Exploring regular polyhedra
Page 2
Instructions on page 300 Original Material © Cambridge University Press, 2014
Exploring regular polyhedra
Page 3
Net of a tetrahedron
Net of an octahedron
Glue
Under
Instructions on page 300 Original Material © Cambridge University Press, 2014
Exploring regular polyhedra
Page 4
Net of an icosahedron
Net of a dodecahedron
Glue Under
Glue Under
Instructions on page 300 Original Material © Cambridge University Press, 2014
Tetrahedron Platonic solids poster
Cube
Octahedron Dodecahedron
Icosahedron Original Material © Cambridge University Press, 2014
Instructions on page 300
308 Blank page
3C 34 Locating 2D shapes
Quick reference
Core activity 34.1: Classifying shapes (Learner’s Book p124)
Learners distinguish between shapes that are polygons and those which are not
by considering the properties of the shapes.
Core activity 34.2: Transforming polygons (Learner’s Book
p126)
Learners transform polygons on co-ordinate grids.
Prior learning Objectives* – please note that listed objec
are covered fully across the
This chapter builds on work earlier
in the stage where learners read 3C: Geometry (Shape and geo
and plotted co-ordinates in all four 6Gs1 – Classify different polygons and
quadrants. They predicted where
a polygon would be 3C: Geometry (Position and m
after a reflection and a rotation 6Gp1 – Read and plot co-ordinates in a
and understood translation as 6Gp2 – Predict where a polygon will be
movement along a straight line.
not parallel or perpendicular to
through 90º about one of its ver
*for NRICH activities mapped to the Cambridge Prim
Vocabulary
polygon
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Classifying shapes Vo c abula r y Transfo rmingsh apes
Let’s investigate poly go n: a closed Let’s investigate
Draw a Venn d iagram to cla ss ify the se sha pe s in to 2-d ime ns io nal s hap e
su ita ble gro ups. Frie ze pa tter ns
having three or more T he se fr ie ze pa tter n s are fo rme d us in g reflection s, r ota tion s an d tr an sla tion s.
straight sides. Inve stiga te pa tter ns in the en vir o nmen t, f or e x am ple o n b uild in g s a n d in art,
or de s ig n y o ur ow n pa tter ns .
1 Dr aw a tr iang le o n a six by six grid. Re ect it,
translate it a nd ro tate it u ntil y ou have a
desig n y ou th in k is attractive or interesting.
1 (a) A sq uare has vertices at (3, 0), (0, 3) an d (−3 , 0). What are the 2 A , B, C an d D are the vertices of a rectangle. and B
coordinates of the fourth vertex ? A are shown on the gr id.
y
(b) hTe po ints ( 3, 2) and (−1, 2) are two vertices of a square. What co uld the 8
other two vertices be ?
7
How many solu tions can y ou nd ? 6
5A
2 Loo k a t the statements abo ut triangles. For each one, say whether it is p oss ib le
or impossible. 4B
● A tr iang le can have two rig ht ang les 3 x
● A tr iang le can have two acute ang les
● A tr iang le can have two o btu se a ngle s 2
1
12 4 -8 - 7 - 6 -5 -4 -3 -2 -1 0 1 2
34 5 6 7 8
D is the p oint ( 3, 4). What are the coordinates of C?
ABCD is re ected in the y-axis. What are the coordinates of the image ?
12 6
ctives might only be partially covered within any given chapter but
book when taken as a whole
ometric reasoning)
understand whether a 2D shape is a polygon or not.
movement)
all four quadrants.
e after one reflection where the sides of the shape are
the mirror line; after one translation or after a rotation
rtices.
mary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 3C 309
Core activity 34.1: Classifying shapes
Resources: Use the clues to identify a shape photocopy master (p314). Sketch the
the Learner’s Book chapter, Classifying shapes.)
Display or hand out the eight shapes on the photocopy master Use the clues to identif
each clue statement in turn (below), checking that learners understand the mathemati
including the word polygon. Discuss with learners how the clues can eliminate shape
Continue until only one shape is left. (Answer: shape B)
Clue statements: I have no curves.
I am not a regular polygon
My sides are not all the same length. I am not a quadrilateral.
I have more than two sides.
I have exactly one pair of parallel sides.
Reinforce this activity by asking:
“Which shapes are polygons?” (Answer: B, C, D, F, G and H)
“Which shapes are regular polygons?” (Answer: C, F, H)
“Which shapes are not polygons? How do you know?”
(Answer: A and E. They have at least one curved side.)
Say that, “We can classify shapes according to their properties, for example shapes w
straight sides (polygons) and those which have at least one curved side.”
Distribute cards cut from the activity sheet Sketch the shape.
Learners work in pairs to sketch the shapes from the description. (Some are not possibl
many solutions.)
Lead a discussion where learners can share their results on sketching shapes. Ensure
vocabulary is understood. Classify the shapes in different ways, for example, polygon
polygons, regular shapes and not regular shapes.
310 Unit 3C 34 Locating 2D shapes
LB: p124
shape photocopy master (p315). Squared paper. (Optional: page 124 from
ify a shape. Read Vocabulary
ical vocabulary,
es on the grid. polygon: a closed 2-dimensional shape having three or
more straight sides.
which have all Look out for!
Learners who do not yet have a good grasp of the
le, some have mathematical vocabulary. Use mathematical
dictionaries, word lists and displays to support the
that all the development of mathematical language
ns and not
Opportunities for display!
Display the cards, learners’ sketches and definitions
of the mathematical vocabulary used.
Summary
Learners distinguish between shapes that are polygons and those that are not.
They understand and use mathematical language related to shape.
Notes on the Learner’s Book
Classifying shapes (p124): the investigation gives learners an opportunity to app
done on classifying shapes as they are challenged to sort shapes and display thei
a Venn diagram. It is important that learners are able to link topics together in th
and data handling.
There is a heavy emphasis on mathematical language in the questions. It is a goo
learners to use mathematical dictionaries or make use of classroom displays to re
words and their meaning.
More activities
Quadrilateral plot (pairs)
You will need squared paper.
Without allowing their partner to see, one learner plots a quadrilateral on a co-or
vertices. The partner works out the co-ordinates of the fourth vertex. Swop roles
The activity can be varied to include other shapes.
Sketch the shape (pairs)
You will need page 124 from the Learner’s Book chapter, Classifying shapes.
Learners make up a set of clues that will identify a polygon, like those on page 1
Games Book (ISBN 9781107667815)
Co-ordinate games – game 2 (p103) is a game for two players. The game focuses
ply the work Check up!
ir categories in “Name two shapes that are polygons and two shapes
his case shape
that are not polygons.”
od opportunity for Draw the Venn diagram below on the board. Point to
emind them of
a position and ask, “What shape could I place here?”
2D shape
regular
polygon polygon
rdinate grid, then tells their partner the name of the quadrilateral and three
and repeat.
124 of the Learner’s Book. Their partner draws a sketch of the polygon.
s on locating a rectangle on a co-ordinate grid in four quadrants.
Core activity 34.1: Classifying shapes 311
Core activity 34.2: Transforming polygons
Resources: Transforming polygons photocopy master (p317). Squared paper.
Work with learners to plot a triangle and then transform it:
plot the points (0, 1) (0, 3) and (2, 1) on x- and y-axes labelled from –4 to +4
join the points and shade the triangle
rotate the triangle 90° clockwise about the point (2, 1) to form the image of the or
triangle
rotate the image 90° clockwise about the point (2, 1)
repeat one more time.
(You will have image 1 to the right.)
Now, reflect the pattern of four triangles in the y-axis.
(You will have image 2 to the right.)
Learners work in pairs on the activity Transforming polygons, that revises the three trans
reflection, rotation and translation.
Discuss the work done. Invite learners to collect examples of patterns of this type, fo
fabrics or wallpaper. Create a classroom display.
312 Unit 3C 34 Locating 2D shapes
LB: p126
Image 1 y
riginal 4
3 (0, 3)
sformations:
2
or examples in 1 (2, 1)
(0, 1)
-4 -3 -2 -1 1234 x
-1
-2
-3
-4
Image 2 y
4
3 (0, 3)
2
1 (2, 1)
(0, 1)
-4 -3 -2 -1 1234 x
-1
-2
-3
-4
Opportunities for display!
Create a classroom display, labelling the shapes and
transformations.
Summary
Learners accurately transform polygons on co-ordinate grids, including combinin
transformations. They are able to predict where a shape will be after a ref l ection
rotation or translation and understand that the image will be the same shape and
the original shape but may be in a different orientation.
Notes on the Learner’s Book
Transforming shapes (p126): this is a short section revising work done on transf
co-ordinates. The emphasis is on learners investigating their own patterns.
More activities
Drawing shapes
(pairs)
You will need squared paper.
Draw this image on the board for the learners.
A
Ask them to rotate the shape 90° clockwise about the point A. (Answer:)
Ask what the name of the polygon formed by the original shape and its image is
In turns, pairs of learners challenge each other to draw a shape on a square grid
the shape and its image make:
a square
a trapezium
a parallelogram
another shape.
ng Check
n,
size as up“!Draw a polygon with co-ordinates … Ref l ect (or
formations and translate, or rotate) the shape. What are the co-
ordinates of the image?”
“Can you give me definitions of the following
words: transformation, ref l ect, translate, rotate,
image?”
s? (Answer: pentagon)
and then translate, ref l ect or rotate (or a combination of these) their shape so that
Core activity 34.2: Transforming polygons 313
Use the clues to identify a shape
B
A
D
C
EF
GH
Instructions on page 310 Original Material © Cambridge University Press, 2014
Sketch the shape - cards
✂
1. 2.
A triangle with an A triangle with two
obtuse angle right-angles.
3. 4.
A triangle with a A triangle without
reflex angle. an acute angle.
5. 6.
An isosceles A symmetrical
triangle scalene triangle.
7. with a right angle.
8.
A right-angled
scalene triangle. A quadrilateral
which is regular
but not symmetrical.
9. 10.
A quadrilateral A quadrilateral with
which is symmetrical a reflex angle.
but not regular.
Instructions on page 310 Original Material © Cambridge University Press, 2014
11. 12.
A quadrilateral with A quadrilateral with
two acute angles. three acute angles.
13. 14.
A quadrilateral with A pentagon which
four acute angles. is symmetrical
but not regular.
15. 16.
A hexagon with four A pentagon without
acute angles. a reflex angle.
17. 18.
A symmetrical A polygon which is
octagon. not a closed shape.
19. 20.
A closed shape A quadrilateral
which is not a with rotational
polygon. symmetry but no
line symmetry.
Instructions on page 310 Original Material © Cambridge University Press, 2014
Transforming polygons
Here is a co-ordinate grid.
y
7 1234 x The points (3, 2) and (1, 2) are two
6 vertices of a square.
5 What could the other two vertices be?
4
3 How many solutions can you find?
2
1
-2 -1
−1
−2
−3
Here is a different co-ordinate grid. Plot the points (2, 0), (4, 2), (2, 4) and
y (0, 2). Join them to form a square.
5 1234 Reflect the square in the y-axis
4 Reflect both the original square and
3 its image in the x-axis.
2 You should have a pattern made of
1 x four squares.
-4 -3 -2 -1 Start with the original square and find
−1 different ways of producing the same
−2 pattern of four squares. You could
−−32 try using reflections, rotations and
−4 translations. Explain your findings.
−5
Instructions on page 312 Original Material © Cambridge University Press, 2014
318 Blank page
3C 35 Angles and triangles
Quick reference
Core activity 35.1 Drawing and measuring angles (Learner’s Book p12
Learners learn how to draw an acute or obtuse angle. They improve their measur
the nearest degree.
Learners investigate angles in a triangle and about a point.
Prior learning Objectives* – please
are cov
Identify and describe properties of triangles and
classify as isosceles, equilateral or scalene. 3C: Geometry
6Gs5 – Estimate, recog
Understand and use angle measure in degrees;
measure angles to the nearest 5°. measure to the
Identify, describe and estimate the size of angles 6Gs6 – Check that the
and classify them as acute, right or obtuse. paper folding; c
Calculate angles in a straight line.
3C: Problem s
6Ps2 – Deduce new in
piece of inform
*for NRICH activities mapped t
Vocabulary
No new vocabulary.
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
27) Investigating and d rawing ang les T he su m of th e a ng le so n
rement of angles to o n a stra ig ht lin e is
Let’s investigate 1 80 ˚.
With ou t mea s urin g, wo r k o u t th e a n gle a t X.
Wor k o ut s ome of the
40° othe r m is s in g a n g le s
X rs t.
40°
70°
80°
1 A n anc ie nt c iv iliza tio n h id den with in a distant Co de mountain
1 14˚ tablets a s a
range, carved their writin g into clay A 6˚ S 12 0 ° matches a letter in
T
serie s of angles. Each s ize of an gle B 12˚ 18˚ U 126°
C 24˚ V 132°
our alp habe t or a digit D 30˚ W 1 38 °
E 36˚ X 144°
from 0 to 9. F 42˚ Y 150°
G 48˚ Z 156°
This clay tablet has bee n sma she d. Wor k ou t H
the letter or number o n each p iece and 54˚ 0 162°
I 60˚ 1 168°
then rearr agengtehethmemt tod iscovedristchoevewrotrhde. word. J
K 66˚ 2 174°
(a) (b) (c) (d) L 7 2˚ 3 1 8 0°
(f) ( h) M 7 8˚ 4 18 6 °
(g) N 84˚ 5 194°
(e) O 90˚ 6 200°
(i) (j)
( k) P 9 6˚ 7 2 0 6 °
Q 102˚ 8 212°
R
108° 9 218°
(l) The word is .
2 Draw the a ngle s that would write the w ord ‘tria ngle ’.
127
e note that listed objectives might only be partially covered within any given chapter but
vered fully across the book when taken as a whole
y (Shapes and geometric reasoning)
gnise and draw acute and obtuse angles and use a protractor to
e nearest degree.
e sum of the angles of a triangle is 180º, for example, by measuring or
calculate angles in a triangle or around a point.
solving (Using understanding and strategies in solving problems)
nformation from existing information and realise the effect that one
mation has on another.
to the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 3C 319
Core activity 35.1: Drawing and measuring angles
Resources: Protractors. Rulers.
Tell learners that they are going to learn how to draw angles using a protractor and ru
learners that they have measured angles with a protractor before and of any common
have previously made when using a protractor, e.g. lining the edge of the protractor u
the lines of the angle, using the wrong scale so that an acute angle is measured as an
or vice versa etc.
Ask learners to experiment first how they might use a protractor to draw an angle of 60˚
learners should talk about what they did with the protractor to try to draw an angle of 60˚
they were successful.
Demonstrate how a protractor is usually used to draw an angle and then write instruc
display with the learners for using a protractor successfully to draw an angle. This mi
Instructions for drawing an angle
1. Draw a straight line with a ruler.
2. Place the protractor on the line, making sure that the 0˚ line is exactly on top of the
3. Slide the protractor horizontally so that the centre mark on the protractor is exactly
of the line where the angle will be drawn, keeping the 0˚ line on top of the drawn l
4. Find and mark the desired angle on the paper by the curved edge of the protractor.
to use the correct scale.
5. Remove the protractor. With a ruler, draw a line between the mark and the end of t
6. Check that the angle is reasonable (i.e. should it be an acute or obtuse angle?) and
the protractor.
Ask all learners to draw two angles, one of 35˚ and one of 110˚, following these instructi
learners should check the each others’ angles by measuring them with a protractor.
Instruct learners to draw a 10 cm line. On the left end of the line they should make a
on the right end of the line they should make a 42˚ angle. It should look like this:
320 Unit 3C 35 Angles and triangles
LB: p127
uler. Remind Opportunities for display!
errors learners Display the poster made with the learners with
instructions for drawing an angle.
up with one of
n obtuse angle Look out for!
Learners who consistently measure angles slightly
˚. Pairs of narrower than they are. It is common for learners to
˚, and whether incorrectly measure from the edge of the protractor,
rather than from where the scale starts at ‘0’.
ctions to Demonstrate how the measurements are different
ight be: when the measurement is not done from the correct
start of the scale. Learners who find this difficult to
e drawn line. remember could make a small sticky note to
y on the end themselves to attach to their protractor, and remove
line. when they are measuring.
. Make sure
the line.
measure with
ions. Pairs of
78˚ angle, and
(not to scale)
Ask learners to visualise the two shorter lines being ex
they could find out the size of the angle where the two
78 42 ideas to the group. They should explain that when the l
triangle is 180˚. The angles drawn total 120˚, so they c
Learners should check that they have drawn the first two angles accurately by ex
that it is 60˚.
Ask learners to choose and draw two more angles on either ends of a straight lin
then extend the lines and measure the angle to check.
Ask one learner to stand at the end of a metre stick, facing along the metre stick
other learners how much further clockwise the learner would need to turn to be f
the learner to turn a further 90˚ clockwise from their current position and ask the
made the full circle (Answer: 210˚). Draw a diagram to show these angles, as in
Ask learners to draw a dot on their paper and then draw four 6 cm lines comin
meet at a point. Learners should measure each of the angles, then check their m
360˚.
Summary
Learners have learnt how to draw an acute or obtuse angle.
They have improved their measurement of angles to the nearest degree.
Learners have investigated angles in a triangle and about a point.
Notes on the Learner’s Book
Investigating and drawing angles (p127): learners will measure and draw angles
degree to solve a puzzle. They will reason about the angles in a triangle and dedu
angles from given information.
xtended until they crossed each other. Ask learners to discuss with a partner how
o lines meet, without measuring it, and then choose some pairs to describe their
lines meet the three lines will have made a triangle. The sum of the angles of a
can deduce that the new angle should be 60˚.
xtending the short lines until them meet and measure the angle made to check
ne. They should calculate what the third angle of the triangle should be and
k. Ask them to turn clockwise approximately 60˚. Ask the 60
facing along the metre stick again (Answer: 300˚). Ask 210 90
e learners again how far is still needed to turn to have
n the ‘Look out for!’ panel.
ng from the dot in different directions, making four angles that
measuring by seeing if the angles they have measured add up to
to the nearest Check
uce the size of upA! sk learners to draw a triangle where two of the
angles are 105˚ and 43˚. Ask them to name what the
third angle will be, then measure it to check.
Ask learners to generate three 2-digit numbers less
than 70 using dice or dominoes. Tell them that the
three numbers are degrees of turn taken clockwise in
sequence. Ask them how many degrees further they
would have to turn to have made a full circle.
Core activity 35.1: Drawing and measuring angles 321
More activities
The accurate angle (pairs or small groups)
You will need Protractors. Rulers.
Learners can challenge each other to draw angles between 1˚ and 179˚. Learners cou
drawing of the angle is.
Does it add up? (individual)
You will need Protractors. Rulers.
Learners draw a rectangle. They mark a point along one edge of the rectangle. They j
the rectangle is divided into three triangles. Challenge learners to measure only one o
without measuring, using their knowledge of the angles in a right angle and the sum
check how accurate their measuring is.
Investigation (individuals or pairs)
You will need Protractors. Rulers.
Ask learners to investigate the question, “Is it possible to draw a triangle with two rig
reasoning statement which could be used for a display. As necessary, provide learners
a triangle with two right angles because …
Ask learners to investigate the statement, “Any triangle can be split with one straight
all of the different types of triangles that they know. When learners report back what
that all triangles can be split into two right-angled triangles, but they have provided e
learners to find the three lines on one triangle that each can split the triangle into two
triangles from their triangles, show them how to take a known right angle, e.g. the cor
Games Book (ISBN 9781107667815)
The drawing angles game (p103) is a game for three players. Players try to draw angl
other learners’ angles for accuracy.
322 Unit 3C 35 Angles and triangles
uld develop their own scoring system to award points for how accurate the
join the all the corners of the rectangle to the point with straight lines so that
of the angles and then work out all the other angles of the three triangles
of the angles on a straight line. They should then measure their angles to
ght angles?” They should present their findings with diagrams and a
s with a template for their reasoning statement, e.g. It is/is not possible to draw
t line into two right-angled triangles.” Tell learners to make sure that they try
t they have found out, make sure they understand that they have not proved
evidence that shows that it is likely to be true. As appropriate, challenge
o right-angles. If learners are finding it difficult to make two right-angle
rner from a sheet of paper.
les as close as possible to a specified angle. They take turns to measure