LB: p36
. Protractors. (Optional: Find the missing angle photocopy master
ke a Vocabulary
icks on top
create an angle: the amount of turn between two lines meeting at
rees of turn a common point.
degrees: a unit for measuring the size of an angle.
e stick,
e in degrees, Use the introductory activity to assess learners’
knowledge of angles, degrees and angles in a straight
line. As necessary, give pairs of learners sticks to
challenge each other to estimate and make different
angles as accurately as possible from 0 to 180, and then
up to 360.
metre stick
remind
s for
display
The instruction could look like:
Steps for measuring angles
1. Estimate the size of the angle in degrees.
2. Place the centre of the protractor where the two lines that make the angle mee
3. baseline along one line of the angle.
4. Measure from the baseline, using the scale that starts at 0°, checking whether
clockwise or anticlockwise.
5. Read off the angle size where the second line crosses the scale on the protract
nearest 5 degrees.
6. Check the reasonableness of the measurement by looking to see if the angle i
obtuse or re ex and that the measurement matches the type of angle, and whe
measurement is close to the estimation.
Give learners the Measuring angles in triangles photocopy master to complete and
partner. Once they have completed the sheet ask learners to calculate the total of t
each triangle on the sheet. They should find that the angles total 180, although if lea
rounded the measurements to the nearest 5 there maybe some small variation.
Ask learners to check that the total of all the angles of a triangle is 180 by tearin
each corner then sticking them down onto another sheet of paper to show that th
straight line.
Example:
Tell learners that this has shown that all the triangles they have measured and dra
activity have angles that total 180, because the sum of angles in a straight line is 1
learners to draw one more triangle each, trying to nd an example where the ang
180, and tear off the corners to see if they can be put together to make a straight
et. Place the Look out for!
it is Learners who don’t know what ‘right angle’, ‘acute’
tor to the and ‘obtuse’ angles are. Remind them that they met
is acute, this in Stage 5, then draw example angles of each
ether the type. Get them to draw examples of their own that are
acute and obtuse.
discuss with a
the angles for Look out for!
arners have Learners who consistently measure angles slightly
narrower than they are. It is common for learners to
ng off incorrectly measure from the edge of the protractor,
hey make a rather than from where the scale starts at ‘0’.
Demonstrate how the measurements are different
awn in this when the measurement is not done from the correct
180. Ask start of the scale.
gles do not total
Opportunities for display!
angle. Display the corners of the triangles arranged to show that
the angles total the same as the angles in a straight line.
Ask some learners to write the hypothesis that all
triangles haveangles that total 180.
Core activity 9.1: Angles in a triangle 83
Explain to the learners that they have not found a mathematical proof that all triangle
angles that total 180, but that they should consider it true for the following activities.
Draw a triangle on the board. Label two of the corners with their angle measurements
or two learners to explain how they can deduce, without measuring, the third angle o
triangle. Repeat with two more triangles.
Summary
Learners have measured the angles of a triangle and explored the sum of the angles o
Notes on the Learner’s Book
Angles in a triangle (p36): learners measure angles in triangles to the nearest 5. They
problems using their knowledge of different types of triangles and that the sum of th
triangle is 180.
More activities
Missing angles (pairs)
You will need Find the missing angle photocopy master (CD-ROM).)
Give pairs of learners the Find the missing angle sheet and instruct them to cut along
table. Learners need to turn over two of the angle cards. If the cards total more than 18
calculates what the other angle of a triangle would be if two of its angles were those
continue until all the angle cards have been taken, or there are no more pairs that total
LOGO triangles (individual)
You will need access to the LOGO turtle.
Learners can construct triangles in LOGO by instructing the turtle to turn the differen
triangle’s corner. They should plan the angles of the triangle and the angles of turn a
Games Book (ISBN 9781107667815)
Angles of a triangle (p95) is a game for two to four players. Players take turns to cover
over three angles wins the game.
84 Unit 1C 9 Angles in a triangle
es have Look out for!
s. Ask one Learners who are quick to recognise generalisations.
of the Encourage them to make posters of their
generalisations, such as:
angle a + angle b + angle c = 180
If angle a and angle b are known, and angle c is
unknown the statement can be written as,
40 + 100 + angle c = 180
of a triangle. Check up!
y solve Ask learners in pairs to draw triangles for each
he angles in a other to measure the angles of, cut out, and
test by tearing and sticking the corners thatthe
angles total180.
g the dotted lines, shuf e the angle cards and place them face down on the
80, they turn them back over. If they total less than 180 then the learner
on the selected cards. They then remove those cards from the set. Learners
less than 180.
nce between 180 (the straight angle) and the desired angle for the
and then test their plan by writing a procedure.
r over three angles that total 180. The last player to be able to cover
Measuring angles in triangles
Measure each angle of each triangle to the nearest 5. Write the angle in
the corner of the triangle.
Check that the measurement matches the type of angle (acute/obtuse/right
angle).
Compare your measurements with a partner’s measurement.
Use a ruler to draw any triangle here.
Measure and label the angles to the nearest 5.
Instructions on page 82 Original Material © Cambridge University Press, 2014
86 Blank page
1C 10 Shapes and Geometric rea
Quick reference
Core activity 10.1: Describing translations (Learner’s Book p38)
Learners are introduced to the four quadrants of the co-ordinate grid and use
co-ordinates to describe translations. They understand translation as a movement
a straight line.
Core activity 10.2: Ref l ecting shapes (Learner’s Book p40)
Learners ref l ect shapes with sides that are not necessarily parallel or perpendicu
the mirror line.
Core activity 10.3: Rotation on a grid (Learner’s Book p42)
The concept of rotation is introduced. Learners rotate some 2D polygons
through 90° about one of the vertices.
Prior learning Objectives* – please n
across th
This chapter builds on the work covered in
Stage 5, where learners read and plotted co- 1C: Geometry (
ordinates in the first quadrant. 6Gp1 – Read and plot c
Learners should already be able to predict 6Gp2 – Predict where a
where a polygon would be after a reflection
where the mirror line was parallel to one of the or perpendicular
sides of the shape.
Learners should already understand translation of its vertices.
as movement along a straight line.
1C: Problem so
6Ps2 – Deduce new info
information has
*for NRICH activities mapped to
Vocabulary x-axis y-axis origin vertex vertices
rotation image clockwise anti-clockwise
co-ordinates quadrants
translation reflection
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
asoning
Describ ing translations Vocab ulary Re ect ing shap es Vocabulary Rotation Vo c abula r y
reflection: a mirror rotation: turns an
Let’s investigate axis:is a reference Let’s investigate view. Let’s investigate object ab ou ta p oint.
N ou r ma kes this pa tter n by re peatin g th e tra ns latio n line; graphs have a T his s hee t of pa pe r h as b ee n Lo o k at the is osce le s tr ia ng le
of a tria ng le. fo ld ed o nc e. image: p osition of draw n o n a gr id. clockwise: the same
horizontal axis (x) shape followin g a re direction as ha nd s o n
and a vertical axis (y). T he s ha pe is c ut o u t a s sh o wn. ection . Ro ta te the tr ia ng le 9 0 ° c loc kw ise a bo u t the a clock turn .
De scr ibe th e f inal s ha pe y o u anti-clockwise: the
coordinates: show w ou ld ge t if y ou o pe ne d it o ut. Draw the image . opposite d irection as
pos ition on a grid ; they Con tin ue rota tin g the tria ng le tw ice more. han ds o n a
are shown as pairs of Ho w ma ny line s of sy m metry will it ha ve ? clock turn .
numbers, for example (
3, 1). 1 Copy the diagram. Re ect the shape in the mirror A
line.
y
t along 4 W ha t sh ap e have y o u m ad e ?
ular to
De scr ibe to a pa rtner h ow to ma ke N our ’s pa tter n. 32
Fin d, or dra w, pattern s of y o ur ow n us in g trans latio ns.
1 Investigate ro tating similar
1 Copy the diagram of a quadrilateral onto a square grid. sha pes y ou see d ur in g the day .
Translate the quadrilateral four squares to the right. 1( 4231), 3 12 3x You may n d
12 4 Write a report o n y o ur f in din gs . d tracipnagper
er he lp fu l.
3
4 1 The hour han d o n an analogue cloc k po ints
translation: moves or s lides to 1 0.
It turns throu gh 90 ° cloc kwise. What
an item w ithou t rotating it. number does it p oint to?
2 Which of these p ieces ts the ho le in the 2 T he diagram shows a sha ded square on a gr id. 2 The diagram shows a trapezium o n a square grid.
middle of the jig saw ? Draw a similar gr id and sha de in three more
squares so the de sig n is sy mmetrical abo ut Copy the s hape on squared paper. Rotate the
both mirror lines. trapezium 90 ° cloc kwise ab out p oin t A and
draw the image.
40
38 42
note that listed objectives might only be partially covered within any given chapter but are covered fully
he book when taken as a whole
(Position and movement)
co-ordinates in all four quadrants.
a polygon will be after one reflection where the sides of the shape are not parallel
r to the mirror line; after one translation or after a rotation through 90º about one
olving (Using understanding and strategies in solving problems)
ormation from existing information and realise the effect that one piece of
on another.
the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 1C 87
Core activity 10.1: Describing
translations
Resources: The four quadrants photocopy master (p96). Co-ordinates photocop
(Optional: Squared paper and/or +/– 10 co-ordinate grid photocopy master (CD-RO
Co-ordinates and the four quadrants
Show a co-ordinate grid of the first quadrant (positive x and y values). Remind learne
both axes start at 0. Identify the x-axis and the y-axis. Ask learners if they remember
notation used to identify the position of a point on a grid (Stage 5, Unit 1B, chapter 6
necessary, demonstrate a few examples for the class to see, asking learners to call out
ordinates of points you plot on the grid; and/or ask learners to plot points according t
ordinates you have provided.
Remind learners that if we count back in ones 3, 2, 1, 0 we can continue countin
using negative values, for example, –1, –2, –3 etc.) Show how to extend the axes
quadrants; or display The four quadrants photocopy master.
Label each quadrant (first, second, third and fourth) pointing out that the order is an
clockwise about the point where all the axes cross. Explain that the point where the a
called the origin, ask what they think its co-ordinates are. (Answer: (0, 0)) Ask “In w
quadrant is the point with co-ordinates (–2, –3)?” (Answer: 3rd quadrant.) “What a
point with the co-ordinates (–2, 3)?” (Answer: 2nd quadrant.) “What about co-ord
two positive numbers?” (Answer: 1st quadrant.)
Give each learner a copy of the Co-ordinates photocopy master and ask them to carry o
in pairs. (You might need to remind some learners that a vertex is a point on a shape wh
sides meet).
After plenty of time for learners to complete the activity, review the work done as a c
1. The first shape is a rectangle.
2. The second shape is a square, and the fourth vertex is at (–1, –2).
88 Unit 1C 10 Shapes and Geometric reasoning
LB: p38
py master (p97). Moving quadrilaterals photocopy master (p98).
OM).)
ers that Vocabulary y
the
co-ordinates: are a pair 4
6). If of numbers used to show 3
t the co- position on a grid; for 2
to co- example (–3, –1). 1
ng past zero 43 2 11 x
to give four ( 3, 1) 2
3 1 234
nti- 4
axes cross is
which axis: is a reference line; the horizontal axis is often
about a denoted x and the vertical axis is often denoted y
dinates with quadrant: a quarter of a grid divided by the x and y
axes; there are four quadrants.
out the activity
here two y
class. 2nd quadrant 1st quadrant
x
3rd quadrant 4th quadrant
origin: the point of intersection (meeting) of the x-
and y-axes; the co-ordinates of the origin are (0, 0).
translation: moves or slides an object in a
straight line.
Ask, “How have you plotted the points?” and, “Why have you worked in that way
anyone get a different result?” If the answer to the last question is yes, discuss w
might have gone wrong (e.g. confusing horizontal with vertical).
Translation in the four quadrants
Give each learner a copy of the Moving quadrilaterals photocopy master. Then a
“W hat is the name of shape A?” (Answer: trapezium)
“W hat are the co-ordinates of the vertices?” (Answers: (2, 6) (4, 6) (4, 2)
“S hape A is moved to the position of shape B. Describe the movement.”
(Answer: 5 squares to the right.)
Remind learners that a translation is the movement of an object or image in a str
without rotation. The translation of Shape A can be described as ‘+ 5 in the x-dir
that the following hints are useful when translating an object or image:
If the translation is parallel to one axis the movement line can be described ju
it is parallel to, e.g. +5 in the x-direction.
When the translation is not parallel to either axis, you need to state the movem
using both axes, e.g. +5 in the x-direction and +1 in the y-direction.
Now say:
“Describe the movement of shape B to shape F” (Answer: –9 in the y-directi
“Describe the movement of shape E to shape B” (Answer: +7 in the x-direct
the y-direction.)
Ask the learners to complete the rest of the Moving quadrilaterals photocopy master
or in pairs.
Check the learners’ work and deal with any misunderstandings.
y?” “Did Look out for!
where they
Learners who struggle with the (x, y) co-ordinate
ask/say: convention, forgetting that the rst number in the pair
(2, 4)) is the x-co-ordinate and the second number is the y-
co-ordinate. It might help to remember that x comes
before y in the alphabet or that you go in the door
before going up the stairs.
raight line, Make sure learners understand that a translation
rection’. Explain involves movement along a straight line, but this line
ust stating the axis might not necessarily be horizontal or vertical, it might
ment line be on a diagonal. Reinforce the understanding that the
description of a translation must include;
ion.) a distance, and
tion AND -3 in a direction
for example, ‘4 in the x-direction’.
r on their own,
Learners should note that in a translation, the shape
stays the same size and orientation (e.g. it looks the
same just moved). When describing a translation the
+ sign can be omitted so it is correct to say +7 in the x-
direction or 7 in the x-direction. When describing
movements in both directions it is usual to describe the
movement in the x-direction first.
Core activity 10.1: Describing translations 89
Summary
Learners plot points in all four quadrants accurately.
They understand translation as movement along a straight line and can describe th
movement using mathematical vocabulary.
Notes on the Learner’s Book
Describing translations (p38): provides opportunities for learners to consolidate their
understanding of the topic. Question 1 is a straight forward translation on a square gr
question 2 sets translation in the context of solving a problem. Questions 3, 4 and 5 r
learners to use co-ordinates in all four quadrants. Learners will require squared paper
activities.
More activities
Co-ordinate message (pairs of learners)
Draw a co-ordinate grid labelling the axes from –5 to + 5. Add 26 points and label the
Write a coded message using the co-ordinates for your partner to decode.
Describing translations (pairs of learners)
You will need Moving quadrilaterals photocopy master (p98).
One learner picks a shape and states its letter. They then give the translation required
Their partner identifies the shape in the new position. Take turns.
Games Book (ISBN 9781107667815)
Co-ordinates (p97) is a game for two players. The game focuses on plotting points in
90 Unit 1C 10 Shapes and Geometric reasoning
he Check up!
r skills and “W hy is the point (1,–4) not the same as (–4, 1).”
rid whilst “A triangle has co-ordinates (1, 3) (2, 1) and
require
r for the (5, 2). It is translated – 8 in the x-direction. What are
the co-ordinates of the image? What can you say
about the y-co-ordinates of the original triangle and
its image?”
hem A, B, C … to Z.
d to move the shape to the location of another shape.
n four quadrants on a co-ordinate grid.
Blank page 91
Core activity 10.2: Reflecting shapes
Resources: Reflection photocopy master (p99). Reflecting shapes photocopy ma
and/or +/–10 co-ordinate grid photocopy master (CD-ROM).)
Ask the learners to tell you what they know about ref l ection. Answers should includ
vocabulary such as ‘mirror line’, ‘identical mirror image shapes’ etc. Make sure they
ref l ection makes a mirror image; it flips an image over a mirror line, without rotating
(Note: the resulting grid, objects and images for the following activity are provid
the
Re ection photocopy master.)
Remind learners that a grid can be useful when ref l ecting shapes. Display a co-ordin
from –4 to +4. Work with learners to plot the points (1, 1), (3, 2) and (2, 4).
Ask, “What information is needed to describe a reflection?” (Answer: need to kn
the mirror line is.) Say that we are able to ref l ect the shape in the x-axis, the
position of the new shape which is called the ‘image’ of the original shape.
“What are the co-ordinates of the image?” (Answer (1, –1) (3, –2) (2, –4))
Now reflect the image (the new shape) in the y-axis. (The Reflection photocopy mast
final result.)
Explain that we sometimes ref l ect shapes on grids other than a co-ordinate grid, and
mirror line can be positioned diagonally across a page. Ask learners to work in pairs
the questions on the Reflecting shapes photocopy master.
Check the learners’ work and deal with any misunderstandings.
92 Unit 1C 10 Shapes and Geometric reasoning
LB: p40
master (p100). Tracing paper for each learner. (Optional: Squared paper
de the use of Vocabulary
y know that a
reflection: is a mirror view e.g.
it.
ded on image: the position of a shape following a reflection
nate grid
now where
en draw the
ter shows the Invite learners to turn the paper around so that the
mirror line appears to be horizontal or vertical.
d that the
to discuss
Establish the following properties of a reflection:
The orientation of the shape changes.
The original shape and the image are the same distance away from the mirror
size of the shape remains the same.
Ask learners to share any strategies they used to help them answer the more diffi
questions.
Ensure that learners realise that moving the paper around so that the mirror line a
horizontal or vertical can often help.
Summary
Learners recognise when shapes of different orientations have been ref l ected
They plot ref l ections in mirror lines using co-ordinate and other grid types.
Notes on the Learner’s Book
Reflecting shapes (p40): revises lines of symmetry. Questions 1 and 2 use squar
questions 3, 4 and 5 use co-ordinates in all four quadrants. Learners will require
activities. Part (b) of question 5 may be challenging for some learners and teache
remind them that the work they have done in questions 3 and 4 provides a strong
More activities
Making symmetrical designs (individuals)
Start with a pattern drawn on squared paper, for example.
Ref l ect it in different lines to make interesting patterns, for example:
Avoid using regular shapes at first because they do not
always appear to change orientation
line. The
icult
appears to be
in a mirror line. Check up!
red grids and Display the Check up! photocopy master (CD-ROM)
squared paper for the
ers might wish to and ask:
g hint. “W hich drawings are right?”
“W hich drawings are wrong? What mistake has been
made?”
Core activity 10.2: Reflecting shapes 93
Core activity 10.3: Rotation on a grid
Resources: Spot the link photocopy master (p101). Tracing paper for each learn
and/or +/– 10 co-ordinate grid photocopy master (CD-ROM).)
Display the Spot the link photocopy master or other pictures related to objects that tu
(rotate). Discuss with learners how they relate to turning:
th e Earth rotates about its axis
th e pattern is made by repeatedly rotating a triangle about a central point
th e road sign represents direction of movement. (Revise meaning of ‘clockwise’ a
‘anticlockwise’.)
Say that we are going to explore rotating 2D shapes about a point. Give learners a cop
Rotating shapes photocopy master. Demonstrate how to nd the answer to the rst q
using a piece of paper to represent the rectangle:
Draw around the sheet of paper on the board.
Mark a right angle on the diagram.
Hold the sharp point of a pencil on the marked spot and turn the sheet of paper aro
Draw its new position, referred to as the image.
Ask the learners to work in pairs to help each other rotate the parallelogram in question 2
Review the learners’ work and discuss any errors or misunderstandings.
94 Unit 1C 10 Shapes and Geometric reasoning
LB: p42
ner. Rotating shapes photocopy master (p102). (Optional: Squared paper
urn Vocabulary
nd reflection: is a mirror view e.g.
py of the
question image: the position of a shape following a reflection.
ound.
Invite learners to turn the paper around so that the
mirror line appears to be horizontal or vertical.
2.
‘Ask learners to create designs with rotational symmetry by repeating the 90˚ rot
twice more.
Example.
Make sure leaners know that in order to rotate a shape they need to know/give:
the point about which the shape is rotated
an angle and direction of turn.
Summary
Learners understand how to rotate shapes about a point using the terms clockw
anti-clockwise to describe the direction of the turn.
They know that to establish a rotation they must give the point about which th
rotated, the angle and direction of turn.
Notes on the Learner’s Book
Rotation (p42): rotation is likely to be a new concept so question 1 sets it in an e
context. Questions 2 – 4 use square grids or co-ordinate grids and learners are r
draw rotations of 90° clockwise. Learners should be provided with squared pape
tracing paper.
More activities
Rotation patterns (individual)
Draw a simple shape on squared paper. Rotate it through 90° three times to produ
smaller angle will produce more intricate designs).
tation Look out for!
Learners who find it easy to create a design with both
wise and rotational and ref l ective symmetry. Ask them to
he shape is investigate which shapes can be rotated three times to
everyday create a design like the one shown, which has both
equired to rotational and reflective symmetry. These could be
er and shared with the class and used to create an effective
display.
Check up!
“What will this shape look like after it has been
rotated?”
“How would you describe a rotation to a friend?”
uce a symmetrical design. Try rotating the shape through different angles (a
Core activity 10.3: Rotation on a grid 95
The four qu
y
2nd quadrant
3rd quadrant
Instructions on page 88
uadrants
1st quadrant x
4th quadrant
Original Material © Cambridge University Press, 2014
Co-ord
1. Here is a co-ordinate grid.
y
6
5
4
3
2
1
654321 1 1 234 56 x
2
3
4
5
6
Plot the points (2, 5) (-2,5) (2, 5) and (2, 5)
Join them together in order.
What shape have you made?
Instructions on page 88
dinates
2. Here is a second co-ordinate grid.
y
6
5
4
3
2
1
654321 1 1 2345 6 x
2
3
4
5
6
Plot the points (2, 2) (2, 3) and (3, 1)
These points are three of the four vertices of a square.
What are the co-ordinates of the fourth vertex of the
square?
Original Material © Cambridge University Press, 2014
Moving qua
C y L
D
10 9 8 7 6 5 4 3 2 1 11 (
10
G B
D
(
9
8
7
6
5A
4
3
2
1
x1 2 3 4 5 6 7 8 9 10
1
2
3
4 (
F
5
6
7E
8
9
(10
11
Instructions on page 88
adrilaterals
Look at the co-ordinate grid.
Describe the following movements:
(a) A to C
(b) G to F
(c) F to E
(d) D to G
Original Material © Cambridge University Press, 2014
Reflection
y
4 x
3
2 12 34
1
- 4 -3 -2 -1
-1
-2
-3
-4
Instructions on page 92 Original Material © Cambridge University Press, 2014
Reflecting shapes
1 First predict where you think the reflection of each shape will be in the
mirror line. Then draw it by looking at the points.
mirror
line
3 Here is a shaded square on a grid. mirror line
Shade in three more squares so
that the design is symmetrical in
both mirror lines.
Instructions on page 92 mirror line
Original Material © Cambridge University Press, 2014
Spot t
Instructions on page 94
the link
Original Material © Cambridge University Press, 2014
Rotating sh
1. Rotate the rectangle 90° clockwise about point A. 2. R
Instructions on page 94
hapes
Rotate the parallelogram 90° clockwise about
point A.
Original Material © Cambridge University Press, 2014
2A 11 The number system (2)
Quick reference
Core activity 11.1: The number system (1) (Learner’s Book p)
Learners order numbers up to 10 000 and identify them on a number line. They c
rounding.
Core activity 11.2: History of number (1)
Learners explore the number system used by the ancient Egyptians. They have an
system with our system as they consider the importance of 10, 100, 1000 as imp
lines and when comparing, ordering and rounding numbers.
Prior learning Objectives* – please note that listed objectives might o
given chapter but are covered fully acros
The work in this
chapter extends and 2A: Numbers and the number system
consolidates work on 6Nn8 – Round whole numbers to the nearest 10
the number system done 6Nn12 – Use correctly the symbols for >, < and =
earlier in the stage. 6Nn13 – Estimate where four-digit numbers lie on
6Nn20 – Recognise historical origins of our numb
something of its development.
*for NRICH activities mapped to the Cambridge Primary objectiv
please visit www.cie.org.uk/cambridgeprimarymaths
Vocabulary
No new vocabulary.
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Number
The nu mber system(1)
Let’s investigate
A li is th in kin g of a nu m ber.
consider the effect of W he n I r o u n d my n u m ber to th e nea re s t Lo o k a t q ue stion1,
10 the a nswe r is 1080. W he n I r ound my 1, to give y o u a .
n opportunity to compare that clue
portant ‘markers’ on number an s w er to th e ne ar es t 1 0 0 th e a n s we r
is 1100.
only be partially covered within any
ss the book when taken as a whole W ha t is the s ma lle st n u mb er A li co u ld be thin kin g of ?
W ha t is the lar ge st nu m ber A li c ou ld be th in kin g o f ?
m
0, 100 or 1000. 1 A number rounded to the nearest 1 0 is 50. What cou ld the number be ?
=
n an empty 0–10 000 line. 2 ? rounded to the nearest 10 is 700. What cou ld the mis sing number be?
ber system; understanding 3 Write in gures a n umber that is b igger tha n o ne thou san d b ut smaller tha n one th ousa nd
ves, one h undred.
4 Find a wh ole number to ma ke th is statement true. 24 0 00
? 2 5 00 0
5 Copy the number line below a nd draw a n arrow ( ) to sh ow the p os ition of 850 0 o n the
number line.
0 10 00 0
44
Unit 2A 103
Core activity 11.1: The number system
(1)
Resources: 0–9 spinner (or use 0–9 digit cards photocopy master (CD-ROM)).
number’ photocopy master (CD-ROM).)
Draw the number line below for the whole class to see and ask learners to look at it. “
the marked divisions represent?” (Answer: 2000)
00
0 10000
Explain that the arrow is pointing to a 4-digit number. “There are two empty boxes re
the thousands digit and the hundreds digit. You must use one of the digits 2, 4, 7 or 9
the empty boxes, to complete the number. What is the number?”
Allow thinking time and then ask for responses. Discuss strategies for finding the nu
the thousand digit must be 4 as the number lies between the marks for 4000 and 60
fin d the hundreds digit by making or imagining further divisions in the number lin
example, dividing the line from 4000 to 6000 into 10 parts where each division wo
represent 200
the number must be 4200.
Use a 0–9 spinner or a set of digit cards to randomly produce four 4-digit numbers. A
learners to:
write the numbers in order starting with the smallest
use < and > to compare pairs of numbers
position the numbers on a blank 0 to 10 000 number line.
(This is revision of work covered in Unit 1 so judge how much or little to cover.)
104 Unit 2A 11 The number system (2)
LB: p44
(Optional: newspapers with articles involving numbers; ‘Find the
“What do Look out for!
epresenting Learners who find it difficult to work with scales, for
9, in each of example:
umber: 4000 5000 6000
000 4200
ne, for
ould 4000 5000
Give these learners some different types of scales and
ask them to practise locating numbers on them in pairs,
with one learner saying a number and the other
locating it on the scale.
Ask
Work in pairs to solve this problem.
Alma and Myrtle start with the same number.
Alma rounds the number to the nearest hundred.
Myrtle rounds the number to the nearest ten.
Alma’s answer is double Myrtle’s answer.
What number could they have started with?
Review work done:
“How did you go about it?”
“What is your answer?” (Answer: 50, 51, 52, 53 or 54)
Summary
Learners extend their knowledge and understanding of the number system.
Notes on the Learner’s Book
The Number System (1) (p44): learners practise rounding numbers and
finding values that are greater or equal to a given number.
More activities
Rounded or not (individuals or pairs)
You will need newspapers with articles involving numbers.
Collect examples of numbers used in news items or reports. Say whether each nu
Find the number
(pairs) need activity sheet ‘Find the number’ (CD-ROM).
You will
There are three activities, with instructions, on the sheet.
(Answer to activity 1: 14 405)
Check up!
Use digit cards to make two different 4-digit numbers and ask:
“H ow do you know that this number is greater/smaller than this one?”
“Show the position of your numbers on a blank 0 to 10 000 number
line. Why have you placed the number there?”
“R ound your two numbers to the nearest 10, 100 and 1000.”
umber is exact or has been rounded.
Core activity 11.1: The number system 105
(1)
Core activity 11.2: History of number (1)
Resources: Egyptian numbers photocopy master (p107).
Explore with learners the ancient Egyptian number system. You can choose to use th
the activity sheet or other materials from books, pictures, videos etc. It is important to
the system was a base 10 system but did not use a zero, so had no place value.
Ask learners to read the information on the sheet and answer the questions to familia
themselves with the Egyptian system. Alternatively they could do some of their own
research.
Ask learners to produce a poster, presentation, video, or some other way of communi
findings, which could include:
Why the symbols were chosen by the Egyptians.
So me examples of different numbers in Egyptian hieroglyphics and modern numer
especially those that are particularly impractical in the Egyptian system.
Was it easy to compare and order numbers?
Do they think rounding would have been important? Why
we no longer use Egyptian numbers.
What the world would be like if we did still use that system, for example:
Ho w would the date be written?
What would the price of shopping be like?
Ho w would learners’ ages be written?
What would be written on a clock?
What symbols would leaners use if they were going to create a system similar to th
Egyptian one?
Summary
Learners recognise that there are different ways of writing numbers.
Games Book (ISBN 9781107667815)
Nine Men’s Morris (p28) is an ancient Egyptian game for two players. It encourages p
106 Unit 2A 11 The number system (2)
he facts on Opportunities for display!
o stress that
Posters produced by learners on Egyptian number
arise system.
n
icating their
rals,
he
players to think strategically to do well.
Egyptian numbers
Scribes in ancient Egypt used signs 12 3 4 5 10
called hieroglyphics to represent
numbers. These signs were pictures 678 9 100
of everyday things. For example,
1 Stroke or tally 1000 10,000 100,000 Millo
10 Cattle hobble (leg iron n
to limit movement)
100 Coil of rope 12,427
1000 Lotus plant
10 000 Finger
100 000 Toad or frog
1 000 000 Man with both arms raised
The Egyptian number system was based on the number 10, possibly
because of the total of 10 fingers and thumbs on both hands. But instead
of using a different symbol for the digits 1 to 9, the Egyptians had one
hieroglyph for 1, one for 10, one for 100 and so on. They did not have a
sign for zero.
Ten of one hieroglyph could be replaced by one of another hieroglyph so
we have hieroglyphs for 10, 100, 1000 and so on. To make the number 20,
for example, two hieroglyphs for 10 are used. The order in which the
hieroglyphs are written down does not affect the number so the system has
no place value.
One reason the Egyptian number system eventually became impractical was
the absence of a zero. In our number system zero is important as a ‘place
holder’ for example 105, 150, 1005, 1050 and 1500 all use the digits 1
and 5 together with zeros but the numbers are different in value.
Instructions on page 106 Original Material © Cambridge University Press, 2014
Here are some examples:
7 25
1. What numbers do these hieroglyphs show?
2. Match the hieroglyphs with the correct numbers.
54 700 307 1200 63 129
3. Draw how a scribe would write these numbers.
19 43
156 10 234
Instructions on page 106 Original Material © Cambridge University Press, 2014
2A 12 Decimals
Quick reference
Core activity 12.1: The decimal system (Learner’s Book p)
Learners consider place value of decimal numbers. They understand how to roun
order decimal numbers. They multiply them by 10 and 100 and divide whole num
by 10 and 100 to find decimals.
Core activity 12.2: Operations with decimals (Learner’s Book p)
Learners add and subtract, double and halve decimals mentally.
Core activity 12.3: Decimals in context (Learner’s Book p)
Learners apply their knowledge to ‘real life’ situations involving money
and measures.
Prior learning Objectives* – please note that listed objectives might only be pa
the book when taken as a whole
This chapter
extends the work 2A: Numbers and the number system
covered in Unit 1A 6Nn3 – Know what each digit represents in one- and two-plac
when the focus 6Nn5 – Multiply and divide decimals by 10 or 100 (answers to
was on whole 6Nn14 – Order numbers with up to two decimal places (includin
numbers. 6Nn9 – (Unit 3A: Round a number with two decimal places to
2A: Calculation (Mental strategies)
6Nc1 – Recall addition/subtraction facts for numbers to 20 and
6Nc2 – Derive quickly pairs of one-place decimals totalling 10
0.78 + 0.22.
6Nc9 – Double quickly any two-digit number e.g. 78, 7.8, 0.78
2A: Calculation (Mental strategies)
6Nc11 – Add two- and three-digit numbers with the same or diff
6Nc12 – Add or subtract numbers with the same and different n
2A: Problem solving (Using techniques and skills in s
6Pt1 – Choose appropriate and efficient mental or written stra
multiplication or division.
6Pt5 – Estimate and approximate when calculating e.g. use ro
2A: Problem solving (Using understanding and strate
6Ps1 – Explain why they choose a particular method to perfor
6Ps6 – Make sense of and solve word problems, single and m
diagrams or on a number line; use brackets to show th
*for NRICH activities mapped to the Cambridge Primary objectives, please
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
The deci mal system Operat ions with decimals Decimals in context
Let’s investigate Let’s investigate 0.6 Let’s investigate
M ar ia is th in kin g of a de cima l nu m ber le s s th ann11. . 0. 5 Che n g b uy s five prese n ts. Sh e sp e nd s a to ta l of $ 2$0.20 .
In a ma g ic sq uare, the nu mber s a d d u p to the sa me ● Th e to ta l co s t of A an d B is $ 7 .0 0.
T h e h u n dre th s d ig it is f o ur m o re n um ber ver tically , ho rizo n ta lly or d ia g o na lly . ● Th e to ta l co s t of B a n d C is $ 6. 0 0.
th a n th e te n th s d ig it. T h e s u m o f th e ● Th e to ta l co s t of C a n d D is $ 7 .0 0.
nd and te n th s d ig it T his ma gic s qu are m u st a dd u p to 1. 5 . 0.4 ● Th e to ta l co s t of D an d E is $ 9. 0 0.
mbers Co mp le te the sq uare. U…se eac h o f the dec ima ls 0. 1 , 0. 2, 0.…3
a n d th e h u n dr eth s d ig it is 1 0 .
1 Wor k ou t the answers to these calculations. W ha t is the co s t of e ac h pr ese nt? U se tr ia l a n d im pr oevme nt.
W ha t n um ber is M ar ia th in kin g of ? (a) 4.5 2.6 8 ( b) 7. 1 9. 45 (c) 3. 8 7. 09 t. Rem em ber to be
(d) 5. 1 3. 92 (e) 4. 6 4. 76 (f) 4.3 5. 99 1 A swimming poo l is 50 metres long a nd 25 sy stema tic .
Which of the answers are less than 10 ? metres wide. How many leng ths of the p ool
1 Write the se numbers in order of size, starting with the smallest. 0.01 will a competitor in a 1 500 metre race have
(a) 1 .01 1 .1 0 .1 0 .1 1 0.11 2 Five of the answers to the following calcu lation s are in this gr id. Wor k o ut to swim ?
(b) 0.1 9 0 .9 0 .91 0.09 the answers to the se calculations. Which answer is miss ing ?
2 Find four examples that ma ke this general statement correct. 2.58 1.34 7.20
If 0.24 ? 0. 27 then any number between 0.24 an d 0 .27 ca n g o in the b ox. 2.15 5.13 4.76
3 The s tude nts in a class ha d a sponsored sw im.They collected $ 429 .24 . (a) 9.23 4. 1 ( b) 8. 16 3 .4 (c) 4. 28 1.7 2 Hamda b uy s a 2 kilo gram bag of tomatoes. She uses 4 00 grams of tomatoes to make
(a) How much is $42 9.2 4 to the nearest hu ndred do llars ? (d) 9. 4 2. 38 (e) 7. 6 5. 45 (f) 3.2 1. 86 soup. How many grams of tomatoes has she left?
(b) How much is $4 29. 24 to the nearest ten do llars ? Which number in the gr id is no t a n answer to any of the calc ulatio ns ?
(c) How much is $4 29.2 4 to the nearest d ollar? 3 Ro z has a 2 metre len gth of r ibb on. She cu ts off a piece of ribbo n 6 5 centimetres
(d) How much is $42 9.2 4 to the nearest tenth of a do llar ? 3 (a) What d o y ou need to ad d to 4. 79 to make 10 ? long. How much r ibb on is left?
(b) What do y ou need to take away from 10 to ma ke 5. 36 ?
4 (a) Fin d the number that is half way between 2.8 an d 3 .4. ? 4 A tria ngle has sides of le ng th 5 cm, 1 2 cm an d 1 3 cm. What is the
Complete this statement.The number 6 is halfway between 2.8 and . 4 Findthe mis sin g numbers. perimeter of the trian gle ?
(a) 4. 8 ? 1 0 (b) ? 3. 6 1 0 (c) 3. 7 6. 3
(b) (d) 10 3 .7 ? (e) 10 ? 8. 1 (f) ? 4 .6 5 A jug ho ld s 1 litre of water.
Fatima po urs ou t 9 0 millilitres of water.
5 Write d own the value of the dig it 9 in each of the se numbers. ? How many millilitres of water is left in the jug ?
5. 4
6 A buc ket h olds 2.7 5 litres of water. How
(a) 72.9 (b) 3 92. 75 (c) 4.6 9 5 Find the mis sin g digits. many millilitres is this?
(d) 13 .09 (e) 19. 11 (f) 9.06 8•? 7 50
?• 6 ?
6 Write these n umbers in gures: 3•? 6
(a) fteen poin t o ne ve. 3• 6 9 ? •8 ?
(b) one hundred an d seven po in t zero seven.
1•3 5
46 48
artially covered within any given chapter but are covered fully across
ce decimal numbers. Vocabulary
o two decimal places for division).
ng different numbers of places). No new vocabulary.
o the nearest tenth or to the nearest whole number.)
d pairs of one-place decimals with a total of 1, e.g. 0.4 + 0.6.
0, e.g. 7.8 and 2.2 , and two-place decimals totalling 1, e.g.
8; derive the corresponding halves.
ferent numbers of digits/decimal places.
numbers of decimal places, including amounts of money.
solving mathematical problems)
ategies to carry out a calculation involving addition, subtraction,
rounding and check working.
egies in solving problems)
rm a calculation and show working.
multi-step (all four operations), and represent them e.g. with
he series of calculations necessary.
e visit www.cie.org.uk/cambridgeprimarymaths
Unit 2A 109