year. LB: p26
about ‘time’ Vocabulary
of second: a small unit of time measurement.
ss list of minute: a unit of time measurement (60 seconds).
rs if they hour: a unit of time measurement (60 minutes).
ulary listed day: a unit of time measurement (24 hours, the time it
takes for the earth to rotate once on its axis).
ur, and how week: a unit of time measurement (seven days).
ork out these fortnight: a unit of time measurement (two weeks).
ttings, and month: a unit of time measurement (28, 29, 30 or
31 days, the approximate amount of time it takes for
Healthy the moon to orbit the Earth).
n pairs to year: a unit of time measurement (365/366 days,
12 months, the approximate amount of time it takes
for the Earth to orbit the sun).
decade: a unit of time measurement (10 years).
century: a unit of time measurement (100 years).
week for
r with it,
Ask pairs of learners to work together to work out the answers to the same question
three years, using what they know about the number of days in a week, months and
learners to write a statement explaining why dates fall on different days of the week
Demonstrate how to find a time interval in years, months and days using a timeli
Britain Queen Victoria was the monarch from 20 June 1837 until she died on 22
1901.
e.g. 7 months 2 days
63 years
20/6/1837 20/6/1900 20/1/1901 22/1/1901
Queen Victoria Reigned for 63 years, 7 months and 2 days.
Ask learners to find out information about monarchs, presidents, or prime ministers
work out how long they lived or reigned using a time line.
ns for the next Look out for!
d year. Ask Learners whose calculation skills are not accurate
k each year.
enough for the level needed to problem solve using
ine. In units of time. Allow them to use a calculator but
2 January make sure that they can use a calculator correctly
and encourage them to make jotting
s from the past to and use the memory functions to solve multi-step
problems.
Learners with a good understanding of the
relationship between different units of time. They
could write and solve their own problems from the
information on the poster involving years and
decades.
Learners who have difficulty knowing how to
start a statement. As necessary, provide this
sentence stem to support learners writing their
statement:
‘Dates fall on different days of the week each
year because . . .’
or
‘Dates fall on different days of the week each
year because the number of days in the year is
not divisible by seven, which means that . . .’
Opportunities for display!
Make a display of important historical figures for your
country or local area including time calculated using
timelines.
Core activity 6.2: Calendars 55
Summary
Learners will have used a calendar and their understanding of days, weeks, months a
calculate the solutions to problems.
Notes on the Learner’s Book
Time intervals and calendars (p26): learners solve problems involving changing unit
They calculate time differences in years, months and days.
More activities
My birthday (individual)
Challenge learners to find out the day of the week their birthday falls on, then in whi
A different calendar (individuals or groups)
Ask learners to research different calendar systems used in the past and by other cult
Games Book (ISBN 9781107667815)
Matching times (p64) is a game for two players. Learners match times given in secon
learner collecting the most pairs of times wins.
56 Unit 1B 6 Time
(1)
and years to Check up!
ts of time.
Ask learners how many hours there are in the month of
June and to show how they used their knowledge of
the units of time to solve the problem.
ich year it will next fall on that same day of the week.
tures.
nds, minutes, hours, days, weeks, years, centuries and millennia. The
Ordering Times
Cut out the cards and order them from midnight to 23:59.
11 12 1 11 12 1
10 2 10 2
93 93 00:00 23:59
8 4 8 6 4
7 5 7 5
6
morning afternoon
11 12 1 11 12 1
10 2 10 2
03:40 04:44 93 93
8 6 4 8 4
7 5 7 5
6
morning afternoon
11 12 1 11 12 1
10 2 10 2
93 93 15:35 22:08
8 6 4 8 6 4
7 5 7 5
morning afternoon
11 12 1 11 12 1
10 2 10 2
93
10:20 20:12 93 84
8 6 4 76 5
7 5
afternoon
morning
11 12 1 11 12 1
10 2 10 2
93 93 18:53 02:32
8 6 4 8 6 4
7 5 7 5
morning afternoon
Instructions on page 50 Original Material © Cambridge University Press, 2014
Camford MetraBus time
Instructions on page 51
etable resource sheet
Original Material © Cambridge University Press, 2014
Keeping
Tia’s Tips for
Sleep
Most children need 10 ho
every night (not during le
Eating
Healthy eating is important to make
sure you get all the nutrients you need
to grow. Eat a balanced diet, with lots
of fruit and vegetables. Children need
about 1800 calories a day.
Instructions on page 54
g healthy
r Healthy Living
ours sleep Look after your teeth
essons!)
Do not eat sweet foods between meals.
Brush your teeth for two minutes twice
a day.
Did you know:
Your heart beats about 80 times a
d minute!
s It takes the body around 12 hours to
d digest eaten food!
Original Material © Cambridge University Press, 2014
60 Blank page
1B 7 Area and perimeter (1)
Quick reference
Core activity 7.1: Making a model house (Learner’s Book p)
Learners measure and calculate the perimeter of rectilinear shapes. They start to
shapes that can be split into rectangles. Learners estimate the area of irregular sh
Prior learning Objectives* – please note that listed obj
Measure and calculate the when taken as a whole
perimeter of regular and irregular
polygons 1B: Measure (area and perim
6Ma1 – Measure and calculate the per
Understand area measured in 6Ma2 – Estimate the area of an irregul
square centimetres (cm²) 6Ma3 – Calculate perimeter and area
Use the formula for the area
of a rectangle to calculate the 1B: Problem solving (Using u
rectangle’s area 6Ps1 – Explain why they chose a part
6Ps2 – Deduce new information from
another.
*for NRICH activities mapped to the Cambridge P
Vocabulary
area perimeter
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Area and perimeter (1) Vocabula ry
o calculate the area of simple compound Let’s investigate CYaoruroclloudiladgruasme vvee area: the
hapes by counting squares. cosrqreucatresspaacneds.move measurement of a
Each of these five tiles is square surface, recorded
Laentd’shiansavnesatriegaatoef 16 cm2. them around into
sFfitn4dCao wmapyletoteartrhaenglaebtheelsmon the different shapes. using square units.
ssootthhaat ttthheetontualmsbhaeprse aharse ian the Work out the perimeter: the
length of each distance around
perimeter of 40 cm. side to help you
the outside of a 2D
shape, recorded using
units of length.
calculate the
1 This pattern is made starting with a sqpuearriemtehtaetri.s 2 cm wide, and by drawing
squares 2 cm wider than the last. Complete the table to show the visible area
of each colour.Visualise or draw the fourth pattern.
First Second Third
Pattern Visible yellow area Visible blue area
First 4 cm2 0 cm2 You could
Secon add the yellow
area to the blue
d area to check
28 Third that it equals
the total area
Fourt h of the pattern.
jectives might only be partially covered within any given chapter but are covered fully across the book
meter)
rimeter and area of rectilinear shapes.
lar shape by counting squares.
of simple compound shapes that can be split into rectangles.
understanding and strategies in solving problems)
ticular method to perform a calculation and show working.
existing information and realise the effect that one piece of information has on
Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 1B 61
Core activity 7.1: Making a model house
Resources: Remembering area and perimeter of rectangles photocopy master (p
shoe boxes) or stiff card to make a similar size box. Coloured paper or fabrics. Rule
shapes photocopy master (p67). Rug area photocopy master (p68). (Optional: dried
This core activity mainly involves one activity – building a model house. It is sug
this is revisited over a series of several sessions, or one extended session.
Show the learners the Remembering area and perimeter of rectangles photocopy mas
Ask learners to complete the information box to the right of the first rectangle, using what
method they think is best. They should then compare their answers with a partner and di
methods they used to find the length, width, perimeter and area of the rectangle.
As a whole group, discuss the methods used, the measurements and the units used to
measurements. Revisit guidance for measurement and calculating perimeters and area
rectangles as necessary, including:
U sing a ruler accurately to measure to the nearest millimetre/centimetre.
C alculating the perimeter of a rectangle by adding double the length measurement
double the width measurement.
P erimeter is recorded using units of length, e.g. ‘cm’.
F inding the area of a rectangle by knowing that the number of square units it cove
as the length measurement multiplied by the width measurement.
A rea is recorded using square units e.g. ‘cm2’.
Show the learners a model house, or pictures of model houses. Tell them that they wi
spending some time making a model house room and decorating it. As appropriate, te
learners that it will be for themselves or to give to younger learners.
Give pairs of learners the bottom of a shoe box, or instruct them in how to make an ope
similar size from a net from stiff card. Explain that this model house will be accessed fro
room and that more than one box can be put next to each other to make connecting roo
house on one level.
62 Unit 1B 7 Area and perimeter
(1)
LB: p28
p66). A model house, or pictures of model houses. Cardboard boxes (e.g.
ers. Scissors. Drinking straws (split in half lengthways). Area of irregular
d rice grains; 1 cm2 paper; tape measures; coloured paper.)
ggested that Vocabulary
ster. area: the measurement of a surface, record in square
units.
tever
iscuss the perimeter: the distance around the outside of a 2D
shape, recorded using units of length.
o record the
as of Look out for!
Learners who are not comfortable with how to nd the
t and area of a rectangle from work done in earlier stages.
Give pairs of learners square centimetre paper to
ers is the same reinforce the concept. Ask them to draw rectangles on
the paper that match some of these dimensions:
ill be 6 cm long, 4 cm wide
ell the 8 cm long, 3 cm wide
5 cm long, 5 cm wide
en cuboid of a 7 cm long, 6 cm wide
om above the 8 cm long, 5 cm wide
oms for the 7 cm long, 4 cm wide
The learners should calculate the area of the
rectangle by multiplying the length by the width
and then check the area by counting the squares in
rows. Encourage them not to count the total squares
individually, but by the number in each row.
Ask learners to calculate the area of floor in their model house ‘room’ by measuring
to the nearest centimetre and using the formula for finding the area of a rectangle. L
use their measuring skills to cut a piece of coloured paper or fabric to make a carpe
Learners should draw a rectangular window with an area of 24cm2 on two of the wa
should have different widths and lengths and they should be on different sized walls
cut these out if they wish.
Tell pairs of learners to create a door in one wall of the room by first choosing the d
should be to suit the size of the room and then drawing it and cutting one long and
so the door can open.
Ask learners to find the total area of wall in the room, not including window and
spaces. Ask the learners to discuss how they could work out the area of paint, til
wallpaper needed to cover these walls. Discuss these methods with the class. Exp
there are two methods for calculating the area of a shape, such as a wall with a w
The wall could be divided into rectangular sections around the window, e.g.
wall
window
The dashed lines have divided the wall into four rectangles around the window
the rectangles can be measured. The area of each rectangle can be calculated.
the wall can be found by adding together the area of each rectangle.
Measure and calculate the area of the wall as if it did not have a window in it.
and calculate the area of the window. Subtract the area of the window from th
wall without a window to find the area of the wall.
Tell learners that for this exercise they will find the second method more efficien
will return to the other method in later chapters and can experiment with checkin
solution by using both methods if they wish.
g two of the sides Look out for!
Learners should
et for the room. Learners who only calculate the perimeter by adding
alls, the windows all four sides. As necessary, give learners
s. Learners can
straws to cut into lengths to make a rectangle that
dimensions it is 6 cm long and 4 cm wide. Point out to them that two
two short sides
they needed to make two straws that are 6 cm and
d door straws that are 4 cm to make this rectangle.
les or
plain that Rearrange the straws in the following ways to show
window. how the perimeter of the rectangle can be calculated.
Show that the perimeter equals double the length add
w. The sides of double the width by arranging the straws as:
The total area of
. Measure double the length double the width
he area of the +
nt, but they Show that the perimeter equals double the length
ng their added to the width by arranging the straws as:
+ +
Explain that the perimeter of any rectangle can be
taken apart in this way because all rectangles have
two pairs of sides that are the same length, so the
method works for any rectangle.
Core activity 7.1: Making a model house 63
Learner should use their accurate measuring skills to cut coloured paper to the correc
cover the walls.
You may wish to break the session here.
Display the Area of irregular shapes photocopy master. Ask learners to imagine
shape is a rug for the room they are creating. Tell them that the star rug is presen
centimetre squared paper.
In pairs, learners should discuss how they could work out the area that will be covered b
and to try to estimate the area of the rug.
Talk about counting the squares covered by the shape to get an estimate of the area of th
Divide the class into three groups and ask the learners in each group to estimate the are
star in one of these ways:
count every square that is entirely covered by the star shape
count every square that is at least partly covered by the star shape
count every square where more than half of it is covered by the star shape.
Compare the solutions and discuss with the class which count they think is the most
accurate and why.
Give learners the Rug area photocopy master. First ask them to estimate which rugs ha
smallest and largest area, and to number them one to five, one being the predicted sma
and five being the predicted largest area. Ask them to estimate the area covered by eac
counting the squares in the way that the class has considered most accurate. They shou
and compare their estimates and counts with a partner and reflect on their accuracy. The
use their preferred rug shape and make a rug using coloured paper or fabric, and the sh
resource sheet as a template.
Ask learners to calculate the perimeter of each window so that they can make window fr
Allow each pair of learners to measure and take one length of a drinking straw (that has
in half lengthways), for each window, that they can then cut into the four sides of the win
stick in place on their room.
Ask learners to calculate the total length of skirting board needed for the room by calc
perimeter and subtracting the width of the door, and the total length needed for the doo
the same way. Pairs of learners should make these and add them to their room.
64 Unit 1B 7 Area and perimeter
(1)
ct sizes to Look out for!
Learners who only use one method to calculate the
that the star area of the compound shapes. As appropriate, ask
nted on one- learners to use both methods, so that they can ref l ect
on what is more effi cient, in this case, for themselves
by the rug and check their calculations.
he star. Look out for!
Learners who have the misconception that shapes with
ea of the the same area have the same perimeters. Use
finding the perimeter of the windows to help learners
see that they can be different. Ask them what pairs of
numbers multiply to give 24 and do these all give the
same answer when they add them?
ave the Opportunities for display!
allest area
ch rug by Display the model house rooms with written
uld talk to explanations from the learners as to how they perimeter.
ey can are being made and the calculations for area and
hape on the
rames.
s been split
ndow and
culating the
or frame in
Summary
Le arners have measured and calculated the perimeter of rectilinear shapes.
Th ey have calculated the area of simple compound shapes that can be split int
Le arners have estimated the area of irregular shapes by counting squares.
Notes on the Learner’s Book
Area and perimeter (1) (p28): learners calculate areas and perimeters of rectang
They estimate areas of non-rectangular shapes by counting squares.
More activities
Rice area (pairs)
You will need some dried rice grains and 1 cm2 paper.
Ask learners to discuss how they would go about finding out how much rice they
floor. One starting point might be to find out how much rice covers 1 cm2.
Cover up (individual)
You will need different coloured papers, ruler and scissors.
Ask learners to investigate ways to make two paper rectangles from different colo
is the same.
Estimate and check (perimeter) (individual)
You will need tape measures.
Ask learners to estimate the perimeter of different rectangular shapes in the class
the rectangles to check the accuracy of their estimates.
Games Book (ISBN 9781107667815)
The rectangle area and perimeter game (p67) is a game for two players. Players
Once a rectangle cannot be placed on the grid, the players find the total of all th
the winner.
to rectangles. Check up!
gular shapes.
Ask learners to make a picture for the wall of their
room that is a rectangle and has an area between 12
cm2 and 20 cm2. Ask them to work out the length of
wood needed to make a picture frame.
Draw an irregular shape onto centimetre squared
paper. Ask learners to demonstrate how they would
estimate the area of the shape.
y would need to completely cover their book, table, or even the classroom
ours, where if one rectangle is placed over the other the area visible of each colour
sroom by estimate the length of two sides and doubling. Learners should measure
make rectangles on a centimetre squared grid that match an area given on a card.
he perimeters of the rectangles they have drawn. The player with the largest total is
Core activity 7.1: Making a model house 65
Remembering area and perimeter of rectangles
Length
Width
Perimeter
Area
Length
Width
Perimeter
Area
Length
Width
Perimeter
Area
Length
Width
Perimeter
Area
Instructions on page 62 Original Material © Cambridge University Press, 2014
Area of irregular shapes
Instructions on page 64 Original Material © Cambridge University Press, 2014
Rug area
These are different shaped rugs that could fit in the model house. The cost
of the rugs is calculated according to the area of the rug.
A B
D C
E
Instructions on page 64 Original Material © Cambridge University Press, 2014
1C 8 2D and 3D shape (1)
Quick reference
Core activity 8.1: Identifying polygons (Learner’s Book p) Learners
classify shapes as to whether or not they are polygons. They identify
and describe properties of a range of quadrilaterals.
Core activity 8.2: Properties of 3D shapes and their cross-sections (Learner’s B
Learners explore the 2D shapes that are made from cutting through a 3D shape.
will use ‘faces’, ‘edges’ and ‘vertices’ to describe the properties of 3D shapes.
Core activity 8.3: Nets (Learner’s Book p)
Learners recognise and make 2D representations and nets of cuboids and prisms
Prior learning Objectives* – plea
fully
Visualise 3D shapes from 2D drawings and nets,
e.g. different nets of an open or closed cube. 1C: Geometr
6Gs1 – Classify differ
• Recognise perpendicular and parallel lines in 2D
shapes, drawings and the environment. 6Gs2 Visualise and
6Gs3 – Identify and d
From Stage 4
• Classify polygons (including a range of trapezium), a
6Gs4 – Recognise an
quadrilaterals) using criteria such as the number
of right angles, whether or not they are regular 1C: Problem
and their symmetrical properties. 6Pt4 – Recognise 2D
section.
*for NRICH activities mappe
Vocabulary
polygon • quadrilateral • parallelogram • rectangle • rhombus • square •
kite • polyhedron • face • edge • vertex/vertices • prism • pyramid
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Ge o me t ry Nets
3D shapes Vo c abula r y Let’s investigate
O n a s ix-s ide d d ice the nu mber s on op p o site face s total 7 .
Po lygons and quad rilaterals Let’s investigate poly hedron: a 3D Co mp le te the nu mber s o n th is ne t s o tha t e ac h pa ir
Ima gine Ka te m a de a s o lid oc ta g o nal py ramid. sha pe with po ly go n of o p po s ite fac es to ta l 7.
Let’s investigate Vo ca b u l a ry She caref ully c ut rig h t thro u gh the s ha pe w ith a kn if e faces.
an d loo ke d to see wh at s ha pe s he ha d m a de in s id e. Rem ember , op p os ite faces wwiilll
W ha t ca n y o u se e in the po ly go n : a closed 2D sha pe w ith three or more face: at surface of a n ot to uch w he n the ne t is l
straight sides. W hic h of th es e s h ap es c ou ld sh e no t ha ve m ad e: 3D shape. folded, so ca nn o t touc h o n
pattern below ? th e n et.
quadrilateral: a poly gon w ith exactly ● a n oc ta g o n ● a r ho m bu s edge: the line where 1 Draw a ne t that cou ld ma ke a 3 D shape tha t wou ld loo k like th is :
Ho w ma ny : four side s. ● a tr ia ng le ● a trape ziu m ?
● s quare s ? two faces of a 3D 2 Measure the faces of this ne t. Draw a p icture of the 3D shape tha t w ould be made
● tra pe zium s ? parallelolgram: a quadrilateral. Both pair s E xp la in to s o me on e h o w sh e c o uld ha ve m ad e ea ch sha pe meet. from this net. La bel the measurements of
● kite s ? of opp osite s ides are parallel. of the o ther s hape s. the leng th, width an d he igh t of the shape.
● r igh t-an g les ? vertex/vertices: the
rectangle: a quadrilateral. Both pairs of oppo site po in t/p oints where 34
sides are parallel and all the ang les are righ t 1 Francesca put s ix sha pes edge s of a 3D s hape
angles. into a bag. Her frie nds m e e t.
each took at shape a t
rhombu s: a quadrilateral. Both pairs of opp osite side s random and described prism: a 3D sha pe
are parallel and all the side s are the same le ngth. their shape. with tw o ide ntica l,
parallel faces, and
square: a quadrilateral. Both pa irs of oppos ite s ides are all other faces are
parallel, all the sides are the same leng th and all the rectangles.
angles are righ t ang les.
py ramid: a 3D sha pe
Book p) 1 These s hapes are not trapezium (als o known is some co un tries as What sha pe cou ld each child be talking ab ou t? with a p oly go n face
They a ‘trapezoid ’): a quadrilateral. One pair of poly gons. G ive (a)
and all other faces
s. at leas t opposite s ides is parallel.
are triangu lar and
one reason why each of the shape s meet at a vertex.
kite: a quadrilateral.Two pairs of a djacent
is not a s ide s are the same leng th.
poly go n.
(a) (b) (c)
8 edges and
5 ver tic e s
30
32
ase note that listed objectives might only be partially covered within any given chapter but are covered
across the book when taken as a whole
ry (Shapes and geometric reasoning)
rent polygons and understand whether a 2D shape is a polygon or not.
d describe the properties of 3D shapes e.g. faces, edges and vertices.
describe properties of quadrilaterals (including the parallelogram, rhombus and
and classify using parallel sides, equal sides, equal angles.
nd make 2D representations of 3D shapes including nets.
m solving (Using techniques and skills in solving mathematical problems)
D and 3D shapes and their relationships, e.g. a cuboid has a rectangular cross-
ed to the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 1C 69
Core activity 8.1: Identifying polygons
Resources: Identifying polygons photocopy master (p78). Quadrilaterals pho
(Optional: skipping ropes (or other long lengths of string).)
Read the vocabulary definition of a polygon to the learners. Ask them to make a che
things to look for so that they can check if a shape is a polygon, e.g.
Question Check
Does it have three or more sides?
Discuss learners’ checklists and ask learners to add any further questions that they ne
identify polygons including:
three or more sides
straight sides
closed shape.
Give learners the Identifying polygons photocopy master. They should use their checklis
if the shapes are polygons. The shapes can be cut out along the dotted lines and sorted
groups, ‘polygons’ and ‘not polygons’. Learners should compare and discuss how they h
their shapes with their group and, as necessary, change and refine their checklists.
Tell learners that quadrilaterals are polygons with four sides. There is one quadrilateral o
Identifying polygons photocopy master. Ask learners to nd and name it (Answer: para
Ask one or two learners to explain how they know that this shape is a parallelogram (wh
of the shape make it a parallelogram?) Agree that a parallelogram is a quadrilateral wh
sides are parallel. Show learners the Quadrilaterals photocopy master. Ask them to nam
shapes at the top of the sheet under the heading ‘Parallelograms’. (Answer:
the most specific name they can give for the first shapes is just ‘parallelogram’. T
may be recognised by the names ‘rectangle’, ‘rhombus’ and ‘square’.) Tell learners
that these shapes are parallelograms by checking that they have the property of opposit
being parallel. They should do this by rst estimating that the sides are parallel by look
then checking by measuring the distance between the lines is the same at different point
70 Unit 1C 8 2D and 3D shape (1)
LB: p30
otocopy master (p79). String (in loops, about 40 cm long).
ecklist of Vocabulary
eed to polygon: a closed 2D shape with three or more straight
sides.
sts to decide quadrilateral: a polygon with exactly four sides.
d into two parallelolgram: a quadrilateral. Both pairs of opposite
have sorted sides are parallel.
rectangle: a quadrilateral. Both pairs of opposite sides
on the are parallel and all the angles are right angles.
allelogram). rhombus: a quadrilateral. Both pairs of opposite sides
hat properties are parallel and all the sides are the same length.
here opposite square: a quadrilateral. Both pairs of opposite sides
me the four are parallel, all the sides are the same length and all
The others the angles are right angles.
s to check trapezium (also known is some countries as a
te sides ‘trapezoid’): a quadrilateral. One pair of opposite sides
king at them, is parallel.
ts. kite: a quadrilateral. Two pairs of adjacent sides are the
same length.
Opportunities for display!
Display a small selection of the learners’ polygon
checklists for learners to refer to during the activities.
Divide the class into four or more groups. Assign each group one of the parallelog
the sheet. Ask them to discuss and argue why their shape is the ‘Odd one out’ us
they can see and know about the shapes.
Give learners the definitions of a trapezium and a kite. Ask them to identify the
the ‘Other quadrilaterals’ section of the resource sheet (Answer: first and seco
trapeziums, third is kite). Explain that for the four sided polygons that do not m
def initions for parallelogram, trapezium or kite, the most specific word the lear
name them is ‘quadrilateral’.
Ask learners to discuss and place the names of quadrilaterals they know under th
Always has right angles Sometimes has right angles Never has right
(rectangle, square)
(parallelogram, rhombus, (none they know
trapezium, kite) names)
Point out that different shapes have properties that they must have, and properties
important to naming the shape, e.g. a trapezium or kite can have none, one or two
parallelogram or rhombus can have four right angles but then it can also be given
name of rectangle or square.
Give each pair of learners a loop of string. Call out different quadrilaterals, or a
a quadrilateral can have and ask pairs to make a matching quadrilateral with the
putting two fingers inside the loop. Pairs of learners should compare the quadrila
have made with other pairs in their group and discuss how they are similar and d
Ask learners to write checklists for the different quadrilaterals that they know, focus
properties that the shapes must have. Save checklist for learners to refer to in chap
grams at the top of Look out for!
sing the properties
Learners who do not check the distance between
ese shapes in parallel lines by measuring at right angles. Get them to
ond are put a ruler along one of the lines and a set-square
match the against the ruler. As they slide the set-square along the
rners have to ruler, the opposite line should show the same position
on the scale if they are parallel.
he headings: Look out for!
Learners who find it difficult to understand that shapes
angles can have more than one name and that shapes with the
w with specific same name can look different. Try supporting their
understanding using analogies such as animals.
s that are not so Explain that a cat could be called a cat or an animal, in
o right angles, a the same way a rectangle can be called a rectangle or a
n the more specific parallelogram. Rectangle is a more specific label for the
shape than parallelogram, but it is still a parallelogram
property that like a cat is still an animal. Just as a Siamese is a
string by each specific type of cat, a square is a specific type of
ateral they rectangle. In the same way as a Siamese is a cat and an
different. animal, a square is a rectangle and a quadrilateral.
sing on the Opportunities for display!
pter 33. Take and display photographs of the learners’ string loop
quadrilaterals and ask learners to label the display with the
names of the shapes and their properties.
Core activity 8.1: Identifying polygons 71
Summary
Learners will have classified shapes as to whether or not they are polygons.
They will have identified and described the properties of a range of quadrilaterals
Notes on the Learner’s Book
Polygons and quadrilaterals (p30): learners explain why some shapes are not polygon
describe quadrilaterals according to their properties and make patterns using more th
different quadrilaterals.
More activities
Guess my shape (pairs or groups)
One learner chooses a shape and the other learners ask questions that can only be ans
specific name of the shape.
Size up (pairs or groups)
You will need skipping ropes (or other long lengths of string).
Learners can make larger string loop quadrilaterals using skipping ropes. As appropri
and that right angles measure 90˚.
Games Book (ISBN 9781107667815)
Collecting quadrilaterals game (p90) is a game for two players. Players attempt to co
properties listed on them.
72 Unit 1C 8 2D and 3D shape (1)
s. Check up!
ns. They Show learners a selection of polygons. Ask them to
han three choose an ‘odd one out’ and explain why that could be
the odd one out. Repeat twice more, asking learners to
choose a different polygon each time.
swered ‘yes’ or ‘no’ about the property of the shape in order to guess the
iate, ask learners to check that sides are parallel by measuring with a ruler
over all the spaces on a grid with quadrilaterals that can match the
Blank page 73
Core activity 8.2: Properties of 3D shapes and their c
Resources: 3D shapes poster photocopy master (p80). Modelling dough. Blunt kn
classroom; use blunt plastic knives used for modelling clay if available.)
Ask learners, in small groups, to make a list of all the 3D shapes they can name. Mak
these shapes. Explain that the 3D shapes that have only faces that are polygons are ca
On the class list of 3D shapes, ask learners to identify which are polyhedral. Show a
3D shapes poster. Check that the learners understand the definitions on the poster a
them to refer to it during the activity.
Give groups of learners some modelling dough. Ask the groups to make a set of the foll
shapes using the dough:
triangular prism
cuboid (rectangular prism)
pentagonal prism
hexagonal prism.
Tell learners that, although these models will not have completely flat faces because the
out of modelling dough, they will help them visualise true prisms.
Demonstrate that a triangular prism can be cut through with a sharp knife so that the
the cut is a triangle, or so that the shape made by the cut is a rectangle. Ask learners t
cutting their group’s triangular prism and think about whether any other 2D shapes c
cutting through the model.
Learners should design and draw a table to record what 2D shapes can be made when
prisms is cut through with a knife. The learners should try to visualise the shape made b
first, then check by carefully cutting with the blunt knife.
Ask groups of learners to draw another table and carry out the same activity to investiga
choice of the following shapes:
tetrahedron (triangle based pyramid)
square based pyramid
pentagon based pyramid
hexagon based pyramid
Gather the class findings to see what different groups have discovered.
74 Unit 1C 8 2D and 3D shape (1)
cross-sections LB: p32
nives (There is a health and safety issue using knives in the
ke a class list of Vocabulary
alled polyhedral.
and display the polyhedron: a 3D shape with polygon faces.
and encourage face: flat surface of a 3D shape.
edge: the line where two faces of a 3D shape meet.
lowing 3D vertex/vertices: the point/points where edges of a 3D
shape meet.
ey are made prism: a 3D shape with two identical, parallel faces,
and all other faces are rectangles.
pyramid: a 3D shape with a polygon face and all other
faces are triangular and meet at a vertex.
shape made by Look out for!
to visualise
can be made by Learners who have difficulty visualising the shapes
made by cuts. Start with cuts that are parallel to one
each of the of the faces, such as the base, and demonstrate how
by the cut the same 2D shape is made by those parallel cuts.
Encourage learners to try to explain why the cuts
ate their make the same shape as the face when they are
parallel to the face. Extend learners’ understanding
by asking them to try to draw diagrams to record the
3D shapes and the shape of the cuts.
Summary
Learners will have explored the 2D shapes that are made from cutting through
They will have used ‘faces’, ‘edges’ and ‘vertices’ to describe the properties o
Notes on the Learner’s Book
3D shapes (p32): learners name 3D shapes from the descriptions of their numbe
faces, edges and vertices.
More activities
How many faces? (individual or groups)
You will need modelling dough.
Learners can investigate what different 3D shapes they can make that have 4, 5, 6
h a 3D shape. Check up!
of 3D shapes.
Show learners pictures of 3D shapes. Ask how many
er of faces, vertices and edges each shape has.
6, 7, 8, 9 or 10 faces.
Core activity 8.2: Properties of 3D shapes and their cross-sections 75
Core activity 8.3: Nets
Resources: Scissors. Sticky tape. Card. (Optional: a purpose made, resources, such
Note: this activity follows on from chapter 7, where learners were making their own m
houses, but the model furniture could be made independently of the model house.
Ask pairs of learners to discuss what furniture would be appropriate to make for their roo
house from chapter 7. They should list some 3D shapes that they could use for different
furniture and make a 2D sketch of those objects. Most of the furniture shapes will be cub
pairs to design one piece of furniture that is a different type of prism.
Learners should make measurements for the height, width and length of each piece of f
be made as a cuboid and label their sketches with these measurements.
Remind learners that the net of a cuboid is made using six rectangles. Each rectangle
the cuboid. The rectangles must be positioned next to each other so that they will fold
a cuboid.
Learners should make templates out of paper for each of the six rectangular faces of the
become a piece of furniture for the model house, using their measurements. Once they
how to position the six faces, so that they will fold up to become a cuboid, they should ta
rectangles together flat then transfer the joined template onto card by drawing around th
rectangles. The net can then be cut out, decorated to look like the piece of furniture, fold
and placed in the model house room.
Ask learners for ideas as to how to make a net in a similar way for another prism. Wr
instructions for how to make any net of a prism, including making it the correct size
model house room. Display the instructions for learners to refer to while they make t
Pairs should follow the instructions to make the piece of furniture they have designed th
cuboid shape.
Discuss how useful and helpful the instructions are for making a net of a prism. Ask
suggestion on how they can be improved. Edit the instructions and save them for lear
in a later chapter.
76 Unit 1C 8 2D and 3D shape (1)
LB: p34
h as ‘Clixi’ or ‘Polydron’ for creating 3D shapes.)
model
om in the model Look out for!
t items of Learners who are unsure about drawing a 2D sketch
boids. Ask the of a 3D shape. Remind them of how they learnt to
draw cuboids in Stage 5. Learners can start by
furniture that will drawing the ‘front’ face of the cuboid as a rectangle.
They can draw the rear face of the cuboid as an
e is one face of identical rectangle, translated diagonally
d up to become from the original, then join each corner of the rear
rectangle to its original on the front rectangle with
e cuboid that will straight lines.
have worked out
ape the paper Opportunities for display!
he taped Display the furniture made from cuboids and prisms
ded into a cuboid, alongside the measurements for them and instructions
on how to make the 3D shapes.
rite a class set of
to t inside the
their own nets.
hat is not a
k learners for
rners to refer to
Summary
Learners will have recognised and made 2D representations and nets of cuboids
Notes on the Learner’s Book
Nets (p34): learners match 3D shapes to the nets that would make them. They dr
would be made from a net, and the net that would make a pictured 3D shape.
More activities
How many nets? (individual or pairs)
You will need a purpose made, resources, such as ‘Clixi’ or ‘Polydron’ for creat
Give learners practical, purpose made resources, such as ‘Clixi’ or ‘Polydron’, fo
shape in different ways to create nets of the shape and draw each of the nets.
Is it a cube? (individual or pairs)
You will need paper and scissors.
Learners can investigate how many different nets of a cube are possible, not incl
Games Book (ISBN 9781107667815)
Don’t make a cube game (p90) is a game for two players. Players rearrange six to
recognise whether their opponent has made a net of cube.
and prisms. Check up!
raw the shape that
Show learners pictures of 3D shapes. Learners should
draw a net of one of the shapes.
ting 3D shapes.
or creating 3D shapes. Once they have made a 3D shape they should ‘undo’ the
luding reflections and rotations.
ouching squares on a grid, trying not to make a net of a cube. They try to
Core activity 8.3: Nets 77
Identifying polygons
Instructions on page 70 Original Material © Cambridge University Press, 2014
Quadrilaterals
Parallelograms
Other quadrilaterals
Instructions on page 70 Original Material © Cambridge University Press, 2014
3D shapes
Polyhedron: a 3D shape with polygon faces.
Face: flat surface of a 3D shape.
Edge: the line where two faces of a 3D shape meet.
Vertex/vertices: the point/points where the edges of a 3D
Prism: a 3D shape with two identical, parallel faces and a
faces are rectangles.
Pyramid: a 3D shape with a polygon face and all other fa
are triangular and meet at a vertex.
Instructions on page 74
s poster
D shape meet.
all other
aces
Original Material © Cambridge University Press, 2014
1C 9 Angles in a triangle
Quick reference
Core activity 9.1: Angles in a triangle (Learner’s Book p)
Learners measure the angles of a triangle and explore the sum of the angles of a
Prior learning Objectives* – please note that listed o
book when taken as a w
Understand and use angle
measure in degrees. 1C: Geometry: (Shapes and
Measure angles to the nearest 5°. 6Gs5 – Estimate, recognise and dra
Identify, describe and estimate the
size of angles and classify them as degree.
acute, right or obtuse. 6Gs6 – Check that the sum of the an
Calculate angles in a straight line.
angles in a triangle or around
1C: Problem solving (Using
6Ps2 – Deduce new information from
another.
*for NRICH activities mapped to the Cambridge
Vocabulary
angle degrees
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Angles in a t riangle Vo cab ulary
a triangle. Let’s investigate angle: the amou nt
J oh n ha s dra w n f ou r d ifferen t tria n g le s a n d mea sure d
an gles in eac h tr ia ng le . Here are all of h is of tur n between two th e
measure men ts. Fin d f o ur gr ou p s o f three a ng le s th at lines mee ting at a
g o to ge ther to ma ke the a n gles o f tria ng le s. ( Do n o t
u se the sa me size a n gle fo r more tha n on e tr ia n g le.) c om m on p oin t.
90° 63° 30° 17° degrees: a unit for
me as ur in g the size of
an angle.
107° 53° 43° 50°
60° 100° 40° 67° T he a n g le s of a tira ng le
le ad d u p to 1 8 0˚ .
1 He len drew this triang le.
She tore off the corners of the tr iang le alon g
the dotted lines an d p ut a ll the corner s
together.
Describe the ang le made by the three an gles of the
triang le put to gether.
2 Measure two of the an gles in each tria ngle and then calculate the s ize of the
third angle.
Write down a ll three ang les of each tria ngle to the nearest 5˚.
(a) (b) (c)
(d) (e)
36
objectives might only be partially covered within any given chapter but are covered fully across the
whole
d geometric reasoning)
aw acute and obtuse angles and use a protractor to measure to the nearest
ngles of a triangle is 180º, for example, by measuring or paper folding; calculate
d a point.
g understanding and strategies in solving problems)
m existing information and realise the effect that one piece of information has on
e Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 1C 81
Core activity 9.1: Angles in a triangle
Resources: Metre sticks. Measuring angles in triangles photocopy master (p85).
(CD-ROM); access to LOGO turtle.)
Remind learners that, in Stage 5, they learnt that when two lines meet at 180 they mak
straight line. Demonstrate that this is true by using two metre sticks. Lay the metre sti
of each other. Hold the sticks loosely together at one end and rotate the top stick to c
angle with the bottom stick until it makes a right angle. Ask learners how many degr
is shown by the two sticks at this point (Answer: 90). Continue rotating the top metre
stopping at a few places for learners to discuss their estimates of the size of the angle
until the 180 angle is reached and the sticks make one straight line.
Add a third metre stick as below.
30 ?
Ask, “If this angle is 30, what is the other angle?” (Answer: 150°) Move the third m
three or four times and ask the same question with different degrees of angle.
Tell learners that they are going to be measuring angles in this session so they need to r
themselves how to do this. Ask learners in small groups to discuss and write instructions
measuring angles to the nearest 5 degrees.
Discuss the instructions made by each group and make a class set of instructions to d
during the activity.
82 Unit 1C 9 Angles in a triangle