culate the times that Look out for!
e times to the local
ces to find out the Learners who have difficulty with time differences.
e differences. As necessary, encourage them to use a time line to
calculate time differences.
mers sheet. Tell
Glasgow airport.
ch flight they should
uest. For others there
p should discuss and
es to write their own
nother group using the
s are local times so Note
The last problem is challenging as it involves
aving at 18:30 on crossing the international date line. This problem
at 09:20 on Thursday may be more appropriate to solve as a whole class,
ago, Chile. Your once learners have had a short while thinking about
g was the flight? it.
they have Check up!
the world.
Ask learners to select two cities on a world map and
es using analogue estimate then find out the time difference between
f flights between the the two cities. Ask them to suggest what the time
might be in each city when children in the other city
are starting school in the morning.
Core activity 31.1: Time zones (2) 275
More activities
Fly away (pairs)
You will need flight timetables or holiday brochures with flight timetables.
Give learners local flight timetables or holiday brochures with flight timetables in so
times of planes travelling to different time zones from their own country or locality.
Time travel (individual or pairs)
Learners can debate whether they think that flying from the Hawaiian Islands to the L
Games Book (ISBN 9781107667815)
Time intervals game (p78) is a game for four players. Players collect cards when their
collects the most cards is the winner.
276 Unit 3B 31 Time (3)
that they can pose and answer questions about the flight times and arrival
Line Islands can be called ‘time travel’.
r time card has the greatest difference to/from a base card. The learner who
Blank page 277
Core activity 31.2 Leap years
Resources: Calendar template photocopy master (p284). Calculating leap years p
blue) ball. Sticky notes.
Ask learners, “Which year was the most recent leap year?” “When will the next lea
Remind them that a leap year is a year with an extra day (February 29th), used t
calendar to keep it in line with the Earth’s orbit around the Sun.
Demonstrate an orbit by placing a large ball on the table and moving a smaller b
ellipse around it. (You may want to show the smaller ball turning and say that it doe
an exact number of times when it goes once round the large ball.)
It takes approximately 365 1 days for the Earth to orbit the sun.
4
Show learners the Calculating leap years sheet. Display the resource sheet on the wa
learners to write a year (either in the past or future) on a sticky note and then place th
on the wall under the outcome for that number on the diagram.
The Iranian Solar Hijri calendar has eight leap years in a cycle of 33 years. Ask learn
work out how many leap years there could be in 33 years of the Gregorian calendar
(Answer: 8, sometimes 9, rarely 7). The Solar Hijri calendar is closer to the true nu
takes for the Earth to orbit the Sun in that time.
Ask learners to find out what day of the week their birthday will fall for the next five years
predict the day of the week it will fall on for the following five years, then check using a c
should discuss how they made their prediction, and whether it was accurate, with a part
a class.
Divide the class into 12 groups. Allocate each group one month and ask them to work ou
would look on a calendar in the year 40 years from now, then use the Calendar template
month’s page of the calendar. Put the pages together to make a calendar for 40 years into
278 Unit 3B 31 Time (3)
LB: p114
photocopy master (p283). A large (yellow) ball and a smaller (green or
ap year be?” Vocabulary
to adjust the
leap year: a year with 366 days.
ball in a circle or orbit: the path a planet takes around the sun (or a
es not always turn moon around a planet).
all. Ask Look out for!
he sticky note
Learners who are unsure that a number is a
ners to multiple of 4. If necessary, show learners how
to check by dividing the number by 4 using a
umber of days it written method or on a calculator to see if the
answer is a whole number.
s. Ask them to
calendar. They Learners who can divide conf idently. Challenge
tner and then as them to find a way of identifying multiples of 4
without needing to divide (for example that the
ut how that month last two digits alone are a multiple of 4). They
to make their should check their method by trying a range of
o the future. numbers.
Summary
Learners have investigated how calendars relate to the orbit of the Earth aroun
use of leap years to adjust the calendar to match the cycle.
Learners have calculated time intervals in days, weeks and months, using thei
calendars and leap years.
Notes on the Learner’s Book
It’s a date (p114): learners calculate the day of the week of different dates using
knowledge about leap years and days, weeks and months.
More activities
Learners can investigate and compare different calendars such as the Gregorian,
dates of significance (such as the current date or their birth date) according to th
nd the Sun, and the Check up!
ir knowledge of
Ask learners if the following are multiples of 4:
g a calendar and 28, 46, 116, 2000, 2014, 2308.
Ask learners if the following will be leap years
and how they know:
2024, 2042, 2062, 2072, 2084.
Solar Hijri, the Vikram Samvat and the Hebrew Calendar. They can find out
he different calendars.
Core activity 31.2: Leap years 279
Time Zon
10 9 8 7 6 5 4 3 2 1 0 1
12 11 10 9 8 7 6 5 4 3 2 1 0 1
Instructions on page 274
ne Map
1 2 3 4 5 6 7 8 9 10 11 12
Equator
1 2 3 4 5 6 7 8 9 10 11 12
(Time Zones are approximate)
Original Material © Cambridge University Press, 2014
Flight t
Summertime Flights from
Destination Airport Length of Flight F
Bourgas, Bulgaria 33 hours
Corfu 4
Heraklion, Crete
Larnaca, Cyprus 3 3 hours
4
41 hours
4
5 hours
Paphos, Cyprus 5 hours
Sharm El Shekh, Egypt
53 hours
Florida, USA
4
Madeira
Enfidha, Tunisia 91 hours
Antalya, Turkey
Dalaman, Turkey 4
4 hours
31 hours
2
41 hours
2
41 hours
2
Instructions on page 275
timetable
m Glasgow Airport, Scotland.
Flight Code Departure Day Departure Time
46812 Friday 18:55
46813 Monday 21:30
47009 Friday 06:40
16:30
47121 Tuesday 09:00
47125 Sunday 14:55
47126 Wednesday 19:35
47127 Wednesday 09:15
47288 Sunday 21:25
47289 Wednesday 13:55
48444 Saturday 22:45
16:35
48445 Thursday 11:45
48446 Wednesday 06:05
49035 08:50
Sunday 21:40
16:50
49036 Tuesday
50162 Monday 15:20
50618 Sunday
51041 Tuesday 09:45
20:10
51042 Friday
51043 Monday
51044 Thursday
Original Material © Cambridge University Press, 2014
Travel agent customers
✂ I’d like a flight I’d like a flight to
leaving Glasgow North Africa, to get
I’d like a flight to after 4pm to Turkey. there by 9am
Cyprus that arrives Monday morning.
before 3pm, local
time.
I’d like a flight that is I need a flight to I need a flight to
less than 4 hours long Florida to get me Cyprus to arrive
for a short break there by 10am on Wednesday evening.
from Friday to Tuesday, local time.
Monday.
I’d like a flight to I would like some Where does the last
sunshine. What flight flight on Tuesday
Turkey for my will take me furthest from Glasgow go to?
sister’s birthday on south on Monday?
Friday.
Instructions on page 275 Original Material © Cambridge University Press, 2014
Calculating leap years
Is the year a
multiple of 400?
Yes No
Is the year a
multiple of 100?
Yes No
Is the year a
multiple of 4?
No Yes
Leap Year Not a Leap Year Not a Leap Year Leap Year
Instructions on page 278 Original Material © Cambridge University Press, 2014
Calendar template
Month . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Instructions on page 278 Original Material © Cambridge University Press, 2014
3B 32 Area and perimeter (3)
Quick reference
Core activity 32.1: Rectangles (Learner’s Book p115)
Learners investigate the area and perimeter of rectangles and squares. They use t
calculating area.
Core activity 32.2: Irregular shapes (Learner’s Book p118)
Learners work out the approximate area of irregular shapes, including parallelogr
counting squares.
Prior learning Objectives* – please note th
across the boo
• Measure and calculate the perimeter of
regular and irregular polygons. 3B: Measure (Area a
6Ma1 – Measure and calcula
• Understand area measured in square 6Ma2 – Estimate the area of
centimetres (cm²) 6Ma3 – Calculate perimeter
• Use the formula for the area of a rectangle 3A: Number and pr
to calculate the rectangle’s area. 6Nc7 – Use place value and
3B: Problem solvin
6Ps2 – Deduce new informa
has on another.
6Ps4 – Use ordered lists or
3A: Problem solvin
6Ps5 – Identify relationships
and letters, e.g. the s
multiples of 3 minus
*for NRICH activities mapped to the C
Vocabulary
formula
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Area and perimeter of rectangles Area and perimet er o f irregu lar shapes
Let’s investigate Let’s investigate
Dav id to o k tw o pa pe r s qu ares. E ac h s quare ha d a n
T ia sa yss:: area of 4 c m 2 .
He arra n ged s o that a c or ne r of e ac h s qu are w as a t
I c a n double the a rea th e ce ntre of the o ther sq uare, like this :
W ha t area d oe s th e arran geme nt co ver ?
o f a re cta n g le by
1 Baby Jamie is a mes sy eater. Work ou t the area of each stain on his bib. (Th is is a s quare
doubling centimetre grid.)
the formula for th e le n g th a n d d o u b lin g
rams, by
the width.
Is T ia c orrect? E x plain y o ur a ns wer.
1 What is the area and perimeter of the front covers of these maga zines ?
(a) (b)
28 cm 28 cm (a)
(c)
20 cm10 cm 13 cm9.7 cm (b)
(c) (d) (e) (d)
16.5 cm9.5 cm 19 cm
(e)
115 11 8
10.5 cm
hat listed objectives might only be partially covered within any given chapter but are covered fully
ok when taken as a whole
and perimeter)
ate the perimeter and area of rectilinear shapes.
f an irregular shape by counting squares.
and area of simple compound shapes that can be split into rectangles.
roblem solving
d multiplication facts to multiply/divide mentally, e.g. 0.8 × 7, 4.8 ÷ 6
ng (Using techniques and skills in solving mathematical problems)
ation from existing information and realise the effect that one piece of information
tables to help solve problems systematically.
ng (Using understanding and strategies in solving problems)
s between numbers and make generalised statements using words, then symbols
second number is twice the first number plus 5 (n, 2n + 5); all the numbers are
1 (3n – 1); the sum of angles in a triangle is 180°.
Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 3B 285
3 cmCore activity 32.1: Rectangles
Resources: Rectangles photocopy master (p292). (Optional: sheets of blank A3 pa
By now, learners should be con dent in calculating the area of a rectangle by multipl
of the rectangle by the width. Explain to the learners that ‘area = length × width’ is k
formula. Explain what we mean by the term formula. Tell learners that formulas use
symbols rather than words, and therefore it is a short way of showing a relationship b
Display the formula l × w = A, and explain that this is a short way of showing that th
multiplied by the width (w) equals the area (A).
Tell learners that the lengths of the sides of a rectangle are not necessarily a whole nu
centimetres. Ask them to measure and mark the lengths of the sides of the rectangles
Rectangles photocopy master in centimetres, telling them that one pair of the sides on
has a length that is not whole centimetres and they should measure to the nearest
0.1 cm. Encourage learners to estimate lengths first and check that their measuremen
reasonable. Once they have measured the sides and labelled them on the rectangles, a
mark one centimetre divisions on rectangle A along the sides and join them to create
squares (and 0.5 cm squares), e.g.
A
7.5 cm
Point out that the area of the rectangles can be seen as three rows of 7.5 cm squares. C
squares to show that there are 21 whole squares and three half squares, making 22
altogether. Make sure learners understand that the formula for the area of a rectangle
286 Unit 3B 32 Area and perimeter (3)
LB: p115
aper (or two sheets of A4 stuck together).)
lying the length Vocabulary
known as a
formula: is a rule to describe the relationship
letters and between amounts; it normally uses symbols instead
between numbers. of words.
he length (l)
umber of Opportunities for display!
s on the Display the formula for area of a rectangle and the
n each rectangle reverse formulas for finding width or length.
nts are Look out for!
ask learners to Learners who do not put any units for area
e a grid of 1cm
or just put cm. Remind them to use the cm2
Count the notation for recording area in centimetre
squares.
1 squares Learners who are unsure about multiplying a
2 whole number and a number with a decimal
place. Remind them of the following techniques:
repeated addition of the number with the
decimal place
using known number facts and adjusting
using an efficient method of multiplication.
is also true
for lengths and widths that are not whole numbers. Remind learners of the formu
replace the letters with the measurements of rectangle A.
lxw=A
l = 7.5 w = 3
So A = 7.5 x 3 = 22.5 cm2.
Rectangle B measures 5 cm by 4.7 cm. Ask learners to calculate the area of the r
replacing 5 and 4.7 in the formula (Answer: 23.5 cm2). To check their calculatio
learners can draw one centimetre squares on the rectangle in the same way as rec
Discuss with learners how they could calculate the perimeter of each of the rect
adding the length of the four sides
adding the length of two adjacent sides, then doubling
doubling the length of two of the adjacent sides, then adding together.
Learners should find the area and perimeter of the other rectangles on the Rectang
master and compare their answers and methods with a partner.
Pairs of learners discuss and then investigate how they could cut, or stick together,
that it has an area of 1000 cm2. Pairs should share their solutions with the class.
Ask learners for suggestions on how to arrange a table to organise and display di
the problem, e.g.
length (l) width (w) area (a)
100 cm 10 cm 1000 cm2
500 cm 2 cm 1000 cm2
50 cm 20 cm 1000 cm2
Remind learners about the inverse operations of multiplication and division. Tell
length × width = area, then the length can be calculated by dividing the area by t
ula, and as a class
rectangle by Look out for!
on is correct Learners who are secure with place value and
ctangle A. multiplying by multiples of ten, but who may
tangles by either: think that the answer to this problem is to make
a square of 10 cm by 10 cm or 100 cm by 100
gles photocopy cm. Ask them to check and correct their
, a piece of paper so multiplication methods.
ifferent solutions for Learners may need reminding that if the rectangle is
a square then the numbers in the width and length
l them that as the columns must be the same.
the length.
Look out for!
Learners who are unsure how to start the
investigation. Suggest that they use trial and
improvement, starting with the numbers that are
closest to each other in the columns of length and
width in the table. They can repeatedly divide
1000 by different widths to see if the length is
greater or shorter than the width, and adjust.
They should use a table to keep track of the widths
that they have tried.
Core activity 32.1: Rectangles 287
Show learners that it is true by using an example in the table, e.g. 1000 ÷ 10 = 100. A
columns, e.g.
length (l) width (w) area (a)
? cm 5 cm 1000 cm2
Learners should calculate the length of the rectangle by dividing 1000 by 5. Display
Ask pairs of learners to use the information in the table and the formula to investigate th
for learners to use calculators for this activity (Answer 31.62 cm (to 2 decimal places), o
than 32 cm).
Summary
Learners have investigated the area and perimeter of rectangles and squares.
They have used the formula for calculating area.
Notes on the Learner’s Book
Area and perimeter of rectangles (p115): learners work out the areas and perimeters
with whole number and decimal measurements. They reverse the formula for area to
find unknown widths. They investigate the dimensions of a rectangle of given area a
More activities
Fold it (individual or pairs)
You will need sheets of blank A3 paper (or two sheets of A4 stuck together).
Tell learners that if you fold a sheet of A3 paper in half (along its longest edge) you g
learners to investigate the area and perimeter of these different size pieces of paper (
edge?
288 Unit 3B 32 Area and perimeter (3)
Add another row to the table with numbers in the width and area
and explain the formula a ÷ w = l
he length of the sides of a square with an area of 1000 cm2 . It would be efficient
or learners might reach the point where they know it is more than 31cm but less
of rectangles Check
and perimeter.
up“!Ask learners for the area and perimeter of a
small rectangle, such as 4 cm by 1.2 cm.”
“Ask learners for the width of a rectangle of area
24 cm2 if its length is 8 cm.”
get an A4 page. Folding an A4 sheet, in a similar way gives an A5 page. Tell
(and smaller folds). What happens if they fold the paper along the shortest
Blank page 289
Core activity 32.2: Irregular shapes
Resources: Investigating the area and perimeter of parallelograms photocopy mas
(Optional: a globe of the Earth or world atlases; tracing paper; 1 cm squared paper;
Ask one or two learners to describe how they have measured the area of irregular sha
Show learners the Investigating the area and perimeter of parallelograms sheet. Ask
suggest ways to count the squares that make up the area of each parallelogram. Ask t
the accuracy of:
only counting squares that are more than half covered
only counting squares that are at least half covered
matching up pairs of half covered squares to count as
Askwlheoarlenecresntoimweotrek soquutatrhees.area of each parallelogram by counting the squares acco
rules they have agreed.
Draw learners’ attention to the table at the bottom of the resource sheet. Ask them to
information to complete the table for each parallelogram.
(Answer:)
shape side measurement side measurement perimeter are
A (cm) (cm) (cm) (cm
B 4 3.6 15.2
C 5 5.8 21.6 12
D 2 5.1 14.2 25
E 5 4.1 18.2 10
5 7.6 25.2 20
15
Pose the question to the class, “How can we find out which ocean on Earth has the larg
area?”
Ask small groups of learners to discuss how they could go about answering the questio
to find out which ocean has the largest surfaces area using their method. They should
method and solution to the class and debate the accuracy of the method with their class
290 Unit 3B 32 Area and perimeter (3)
LB: p118
ster (p293). Comparing land area photocopy master (p294).
; coloured tissue paper.)
apes in the past. As appropriate, use the empty column in the table for
k them to learners to record the height of the parallelogram
them to discuss (perpendicular to two of the sides). Ask them to look at
the side measurement, height and area of the
ording to the parallelograms and make a generalisation about the
relationship between the height, length and area of the
find the parallelogram, e.g. the area of a parallelogram equals
the length multiplied by the height. Ensure learners
ea understand that it is the height and not the width that is
m2) multiplied to the length. Learners can explore this
2 further by cutting out a parallelogram from the resource
5 sheet, cutting it into two pieces
0 along one of the grid lines then rearranging to make a
0 rectangle. Learners should use the formula they know to
5 check the area of the rectangle.
gest surface
Look out for!
on and to try Learners who have trouble thinking of a way to
present their compare or measure the ocean surface areas.
smates. Encourage them to consider one of these methods:
tracing the outlines of the different oceans and
then laying them over each other to compare the
area
tracing the outlines of the different oceans and then
laying each over 1 cm squared paper and calculating
the scale area in centimetre squares.
Discuss issues that learners found with trying to solve the problem such as:
identifying/deciding where the different oceans start and finish
the shape of the oceans are irregular
the surface of the Earth is curved
differences between using a globe and world atlases
different representations of the Earth on different maps.
Show learners the Comparing land area sheet. Ask learners to write statements
comparative area of different countries and continents shown on the images, e.g. ‘
approximately the same area as ’, or ‘ has an area approxim
tlaimrgeesr than ’.
Summary
Learners have worked out the approximate area of irregular shapes, including
parallelograms, by counting squares.
Notes on the Learner’s Book
Area and perimeter of irregular shapes (p118): learners work out the area of irr
shapes by counting squares, they draw shapes of a specific area and investigate
triangles in a pattern.
More activities
Triangles (individual)
You will need 1 cm squared paper.
Learners investigate the area of right-angled triangles drawn on a centimetre squ
triangles in the same way.
Map-on-map (individual or small groups)
You will need a globe of the Earth or world atlases. Tracing paper. 1 cm square
Learners can create their own picture showing the comparative area of different
from maps.
Games Book (ISBN 9781107667815)
Irregular area game (p87) is a game for two to four players. Players work out the
counting squares. They compare the area of the shapes. The learner with the sha
to describe the Opportunities for display!
has
Display images from the resource sheet with
mately three learners statements comparing the land areas.
regular Check up!
the area of
Ask learners to mark four points on a grid of centimetre
squares and join them with a ruler to make an irregular
quadrilateral. Learners should work out the approximate area
of the quadrilateral by counting squares, and explain how
they know that the method they have used makes a good
approximation of the area.
uare grid. Some learners could also investigate isosceles, equilateral and scalene
ed paper. Coloured tissue paper.
continents, countries, counties or states using coloured tissue paper and tracing
e approximate area of a shape (to the nearest half centimetre square) by 291
pe with the largest area wins the round.
Core activity 32.1: Irregular shapes
Rectangles resource sheet
A
B
C
D
E
F
Instructions on page 286 Original Material © Cambridge University Press, 2014
Investigating the area and perimeter
of parallelograms
1. Measure the lengths of the pairs of sides for each parallelogram.
2. Calculate the perimeter for each parallelogram.
3. Use the squares to work out, approximately, the area of each parallelogram.
4. Copy and complete the table to show the measurements.
A
B
C
D
E
shape side measurement side measurement perimeter area
(cm) (cm)
A Original Material © Cambridge University Press, 2014
Instructions on page 290
Comparing the land area
A
s
Perth
Instructions on page 291
of Australia with Europe
Alice
springs
Brisban
e
Sydney
Original Material © Cambridge University Press, 2014
Comparing the land area of North A
Instructions on page 291
America with Europe and North Africa
Original Material © Cambridge University Press, 2014
Comparing the land area of Afri
Netherlands
Belgium
Portugal
Spain France Germany
United States
Instructions on page 291
ica with the rest of the world
Switzerland
y
Italy
Eastern
Europe
India
India
Part 2
China
China
Part 2
UK
Japan
Original Material © Cambridge University Press, 2014
3C 33 2D and 3D Shape (2)
Quick reference
Core activity 33.1 Quadrilateral prisms (Learner’s Book p120)
Learners will visualise and describe the properties of different quadrilaterals,
quadrilateral prisms and pyramids.
Learners will explore and make nets for a variety of 3D shapes and recognise
shapes from 2D representations.
Core activity 33.2 Regular polyhedra – optional extension activity only. (Lea
p122) Learners will visualise and describe the properties of regular polyhedra.
Learners will explore and make nets for a variety of 3D shapes and recognise sh
from 2D representations.
Prior learning Objectives* – please note that listed objectives
covered fully across the book whe
• Visualise 3D shapes from
2D drawings and nets, e.g. 3C: Geometry (Shapes and geome
different nets of an open or 6Gs2 – Visualise and describe the propertie
closed cube. 6Gs3 – Identify and describe properties of q
• Recognise perpendicular and trapezium), and classify using p
and parallel lines in 2D 6Gs4 – Recognise and make 2D representa
shapes, drawings and the
environment. 3C: Problem solving (Using techn
6Pt4 – Recognise 2D and 3D shapes and
cross-section.
*for NRICH activities mapped to the Cambridge Primary
Vocabulary
tetrahedron • cube • octahedron • icosahedron • dodecahedron
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Ge o me t ry Platonic solids – extension only Vocabu lary
Quad rilateral p ris ms and py ramids Let’s investigate regular poly hedra:
T his tetra hedr o n is g o in g to be
Let’s investigate painte d. W ho le fac es w ill be 3D s ha pes where a ll
T his c u be is g oin g to b e pa in te d . pa in te d in o ne c o lour . faces are the same 2 D
W h ole fac es w ill b e pa in te d in on e c o lou r. W ha t is the s malle s t n um ber of regular shape.
W ha t is the s malle s t n um ber of co lo urs colour s ne ede d so that n o face is
nee de d s o th at n o face is ne x t to a fa ce of ne xt to a fac e of th e sam e c o lour ? tetrahedron: a
th e sam e c olo ur ? regular 3D sha pe
Wha t a bo ut an octa hedron ?
1 Copy th is sor tin g d iagram. You c o uld try w okrin g with four equilateral
g sy stem atic ally , ec.agn. These question s extend understandin g bey ond
q ua drila tera ls an it be d o ne w ith Stage 6. O nly attempt them if y ou want a triang le faces.
1, 2 , 3 c o lo ur s ? challenge.
para llelo gra ms cube :a regular 3D s hape
1 Th is is par t of a net of a dodecahedron. with six s quare
reg u lar w many pentagons are miss ing from the net?
faces.
Ho
octahedron: a
regular 3D shape
with eigh t equilateral
triang le faces.
icosahedron: a
regular 3D shape
with 20 equilateral
triang ular faces.
dodecahedron: a regular
3D sha pe w ith 12
pentagonal faces.
arner’s Book Write these s hape names into the correct sections of y our diagram. 12 2
hapes kite rectangle pentago n trape zium s quare r ho mbus
12 0
might only be partially covered within any given chapter but are
en taken as a whole
etric reasoning)
es of 3D shapes e.g. faces, edges and vertices.
quadrilaterals (including the parallelogram, rhombus
parallel sides, equal sides, equal angles.
ations of 3D shapes including nets.
niques and skills in solving mathematical problems)
their relationships, e.g. a cuboid has a rectangular
objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 3C 297
Core activity 33.1: Quadrilateral
prisms
Resources: Quadrilateral prism bases photocopy master (p302). Tracing paper.
Give learners the Quadrilateral prism bases sheet and ask them to identify each of th
using the most precise vocabulary that they know. Ask learners how they identified t
different quadrilaterals (encourage them to talk about parallel sides, equal sides and e
angles in their explanations).
Ask learners to each think of a type of prism or pyramid. In pairs they should take turns
to their partner the number of faces, edges and vertices and the shape of the faces so th
partner can work out what solid they are thinking of.
Ask two or three learners to explain how they knew when their partner’s shape was a
a definition of a prism with the class, e.g. a 3D shape with two identical, parallel face
other faces are rectangles. Tell learners that so far they have only looked at prisms wh
identical faces are regular polygons and explain that it is also possible to make a pris
irregular polygons that are parallel, with rectangles joining them.
Ask learners to choose one of the quadrilaterals on the Quadrilateral prism bases sheet
visualise a prism based on that shape. They should take turns to describe the prism the
visualising to a partner, without using the name of the quadrilateral, so that their partner
out what shape they are thinking of.
Tell learners that they are going to make an irregular quadrilateral based prism from a
they are going to draw themselves. They can trace two copies of their chosen
quadrilateral from the resource sheet, but they will need to measure and draw the rect
their prism. Tell learners that if the polygons are irregular it is likely that the rectangl
be identical. Ask three or four learners to describe how they might go about deciding
of the sides of their rectangles and how they will draw them accurately. Learners sho
prototype of their net on paper first, to check that it works, and then transfer the desig
card to make the prism. (Remind them that they will need
298 Unit 3C 33 2D and 3D Shape (2)
LB: p120
. Scissors. Thin card. Glue.
he shapes,
the
equal
to describe
hat their
a prism. Write Look out for!
es, and all
here the two Learners who quickly draw an accurate net using the
sm with irregular quadrilateral provided. Encourage them to
design their own irregular quadrilateral, one that
t and does not have a more specific name than
ey are ‘quadrilateral’, to turn into a prism. Ask them to
measure the sides and angles, and check that none of
can work the pairs of sides are parallel before using it to make
a prism.
a net that
tangles for
les will not
g the length
ould make a
gn to thin
to add flaps so that the net edges can be glued together.) Tell learners that once th
that their net works to make another copy of it so that they can display both the n
shape for other learners to see how they constructed their shape.
Learners should check the number of faces, edges and vertices their quadrilater
report back to the class. They should all find that they have six faces, 12 edges a
Ask learners to describe ways in which their prism is different and similar to a c
them to talk about parallel faces and equal edges in their comparison.
Summary
Learners will have visualised and described the properties of different quadril
quadrilateral prisms and pyramids.
Learners have explored and made nets for a variety of 3D shapes and recogni
from 2D representations.
Notes on the Learner’s Book
Quadrilateral prisms and pyramids (p120): learners sort different quadrilaterals.
pyramids and prisms by their properties and make generalisations about the prop
More activities
Pyramid (individual)
You will need thin card, scissors and glue.
Learners draw a net for a quadrilateral based pyramid and then cut it out and stic
Cross-section (individual or pairs)
Learners can visualise and investigate which 2D shapes can be made on a cross-
Re ex base (individual)
You will need thin card, scissors and glue.
Challenge learners to make prisms that have a base shape that has one or more in
hey have checked Opportunities for display!
net and the 3D Display the learners’ nets and prisms so that they
can all see the variety of nets, and also the
ral prism has and similarities between the nets, that have made the
and eight vertices. different prisms.
cube, encouraging
laterals, Check up!
ise shapes
Show learners a net of a quadrilateral prism. Ask them
They describe which 3D shape would be made from the net and how
perties. they know.
ck it together to make a solid.
-section with different prisms when cutting straight through them.
nternal angles that are greater than 180 degrees.
Core activity 33.1: Quadrilateral prisms 299
Core activity 33.2: Regular polyhedra
Resources: Exploring regular polyhedra photocopy master (p303). Platonic sol
(Optional: Stellated dodecahedron (CD-ROM). The Kepler-Poinsot solids poster (C
3D solids have been covered extensively in Stage 6 and earlier stages. Revise what ha
been covered as required. Alternatively, you can challenge your more able learners to
polyhedra other than the tetrahedron. The content of this activity is beyond the scope
and therefore is optional only.
Tell learners that they are going to explore ‘regular polyhedra’. Ask them to discuss i
then report back, what they think a ‘regular polyhedron’ might be. Tell learners that a
polyhedron has all identical faces and that they know two regular polyhedra – the tet
and the cube.
Give learners the Exploring regular polyhedra sheet, pages 1 and 2. Ask them to cut ou
tetrahedron net and the open cube net and fold up the nets to make a tetrahedron and o
Tell learners that the squares and equilateral triangles can be joined to make a net of a r
polyhedron because every side of the shape must touch the side of another shape when
the shapes fold up, and they do for these shapes. Ask learners to cut out the arrangeme
pentagons and the arrangement of seven hexagons and see if they will fold so that the s
They should find that the pentagons fold up so that they touch, making a dish shape, an
hexagons are already touching when they are flat, they cannot be folded to a touching p
Finally ask learners to cut out the eight heptagons and show by arranging them whether
would be possible to make a polyhedron only using regular heptagons (Answer: not po
Explain that there are only five (convex) regular polyhedra, and that they are known as t
Solids, named after Plato, the philosopher from Ancient Greece.
Show learners the Platonic solids poster. Ask them to talk, in pairs, about the shape of t
each polyhedron and the number of faces, edges and vertices. Give learners pages 3 a
Exploring regular polyhedra sheet. Ask them to choose shapes to construct with the net
check the number of faces, edges and vertices.
300 Unit 3C 33 2D and 3D Shape (2)
LB: p122
lids poster photocopy master (p307). Scissors. Glue.
CD-ROM).)
as already Vocabulary
o learn about
e of Stage 6 regular polyhedra: 3D shapes where all faces are the
same 2D regular shape.
in pairs, and tetrahedron: a regular 3D shape with four equilateral
a regular triangle faces.
trahedron cube: a regular 3D shape with six square faces.
octahedron: a regular 3D shape with eight equilateral
ut the triangle faces.
open cube. icosahedron: a regular 3D shape with 20 equilateral
regular triangular faces.
n sides of dodecahedron: a regular 3D shape with 12 pentagonal
ent of six faces.
sides touch.
nd as the Opportunities for display!
position. Display the polyhedra that the learners have made,
r or not it along with labels showing the number of faces, edges
ossible). and vertices.
the Platonic
the faces on
nd 4 of the
ts and then
Summary
Learners will have visualised and described the properties of regular polyhed
Learners will have explored and made nets for a variety of 3D shapes and hav
solids from 2D representations.
Notes on the Learner’s Book
Platonic solids (p122): learners match names to the platonic solids and identify
from the net of a dodecahedron. Please note, that like the Core activity, this mat
the scope of Stage 6 and therefore is optional.
More activities
Is it fair? (individual or pairs)
You will need regular solids from the core activity.
Learners know that a fair dice can be made with a cube, all numbers on the dice
fair dice.
Star challenge (individual)
You will need Stellated dodecahedron photocopy master (CD-ROM).
Challenge learners to make a stellated dodecahedron using the net on the Stellate
least A3 paper. Learners could colour the net before cutting out and assembling.
Kepler-Poinsot (whole class)
You will need The Kepler-Poinsot solids poster (CD-ROM).
Show learners The Kepler-Poinsot solids poster. These are named after Johannes
are made and the properties of the shapes. Explain that these are also regular pol
creating ‘caves’ in it.
Games Book (ISBN 9781107667815)
The dodecahedron and octahedron game (p97) is a game for two to four players.
learner to make a net of their shape first is the winner.
dra. Check up!
ve recognised
Show learners pictures of different polyhedral:
what is missing ask them to name them
terial is beyond ask them to describe what the net of the shape
might look like.
are equally likely. Ask them to investigate whether all regular polyhedra make
ed dodecahedron photocopy master. It is recommended that this is copied on to at
s Kepler and Louis Poinsot. Ask learners to comment on how they think the shapes
lyhedra, but they are ‘concave’, some of the surfaces are angled into the shape
. Learners collect 2D shapes to make a net of a dodecahedron or octahedron. The
Core activity 33.2: Regular polyhedra 301
Quadrilateral prism bases
Instructions on page 300 Original Material © Cambridge University Press, 2014
Exploring regular polyhedra
Page 1
Instructions on page 300 Original Material © Cambridge University Press, 2014