. the number of rows. This means that the area of a
rectangle can be calculated by multiplying its length
em to cut by its width.
by
. Pairs of
d 54 cm2 by
Show learners the Finding the area of compound shapes sheet. Read through the
section of the sheet, explaining how the shapes can be divided into rectangles, th
each rectangle can be measured and calculated, and the area of the original shap
found. Ask learners to follow the instructions to find the area of the shapes at th
of the resource sheet. (Answers: 22 cm2, 26 cm2 and 33 cm2)
Ask groups of learners to compare and discuss the ways they divided the shapes o
resource sheet into rectangles, and their working and solutions.
Remind learners that perimeter is the length all the way around the sides of a shape
perimeter is measured using units of length. Ask learners to find the perimeters, to
centimetre, of the three shapes at the bottom of the Finding the area of compound
sheet. (Answers: 26 cm, 24 cm and 26 cm)
Learners should discuss in groups and then share with the class, if they have found
strategies for measuring and calculating the perimeter of the compound shapes ma
rectangles.
Summary
Learners have practised and re ned their methods of estimating the area of an
shape by counting squares.
They have measured and calculated the perimeter and area of rectilinear and c
shapes that can be split into rectangles.
Notes on the Learner’s Book
Area and perimeter (2) (p74): learners make compound shapes of specified area
They calculate the area and perimeter of rooms that are rectilinear and compoun
More activities
Rectangle patterns (individual)
Learners can make patterns by repeatedly adding congruent rectangles, they can
e.g.
Floor area (individual or small groups)
Learners can use dividing compound shapes into rectangles to find the floor area
Games Book (ISBN 9781107667815)
The compound area game (p75) is a game for two to four players. Players try to m
e top Look out for!
he area of Learners who become confused with the words of the units
pe can be used for perimeter and area of 2D shapes. Learners may find
he bottom it useful to stress the syllable ‘rim’ in ‘pe-rim-eter’ to help
them remember that it is a measure of something similar to
on the the edge of a container.
e, so Look out for!
o the nearest Learners who quickly recognise that the perimeter of the
compound shapes in these sheets is the same as the
shapes perimeter of the smallest rectangle the shape could t
inside. Get them to investigate whether this is true for shapes
d any good made from more than two rectangles (Answer: not always).
ade from two
n irregular Check up!
compound
Place two books on a table top so that they do not make
a using rectangles. a rectangle, but sides are touching. Ask learners to nd
nd. the area and perimeter of each book, and the area and
perimeter of the shape made by the two books.
record the area and perimeter of the shape as each rectangle is added.
a of rooms in the school that can be divided into two or more rectangles.
make a shape using two rectangles that matches the area written on a card. 175
Core activity 19.1: Calculating area and perimeter
Estimating area by c
Instructions on page 174
counting squares
Original Material © Cambridge University Press, 2014
Making compound shapes
A
B
CD
E F
G H
Instructions on page 174 Original Material © Cambridge University Press, 2014
Finding the area of compound shapes
To find the area of a shape like this, try
dividing it into two or more rectangles.
Find the area of each rectangle, then the
total area of all the rectangles that make
the shape.
This shape can be split into two
rectangles in these different ways.
Left rectangle has an area of 5 cm × 2 cm = 10 cm2
Right rectangle has an area of 3 cm × 4 cm = 12 cm2
Top rectangle has an area of 8 cm × 2 cm = 16 cm2
Bottom rectangle has an area of 3 cm × 2 cm = 6 cm2
The total area of the shape is 22 cm2.
Instructions on page 175 Original Material © Cambridge University Press, 2014
Draw a line on each of these shapes to divide it into two rectangles.
Work out the area of each new rectangle by multiplying the lengths
of the sides. Then calculate the area of the whole shape.
7 cm 6 cm
4 cm 1 cm
5 cm 4 cm 4 cm
6 cm
2 cm 1 cm
3 cm 3 cm
3 cm
3 cm
2 cm
3 cm 7 cm
3 cm
4 cm
5 cm
Instructions on page 175 Original Material © Cambridge University Press, 2014
2C 20 Graphs, charts and tables
Quick reference
Core activity 20.1: Tables and line graphs (Learner’s Book
pL7e6a)rners extract information from and represent information in tables and lines g
Core activity 20.2: Pie charts (Learner’s Book p78)
Learners learn to interpret pie charts.
Prior learning
• Answer a set of related questions by collecting, selecting and organising rele
data; draw conclusions from their own and others’ data and identify further
questions to ask.
• Draw and interpret frequency tables, pictograms and bar charts, with the verti
axis labelled for example in twos, fives, tens, twenties or hundreds. Conside
effect of changing the scale on the vertical axis.
• Construct simple line graphs, e.g. to show changes in temperature over time.
• Understand where intermediate points have and do not have meaning, e.g.
comparing a line graph of temperature against time with a graph of class
attendance for each day of the week.
• Relate finding fractions to division and use to find simple fractions of quantitie
• Understand percentage as the number of parts in every 100 and find simple
percentages of quantities.
• Express halves, tenths and hundredths as percentages.
• Know that US ‘cup’ measurements can be used for mass and capacity.
Vocabulary
line graph • ready reckoner • pie chart
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Handling data
Pie charts Vocabulary
Graph s a nd tab les Vocabulary Let’s investigate pie chart: a graph
George’s friends voted on what they wanted to do using a divided circle
Let’s investigate line graph:a graph
during their holiday. Complete the key from the clues. wher e each section
represents part of the
This graph shows how much water had dripped from that uses one or more a leaky
tap in five minutes. Use the graph to work out lines to join points how much water Holiday activities total.
would have dripped from the tap in that represent data. an hour. ready reckoner:a Clue s
graphs. 800 table of numbers ● Volleyball was
700 used to help Key more popula r
600 calculate or convert
50 0 than horse ridin g
400 between units.
Water ● Swimming had
30 0(millilitr es)
over 40% of the
20 0
10 0 votes.
● Less than 10%
0
0 1 Tim2 e (minu3 tes) 4 5 1 A pet shop sells a range of sh.This opifethcehafrtrienshdosws the
sh that were sold in one week. voted for
1 Copy and complete the currency conversion table. (a) What is the most common typetroafmgpolodlisnhi?ng.
Jap ane se Yen (¥) Euro (€) US Doll ars ( $) (b) If a total of 50 gold sh were sold in that
week,estimate the number of each type
130 1 130
2 of gold sh sold. Gold sh
5 • Common Gold sh. Oranda
10 gol d s h
20 • Fantail Gold sh.
50 • Oranda Gold sh.
100 Fantail
gold s h
2 (a) How many Japanese Yen are equivalent to €20?
(b) How many US Dollars are equivalent to ¥1300? Co mm on
(c) How many Euros are equivalent to $6.50? gold s h
(d) How many Japanese Yen are equivalent to €6?
(e) How many US Dollars are equivalent to ¥3900?
(f) How many Euros are equivalent to $71.50?
76 78
Objectives* – please note that listed objectives might only be partially covered
within any given chapter but are covered fully across the book when
taken as a whole
evant 2C: Handling data (Organising, categorising and representing
tical data)
er the 6Dh1 – Solve a problem by representing, extracting and interpreting
.
data in tables, graphs, charts and diagrams for example: line
es. graphs for distance/time, a price ‘ready reckoner’, currency
conversion; frequency tables and bar charts with grouped
discrete data.
2C: Problem solving (Using understanding and strategies in
solving problems)
6Ps6 – Make sense of and solve word problems, single and multi-step
(all four operations), and represent them, e.g. with diagrams
or on a number line; use brackets to show the series of
calculations necessary.
*for NRICH activities mapped to the Cambridge Primary objectives,
please visit www.cie.org.uk/cambridgeprimarymaths
Unit 2C 181
Core activity 20.1: Tables and line
graphs
Resources: Conversion tables and graphs photocopy master (p186). (Optional:
internet); equipment for experiment of choice.
Give learners the Conversion tables and graphs sheet. Talk about the ready reckoner
converting between US cups and millilitres and the line graph for cups and grams. Yo
to remind learners that the US cup can be used as a measure of both capacity and ma
the learners to complete question 1 on the sheet (Answer: 960 ml and 600 g). Demo
to answer question 1(b), using a straight edge to draw a line up from 4 cups on the gr
the amount in grams. Point out the key features of a line graph, i.e. the title, the axis
axis scales going up in regular intervals. Learners should check that they found the sa
Ask learners for any advice they can share with the class for accurately reading the ta
graph. Remind learners that the line on the graph shows continuous data. Demonstrat
point on the line can be read as cups and as grams.
Learners should complete the remainder of the sheet and then compare their methods a
solutions with other learners in a small group.
Ask learners to reflect on and discuss which is easier to use, the ready reckoner or th
graph. As necessary, add to the discussion that for cup amounts that are on the ready-
it is easier to use that because they can be read straight off the table, for amounts bet
values it might be easier to read the conversion off the line graph.
Learners should use the information in the resource sheet line graph to make a ready
cups to grams, by selecting points on the line and recording them in both grams and
Ask learners to discuss, in small groups, how they will go about drawing a similar line gr
the conversion, and the relationship, between cups and millilitres on squared paper. Eac
should then draw the graph and compare the graph with those of their group.
182 Unit 2C 20 Graphs, charts and tables
LB: p76
recipe books with amounts in US cup measures (or access to the
for Vocabulary
You may need
mass. Then tell line graph: a graph that uses one or more lines to join
onstrate how points that represent data.
ready reckoner: a table of numbers used to help
raph to nd calculate or convert between units.
labels, the
same answers. Look out for!
able or the Learners who do not find the correct solutions.
te that any Encourage them to annotate the graph by drawing
lines from the x-axis and the y-axis to the point on the
and line that they are trying to convert. Ensure that the
lines they draw are at right angles to the axis. For
he line questions where they need to round to the nearest
- reckoner
tween 11
reckoner for 2 cup, encourage learners to mark the 2 cups on the
cups. horizontal axis by measuring the interval between the
cup divisions and halving it.
raph to show
ch learner Opportunities for display!
Display the learners’ conversion graphs.
Summary
Learners will have extracted information from, and represent information in, tabl
graphs.
Notes on the Learner’s Book
Graphs and tables (p76): learners extract and interpret data in tables and line gra
construct their own line graphs and bar charts to represent data.
More activities
Recipe converter (individual or pairs)
You will need recipe books with amounts in US cup measures (or access to the
Learners can find recipes (online or in books) that are given in US cup amounts
Experiments (small groups or whole class)
You will need equipment for experiment of choice.
Learners could draw a line graph linked to a scientific investigation, which is no
th e temperature of water as it is heated
th e growth of a plant over time
th e amount of liquid in a container as it evaporates.
les and line Check up!
aphs. They
Tell learners that in some shops 1 kg potatoes can be
bought for $1.50. Ask them to make a ready-reckoner
and a line graph to show prices of potatoes from 100 g to
10 kg.
e internet).
s and convert the measurement using their ready reckoner or line graph.
ot necessarily a straight line. For example:
Core activity 20.1: Tables and line graphs 183
Core activity 20.2: Pie charts
Resources: Favourite foods pie charts photocopy master (p187). Comparing ba
paper. Metre sticks. (Optional: newspapers or magazines with pie charts (or access t
Display the pie charts on the Favourite foods pie charts photocopy master. Ask learne
use what they know about fractions of a shape to say what fraction of children chose
each flavour of crisps in ‘Red Group’ and in ‘Blue Group’. Ask learners to write dow
number of children that would have chosen each flavour if the groups had eight child
them. Demonstrate how the pie chart represents the data by arranging eight learners i
circle. Place three metre sticks in the circle to divide it up as the ‘Red Group’ pie cha
Key
Learner
Metre stick
Ask learners to label the three sections of the human pie chart with the flavour, the fr
the number of learners. Tell learners that the size of the sections of the pie chart are
as percentages. Remind them that the whole set is 100% and ask three learners to lab
sections with 50%, 25% and 25%. Repeat the activity with the ‘Blue Group’ pie char
sections have been labelled with percentages add eight more learners to the circle, as
of the ‘Blue Group’ had been 16. Ask learners to rearrange the metre sticks and repl
labels that need replacing. They should find that only the number of learners has cha
fraction and percentage of the whole is the same.
Ask learners to solve the word problems on the resource sheet. They should write down
calculations they use, using brackets as necessary, and compare their methods and sol
a partner (Answer: (1) 9, (2) 18).
Tell learners that pie charts provide similar information to bar graphs. They can both
easily compare different parts of a set of data, but with a pie chart it is easier to also
184 Unit 2C 20 Graphs, charts and tables
LB:
p78
ar graphs and pie charts photocopy master (p188). Rulers. Squared
to the internet).)
ners to Vocabulary
wn the pie chart: a graph using a divided circle where each
dren in section represents part of the total.
into a
art, i.e.
raction and Look out for!
often given
bel the Learners who are unsure about fractions and
rt. After the percentages. As necessary, remind them of their
s if the size learning in Stage 5 about finding simple fractions and
lace any percentages of quantities.
anged, the
n the
utions with
be used to
compare parts to the whole set of data. Show them the Comparing bar graphs an
sheet as an example.
Ask learners to conduct their own survey of ten children where they will choose bet
options of food. They should represent the data collected by completing the third pi
Favourite foods pie charts sheet (each section is one tenth or 10% on the chart). Le
write statements about the data represented. They could use the sentence template
(fraction/percentage) of the group chose .
More than (fraction/percentage) of the group chose .
Summary
Learners will have learnt to interpret pie charts.
Notes on the Learner’s Book
Pie charts (p78): learners estimate the number that sectors of a pie chart represe
extract and interpret data from a pie chart and present it in the form of a bar char
More activities
In the news (individual or pairs)
You will need newspapers or magazines with pie charts (or access to the intern
Learners can find examples of pie charts online or in newpapers or magazines. T
each chart.
Different charts (individual)
Learners could represent the data collected for their pie chart (in the core activity
clarity, precision, and efficiency.
Games Book (ISBN 9781107667815)
The pie chart game (p106) is a game for two players. Each player starts with 50%
largest percentage of the pie chart at the end of the game is the winner.
and pie charts Look out for!
tween three Learners who quickly complete the ten section pie
ie chart on the
earners should chart. As appropriate, challenge learners to use a
es such as:
different size set of data that can easily be marked on
ent. They
rt. the pie chart, e.g. 5, 20, 30 or 40. Ask them how
many people each 10% or 1 interval on the pie chart
represents. 10
Opportunities for display!
Display learners’ pie charts with the statements they
have made about the data represented in them.
Check up!
Ask learners to talk about, and answers questions on, the
pie chart they have made.
net).
They should write a series of statements that are true about the data represented in
y) using different charts and graphs. They can compare the representations for
% of a pie chart. They add on percentages using a spinner. The player with the
Core activity 20.2: Pie charts 185
Conversion tables and graphs
US cups can be used to measure capacity and mass.
This ‘ready reckoner’ table converts between US cups and millilitres.
cups (US) millilitres
1 240
2 480
3 720
4 960
5
10 1200
20 2400
4800
This line graph converts between US cups and grams.
2000 Conversion between US cups and gr ams
1800
1600
1400
Mass in grams 1200
1000
800
600
400
200
0
0 1 2 3 4 5 6 7 8 9 10 11 12
US
cups
1. (a How many millilitres are equivalent to 4 US cups?
) How many grams are equivalent to 4 US cups?
2. C(bonvert these measurements to the nearest 1 cup, using the ready
2
)reckoner table and the line graph.
(a) 700 ml
(b) 1 litre
(c) 0.8 kg
(d) 100 g
3. Use the ready reckoner table and the line graph to work out how many
millilitres and how many grams are equivalent to 15 cups.
Instructions on page 184 Original Material © Cambridge University Press, 2014
Favourite food pie charts
Our favourite flavours
of crisps in Blue Group
and Red Group
Red Group Blue Group
Ready salted Cheese and Ready
onion salted
Salt and Salt and
vinegar vinegar
Cheese and
onion
1. If there were 12 children in Red Group, how many children did not
choose cheese and onion?
2. If there were 24 children in Blue Group, how many children chose
cheese and onion?
Title:
Instructions on page 184 Key
Original Material © Cambridge University Press, 2014
Comparing bar graphs and pie charts
There were four candidates running for election.
Here are the results.
Candidate 1 says: “Look at the bar graph. I got more votes than each of
the other candidates.”
Votes cast
40
35
Percentage of the vote 30
25
20
15
10
5
0 23 4
1 Candidate
The other candidates say: “Look at the pie chart. More people voted
against Candidate 1 than for Candidate 1.”
Votes cast
Candidates
1
2
3
4
Instructions on page 185 Original Material © Cambridge University Press, 2014
2C 21 Statistics
Quick reference
Core activity 21.1: The three averages (Learner’s Book p80)
Learners find the mode, median, mean and range of sets of data. They use brack
calculations necessary to work out the mean of a set of data.
Core activity 21.2: Using statistics to persuade (Learner’s Book p82)
Learners explore how statistics are used, and use statistics themselves to form a
Prior learning Objectives* – please note that listed objective
across the book when taken as
Answer a set of related
questions by collecting, 2C: Handling data (Organising, ca
selecting and organising 6Dh2 – Find the mode and range of a set o
relevant data. 6Dh3 – Begin to find the median and mean
Draw conclusions from their 6Dh4 – Explore how statistics are used in e
own and others’ data and
identify further questions to 2C: Problem solving (Using unde
ask. 6Ps2 – Deduce new information from exist
Find and interpret the mode
of a set of data. information has on another.
6Ps6 – Make sense of and solve word pro
them, e.g. with diagrams or on a nu
necessary.
*for NRICH activities mapped to the Cambridge Primar
Vocabulary
average mode mean median range statistics
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Average an d ran ge Vocabulary U sin g sta tistic s
Let’s investigate
average: a measure Let’s investigate
used to nd the middle The council are planning transport for learners to and from school. This is what
of a set of data. they found out about how 9 year old and 13 year old learners get to school.
kets to show the series of The mean average of the numbers on these cards is 5. mode:a type of average, Kwealk Kwealk Describe the difference
persuasive argument. What number is on the fifth card? the value ybu s ybu s between how 9 year olds
and 13 year olds go to
1 Kali, Summer,Benji and Kyle and in aoscectuorfsdtahteamthaotst. car car school. What could be
learning to skip. mean: a type of the explanations for these
Whilethey were practisingthey cycle cycle
recorded how many skips they average, calculated other other differences?
did in a row. by nding the total
Here are their attempts: of all the values 1 The four countries of Fratania,Spanila, Brimland Vocabulary
in the set of data and Gretilli celebrate a dry weather festival
and dividing by the
during the months of January to May.They statistics:the collection, are each
number of values.
median: a type of trying to encourage tourists to visit organization,
average, the middle their own countries. Here are graphs of each presentation, country’s rainfall
value in a set of values
ordered from least to last year for the ve months of interpretation and the festival. analysis of
greatest.
data.
7
KaBliu s 1st 2n d 3rd 4th 5th 6th 7t 0 range: from the Fratania Sp anila
Sum mer 6566 8 11 2 lowest to the highest 12 0 12 0
Benji 0try h7 4 value.
try3 try 0 try 3 try 8 try 4 11 0 11 0
Kyle 0 01 0 0tr R a i nf al l R a i nf al l
2 in mm in mm
4 7 76 5y 10 0 10 0
(a) Copy and complete this table: (b) Who do you think has 90 90
80 MJ a anur ac rhy A pr il 80
Ran ge Mode Median Mean been most successful Fe bAr uprairly Ma rMca hy May Januar y Febr u ar y
at skipping?
Kali
Sum mer Explain your answer Brimla nd Gretilli
Be nji using the information 12 0 12 0
Kyle R a i nf al l R a i nf al l
in your table. in mm in mm
11 0 11 0
80 10 0 10 0
90 Fe bAr uprairly Ma rMca hy 90 May Januar y Febr u ar y
80 JMa anur ac rhy A pr il 80
82
es might only be partially covered within any given chapter but are covered fully
a whole
ategorising and representing data)
of data from relevant situations e.g. scientific experiments.
n of a set of data.
everyday life.
erstanding and strategies in solving problems)
ting information and realise the effect that one piece of
oblems, single and multi-step (all four operations), and represent
umber line; use brackets to show the series of calculations
ry objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 2C 189
Core activity 21.1: The three averages
Resources: Finding mode and median averages photocopy master (p197). Rolli
Resources for learners’ experiments.
Pose learners this question to discuss in pairs (display the question written on the bo
“On average, how many days are there in a month?”
Ask three or four pairs to recount their discussion to the class. Ask learners to describ
think ‘average’ is in a sentence on a sticky note of paper and display the definitions
by sticking the notes to the board. If possible, choose some notes that accurately desc
‘average’ and read them to the class. Brie y explain that ‘average’ is a term used for o
information that provides useful information about a whole set of data.
Remind learners that in Stage 5 they worked out the mode of a set of data. This is a t
average that provides information about the most popular or frequent value in a set of
Ask learners to write down the number of days in each month (to simplify, do not co
years), starting with January. (Answer: 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)
Ask learners, “Which is the most frequent number of days in a month?” Explain that
mode, there are on average 31 days in a month. Discuss with learners whether ‘31’ pr
useful piece of information about the set of numbers of days in months. This discussi
include:
yes, it tells us the most common number of days in a month
no, five month have less than 31 days, and no months have more than 31 days.
Write this set of data on the board:
10, 12, 13, 15, 15, 18, 19, 19, 20, 31, 31, 31
Ask learners to imagine that instead of the months we use, another civilization divided
calendar up into these months. Again the mode of this set would be 31. Although 31 i
common number of days, it does not helpfully represent the whole set of data.
Tell learners that ‘range’ is useful for comparing sets of data. Tell them that range is no
average, it tells us the difference between the lowest and highest value in a set of data.
range of a set of data subtract the lowest value from the highest value.
190 Unit 2C 21 Statistics
LB: p80
ing cars photocopy master (p199). Calculators. Sticky notes.
oard): Vocabulary
be what they average: a measure used to find the middle of a set of
cribe data.
one piece of
mode: a type of average, the value in a set of data that
type of occurs the most.
f data. mean: a type of average, calculated by finding the total
onsider leap of all the values in the set of data and dividing by the
number of values.
median: a type of average, the middle value in a set of
values ordered from least to greatest.
range: from the lowest to the highest value.
31 is the Teacher note:
rovides a Use learners’ description of ‘average’ to informally
sion should
assess prior knowledge and understanding.
d their
is the most
ot an
To find the
Ask learners to work in pairs to look at the two sets of data (the real and imaginary
months) and write down the range of each set of data. Ask them to write a statemen
data using the mode and range, e.g. ‘The average number of days in the months is
of days is from 28 to 31 so the range is 3.’ and ‘The average number of days in the
months is 31, the number of days is from 10 to 31 so the range is 21.’
Tell learners that by presenting the average and the range they are making a usef
provides information about the whole set of data.
Tell learners that they are going to learn about other types of average. Explain th
average is the middle value when the data is written in order from least to greates
learners in height order, from shortest to tallest. Count the number of learners,
find the middle point in the line and declare the learner (or learners) at this point
average height for the class. The range is the shortest to the tallest learner.
Ask learners to write out the real number of days in each month again, this time
size from least to greatest, i.e. 28, 30, 30, 30, 30, 31, 31 , 31, 31, 31, 31, 31
As there is an even number of pieces of data in this set, the median is half way b
middle values. In this case the median average is 31, the same as the mode avera
learners to find the median average of the imaginary number of days in the mon
board (Answer: 18.5).
Give learners the Finding mode and median averages sheet. Ask learners to comp
with a partner where asked.
Tell learners that the third average they are learning about in this session is the ‘m
type of average that most people are referring to when they say ‘average’. The m
found by finding the total of all the data, then dividing that total by the number o
data. Learners might find it useful to think about it as ‘if all the values were
shared equally, what would every number be?’ Demonstrate calculating the avera
days in a month on a calculator. Give learners calculators so that they can calcula
the same time, following the same steps on the calculator: (28 + 30 + 30 + 30 + 3
31 + 31 + 31 + 31 + 31) ÷ 12 = 30.416667. Write the calculation on the board an
each part means.
Tell learners that to work out the median and mean averages the data must be num
days in the Look out for!
nt for each set of
s 31, the number Learners who are unsure how to write their statements.
e imaginary As necessary, provide sentences templates/stems to help
learners to express that they have found out as a
ful statement that sentence.
hat the median Look out for!
st. Arrange the
Learners who may have difficulty keeping track of
t the median where they are in a sequence of numbers when
inputting them into the calculator, or who might
e in order of make a mistake halfway through the list and
feel they need to start at the beginning. Some
between the calculators, including computer on-screen calculators,
age. Tell list all of the entries as they are made. Show learners
nth listed on the how to use the ‘Clear Entry’ function on their
calculator (sometimes shown as ‘CE’ or ‘C’) to
plete the sheet, only clear the last entry and carry on with the
calculation.
mean’. It is the
mean average is
of pieces of
age number of
ate the mean at
30 + 31 + 31 +
nd explain what
merical.
Core activity 21.1: The three 191
averages