Show a Decimal number square representing decimals to 1, in hundredths. Estab
Establish, for example, that 0.35 = 35 and that this fraction could be simplif i e
100
Summary
Learners recognise and use equivalent fraction and decimal forms.
They convert a fraction to a decimal using division.
Notes on the Learner’s Book
Fractions and decimals (p101): requires learners to convert fractions to decimals
importantly, to understand the relationship between fractions and decimals. Ques
a common misconception and asks learners to explain their answer.
More activities
Using digit cards to make equivalent fractions and decimals (individua
pairs)
You will need Using digit cards to make equivalent fractions and decimals (CD
Instructions are on the sheet.
Teachers should encourage learners to look for alternative answers.
Answers 2. 8 = 0.5 3. 3 = 0.3 4. 3 = 0.5 or 3 = 0.6
:1. 4 = 0.5 or 4 = 0.8
16 10 65
85
blish the link to money notation, for example $0.35 = 35 cents.
ed to 7.
20
Check up!
“Sanjiv converts fractions to decimals. He writes:
0.5 = 1 0.2 = 1 0.4 = 1
5 2 4
s and, more Has he got them right? What does he need to know to
stion 3 presents convert fractions to decimals?”
“Ahmed says that 0.34 is 34. Why might he say this?
als or What does he need to know to convert fractions to
D-ROM).
decimals?”
5. 7 = 0.7 6. 2 = 0.5 or 2 = 0.4 7. 1 = 0.1
10 10
45
Core activity 28.1: Fractions and decimals 247
Core activity 28.2: Percentages
Resources: (Optional: Percentages of a quantity jigsaw (CD-ROM).)
Ask, “Which is greater 1 or 15%? How do you know?”
5
Say that, “We can find an equivalent fraction with 100 as the denominator in order to
a fraction is as a percentage and 1 is 20 = 20%”
5 100
So, 1 > 15%
5
“Practise converting fractions to percentages. Also practise converting percentages to fr
writing the percentage as a fraction with 100 as the denominator and then simplifying.
Change the following fractions to percentages, by finding equivalent fractions with a d
of 100.
1 1 7 11
10 100 10 2 4
(Answer: 10%, 1%, 7%, 50%, 25%)
What is 1 as a percentage? What do you notice?
3
(Answer:31 = 3331% (it doesn’t work out to a whole
number))
Change the following percentages to fractions:
15% 25% 66% 75%”
(Answer: 15 = 3 25 = 1 66 = 33 75 = 3)
20 100
100 100 4 50 100 4
Review the work done and then ask, “What is 10% of 240?”
(Answer: divide 240 by 10 to give 24.)
Emphasise the importance of knowing what 10% of a quantity is by showing:
“If I know 10% I can work out 20%, 30%, 40% . . . (× 2, × 3, × 4 etc)
“If I know 10% I can work out 5% (divide by 2).”
248 Unit 3A 28 Fractions, decimals and percentages
LB: p102
o find what
ractions by Remind learners that ‘per cent’ is derived from the Latin
denominator per centum meaning ‘by the hundred’. And that
45% is the same as 45 .
100
“What is 1% of 240?” (Answer: divide 240 by 100 to give 2.4.) 30%
“If I know 1% I can work out 2%, 3% . . .”
We can display this information in a diagram:
20% 48
3% 7.2 1% 2.4 240 10% 24
2% 4.8 50% 120
25% 60
Discuss with learners how to work out other percentages, for example:
13% of 240 = 10% of 240 + 3% of 240
= 24 + 7.2 = 31.2
Summary
Le arners understand that a percentage is one part in a hundred so 1010= 1%
Th ey convert between fractions and percentages and between percentages and
Le arners understand that if they know 1% and 10% of a quantity they can use
work out other percentages.
Notes on the Learner’s Book
Percentages (p102): provides a variety of examples, both in and out of context. L
are required to convert fractions and percentages and nd percentages of quantit
heavy emphasis on working with 1% and 10% and using these answers to work o
Question 2 sets this principle out clearly.
72
50% 120
%. Check up!
d fractions.
e these to “What is 10% of 150? What is 1% of 150?
Learners How can I use these answers to work out 12% of
ties. There is a 150?”
out others. “Which is larger 2 or 66%? How do you know?”
3
Core activity 28.2: Percentages 249
More activities
Percentages of a quantity jigsaw
(pairs)
You will need Percentages of a quantity jigsaw (CD-ROM).
Cut out the jigsaw pieces and then assemble so a percentage matches with that percen
Example: 50% of 480 = 240
Learners may find it useful to construct a diagram similar to the one used in the core
Games Book (ISBN 9781107667815)
Percentages of numbers (p48) is a game for two players. The focus is finding percent
250 Unit 3A 28 Fractions, decimals and percentages
ntage of 480.
e activity but starting with 480 in the middle.
tages of whole numbers.
Decimal number square
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20
0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30
0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40
0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60
0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70
0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80
0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.90
0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00
Instructions on page 247 Original Material © Cambridge University Press, 2014
252 Blank page
3A 29 Ratio and proportion
Quick reference
Core activity 29.1: Using ratio and proportion (Learner’s Book p104)
Learners will investigate equivalent ratios and write a ratio in its simplest form. T
describe quantities using ratio and proportion. They will solve problems involvin
direct proportion.
Prior learning Objectives* – please note that listed objectives
are covered fully across the book
Use fractions to describe
and estimate a simple 3A: Numbers and the number sy
proportion, e.g. 1 of the 6Nn30 – Solve simple problems involving ra
5 3A: Problem solving (Using techn
6Pt1 – Choose appropriate and efficient m
beads are yellow.
Use ratio to solve problems, calculation involving addition, subt
e.g. to adapt a recipe for six 3A: Problem solving (Using unde
people to a recipe for three 6Ps4 – Use ordered lists or tables to help
or 12 people. 6Ps7 – Solve simple word problems involv
*for NRICH activities mapped to the Cambridge Primary
Vocabulary
ratio proportion direct proportion
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
They will Rat io and proportion Vocab ulary
ng ratio and proportion: u sed
Let’s investigate to compare a part
Ca leb ha s two litres of red p aint an d three litres agains t the w hole.
of y ello w pa int. T he oran ge he wa nts to ma ke ratio: used to
is ca lled Glor io u s S un r ise . compare a part G lor io us
agains t an o ther part. of
S un r is e n ee ds a ratio of tw o a mo u n ts
y ello w f or e very on e am o u n t of re d ( 2 : 1). There w ill b es ome
e pa in t lef t
How many litres of G lor io us S u nr ise over.
can Ca le b ma ke w ith h is red a nd y ello w pain t?
1 These tile patterns sho uld all have a ratio of three red
tile s for every two y ellow tiles (3 : 2).
(a) What sho uld be the co lour of the m iss in g tile in each pattern?
(i)
Write the pr op otrio
io n a s a frac tionn.
(ii) (iii) (iv)
(b) What proportio n of the tile s in these patterns sho uld be red?
(c) What proportion of the tile s in the se patterns sh ould be y ellow?
10 4
might only be partially covered within any given chapter but
k when taken as a whole
ystem
atio and direct proportion.
niques and skills in solving mathematical problems)
mental or written strategies to carry out a
traction, multiplication or division.
erstanding and strategies in solving problems)
solve problems systematically.
ving ratio and direct proportion.
objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 3A 253
Core activity 29.1: Using ratio and proportion
Resources: Ratio and proportion poster photocopy master (p257). Ratio – jewe
colours). (Optional: paint charts or brochures made by paint manufacturers, on-line
Remind the learners that proportion and ratio are useful ways to describe combination
in patterns, recipes or populations. Proportion is how to describe how much one part
whole. Ratio is a comparison of part to part, where the parts are measured in the sam
Show learners the Ratio and proportion poster and point out the bracelet example. A
to count the total number of beads, the number of white beads and the number of bla
Recreate the beads used to make the bracelet using real beads, coloured cubes,
or moveable pictures on the board. Rearrange the beads to show that 2 of th3e beads ar
black. Explain that this is finding the proportion of beads that are black, comparing th
black beads to the whole set.
Rearrange the beads again to show that for every one white bead there are two black
Explain that this shows the ratio between white and black beads in the bracelet, it is
comparing and describing the white part of the set to the black part of the set. Demo
: 2, 2 : 4, 3 : 6, 4 : 8, and 5 : 10 are all the same ratio. Remind learners of how they re
fractions to their simplest form in an earlier session. Explain that learners should aim
reduce the ratio to its simplest form, in the case of the bracelet 1 : 2.
Give pairs of learners the Ratio – jewellery designing photocopy master. Ask them to talk
complete the information asked for on the sheet. Once they have completed the sheet,
four pairs of numbers of beads from the jewellery on the board that can be described
1:2
(Answers: Bracelet 5 : 10, Ring 1 : 2, Earring 2 : 4, Necklace 10 : 20).Ask learner
and predict what the ratio of white to black beads in the whole set of jewellery. Choose
three learners to explain their reasons for their prediction about the ratio of the whole
Learners should check, and find out that the ratio for the set is also 1 : 2.
254 Unit 3A 29 Ratio and proportion
LB: p104
ellery designing photocopy master (p258). Beads or cubes (of two
e or on paper; red and blue paint; brushes.)
ns of things Please note:
is of the The words ‘ratio’ and ‘proportion’ and the fraction
me units. notations for these are used in different ways in different
locations around the world. The teachers’ guidance here
Ask learners relates to how these terms and notation are used in the
ack beads. UK.
re Vocabulary
he
proportion: used to compare a part against the whole.
beads.
ratio: used to compare a part against another part.
onstrate that 1
educed direct proportion: two amounts that are put together in
m to also a ratio, so that as one increases the other increases by
the same multiple.
k about and
Look out for!
write the Learners who have difficulty with equivalent
d by the ratio
fractions. As necessary, instruct them to choose a
rs to discuss ratio where one of the numbers is ‘1’. They will
then be able to use the simple four cell diagram to
two or the left.
e set. Learners who quickly grasp the concept of
ratio. Encourage them to try choosing a ratio where
neither number is ‘1’. They will need to use the
second method described (multiplying both
numbers by the same number).
Learners should choose a ratio other than 1 : 2, reduced to its simplest form, for des
different pieces of jewellery that have beads that match the chosen ratio, but with ea
different numbers of beads. Learners could create a four cell table such as this on
them work out the direct proportion, e.g.
blue beads yellow beads
3 1
12 ?
Remind learners that often when ratio problems need to be solved four pieces of
needed, and only three are supplied. By putting the three pieces of information i
learners can see the relationships between the different values and which piece is
example the ratio of 3 : 1 has been chosen and a learner wants to know how man
would go with the 12 blue beads to keep the ratio the same.
To solve this problem learners can either:
notice that in the first row the blue beads in three times more than the yellow b
the second row also have three times more blue beads that yellow beads, and d
by three.
notice that there are four times as many blue beads in the second row, so there
four times as many yellow beads in the second row to make the same ratio.
Learners should draw the jewellery they have designed or make them out of beads
label the jewellery with the number of beads in each piece, the ratio and the propor
of bead.
Ask some learners to explain why they did, or did not use the four cell table to h
calculate the direct proportion. If they used another method, ask them to demons
class.
signing four Look out for!
ach having Learners who might think that they can add or
subtract to find numbers that have the same ratio,
ne to help rather than multiply or divide. If so, take firstly 6
blue beads and 2 yellow beads then double this to 12
information are blue beads and 4 yellow beads and ask them to sort
into a table the the beads into sets that show the ratio, e.g. 3 blue
s missing. In this beads and 1 yellow bead. They should find that if the
ny yellow beads ratio is correct they can sort them into these sets
with no beads left over. They will also be able to see
beads, so make the total number of beads is a multiple of the beads
divide 12 beads in the ratio. Now go back to the 6 blue beads and 2
e should be yellow beads and add one to each group so that there
are 7 blue beads and 3 yellow beads. Ask learners if
s. They should it is still possible to sort them into groups of 3 blue
rtion of each type beads and 1 yellow bead with no beads left over.
help them Opportunities for display!
strate it to the Display the collections of jewellery with the number
of beads in each piece, the ratio and the proportion of
each type of bead.
Core activity 29.1: Using ratio and proportion 255
Summary
Learners will have investigated equivalent ratios and written a ratio in its simplest
Th ey will have described quantities using ratio and proportion.
Th ey will have solved problems involving ratio and direct proportion.
Notes on the Learner’s Book
Ratio and proportion (p104): learners solve problems involving ratio and proportion
contexts of tiles, coins and milkshakes. They investigate whether statements of ratio a
proportion are true or false.
More activities
Paint (individual)
You will need paint charts or brochures made by paint manufacturers, on-line or on
Show learners paint charts or brochures made by paint manufacturers, on-line or on p
make the shades of purple.
Ask learners to make their own paint colour chart by using blue and red paint and mi
1: 3 to make seven different shades that can be painted onto a strip of card. Learners
each paint colour to make one litre of the shade of purple.
Odd one out ratio (pairs or small groups)
Ask learners to make ‘odd one out’ sets of ratios, where all the ratios are equivalent e
Fruit cocktail (Individual or small groups)
Learners can make a recipe book of fruit cocktail drinks using proportion, ratio and m
Games Book (ISBN 9781107667815)
The smoothie ratio (p52) is a game for two to four players. Players fill ‘glasses’ with f
complete two smoothies is the winner.
256 Unit 3A 29 Ratio and proportion
form. Check up!
in the G ive learners a selection of the jewellery designs
and made by the learners, and labels that describe their
ratio and proportion. Ask learners to match the labels
to the jewellery and explain how they know.
A sk learners to solve the problem:
“At a bird table, the ratio of sparrows to starlings
is 1 : 4. If 24 starlings visited the table, how many
sparrows had visited?”
n paper. Red and blue paint. Brushes.
paper. Ask learners what combinations of paint colours might be used to
ixing them in small quantities to the ratios 3 : 1, 2 : 1, 3 : 2, 1: 1, 2 : 3, 1: 2,
should label each strip with the ratio and the quantities they would need of
except one. They should challenge other learners to find the ‘odd one out’.
millilitres to describe the two fruit juice parts.
fruit cards to match the ratio written on the glass. The first player to
Ratio and pro
Proportion is used to compare a part against the whole.
Ratio is used to compare a part against another part.
Proportion statements
One fifth 1 of the drink is cordial.
(5)
Four fifths 4 of the drink is water.
(5)
Ratio statements
For every one cup of cordial, there are
four cups of water (1:4).
For every four cups of water, there is
one cup of cordial (4:1).
For
Fo
Instructions on page 254
oportion poster
Fruit
cordia
l
Proportion statements
1
One third ( 3) of all the beads are white.
2
Two thirds ( 3) of all the beads are black
Ratio statements
r every one white bead, there are two black beads (1:2).
or every two black beads, there is one white bead (2:1).
There are 10 black beads and 5 white beads.
The ratio 10:5 is the same as the ratio 2:1.
Original Material © Cambridge University Press, 2014
Ratio – jewellery designing
Bracelet
Number of white beads
Number of black beads
Ratio of white beads to black beads
Proportion of white beads
Proportion of black beads
Ring
Number of white beads
Number of black beads
Ratio of white beads to black beads
Proportion of white beads
Proportion of black beads
Pair of Earrings
Number of white beads
Number of black beads
Ratio of white beads to black beads
Proportion of white beads
Proportion of black beads
Necklace Original Material © Cambridge University Press, 2014
Number of white beads
Number of black beads
Ratio of white beads to black beads
Proportion of white beads
Proportion of black beads
Instructions on page 254
3B 30 Metric and imperial measu
Quick reference
Core activity 30.1: Capacity and mass (Learner’s Book p108)
Learners learn the vocabulary associated with imperial units in common use
for capacity and mass, and convert to metric equivalents.
Core activity 30.2: Distance (Learner’s Book p110)
Learners learn the vocabulary associated with imperial units in common use
for length/distance, and convert to metric equivalents.
Prior learning Objectives* – please note that l
the book when tak
• Read, choose, use and record standard
units to estimate and measure length, 3B: Measure (Length,
mass and capacity to a suitable degree 6Ml1 – Select and use standa
of accuracy. 6Ml2 – Convert between units
• Convert larger to smaller metric (units three places, e.g. reco
6Ml3 – Interpret readings on d
decimals to one place) e.g. 2.6 kg to 6Ml4 – Draw and measure lin
2600 g. 6Ml5 – Know imperial units st
• Order measurements in mixed units.
• Round measurements to the nearest 3A: Number and prob
whole unit. 6Nn16 – Recognise and use de
• Interpret a reading that lies between
3B: Problem solving
two unnumbered divisions on a scale. 6Pt2 – Understand everyday
• Compare readings on different scales.
use these to perform s
6Pt5 – Estimate and approxim
*for NRICH activities mapped to the Cam
Vocabulary
miles • feet • inches • gallon • quart • pint • pounds • ounces
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
ures
Me asu re Met ric and imp erial measures (2)
Met ric and imp erial measures (1) Let’s investigate Vo c abula r y
A 6 inc h r uler w ith mar ks on ly at 1 inc h, 3 inc he s, an d
Let’s investigate
Kab ir ha s three f uel c on tainers . O ne h old s 7 ga llo n s, Vocab ulary 6 inc he s ca n b e u se d to mea sure 2 inc he s by u sin g the mile s : an imp erial d ista n ce
o ne h o lds 4 ga llo n s a n d o ne h old s 3 g allo ns . On ly th e between 1 a nd 3 inc he s. I t ca n b e us ed to measure of le ng th mea sure 5 inc he s
7 ga llo n c o n ta in er is fu ll, the others are e m pty . ga llon : an im per ia l
measure of capac ity u sin g th e d istan ce betwee n 1 a n d or distance.
W ha t is the q uic kes t way to tra n sfer th e f ue l so tha t or liqu id volume.
two o f the co nta iner s c o n tain 2 ga llon s eac h, a nd the 6 inc h es . L o o k a t th e rile r be lo w. I t o nly ha s 0 inc he s y ards:a n im per ia l
third co nta ins 3 gallon s ? quart: a n imperia l
measure of capac ity or and 1 2 inc hes mar ked. measure of len gth or
liqu id v olume,
distance, there are
there are four quarts
in a gallon. p int: an U sin g w hat y o u kn ow ab o u t the 6 inc h r uler w ith o nly 1 7 6 0 y ards in a mile.
3 ma r ks o n it; w ha t is the few est n u mb er of mar ks feet: an im p erial y o u
mea sure
co uld p ut o n a 1 2 inc h r uler a n d still be a b le to
every d istan ce fr om 1 in ch to 1 2 inc he s ? meas ure of le n gth,
there are three feet
im pe ria l in a y ard.
0 1122
measure of capacity
iinc he s: an imperia l m
C o nv e r sio n t a ble – C o nv e r sio n t a ble – or liqu id volume, there me eoaf sluerngth, t e are 12
are two pints in tihnecrhes in a foot.
Co n side r the differe nce in inhces
LitLrietsr es t o I mI pmepreiar lia l P int sLitr eIsm pet or iIaml Ppeinrtisa l Litre s a q ua rt. es be tween differe nt pa ir s of .
This is a ru ler that shows minacrhksess a nd centimetres.
P int1s 1. 7 6 Pints 1 0 .5 6 8 p ou n d s: a n im per ia l
2 3. 5 2 2 1 . 13 7 measure of mass.
5 8. 8 0 5 2. 8 41 ou nces:an im perial IN CH ES 234 56 7 8 9 10
10 17 .6 0 10 5. 6 8 3 measure of mas s, 019CE N1T2I M0E T22R1E S232 243 254 256 276 8 9 10 11 12 13 14 15 16 17 18
1 Sa lly has measured the surface area of the there are 16 ounces 1 This is Harvey , an inch worm!
hou se s o that she can wor k ou t in a pound. walls in her 1
how much pa in t s he needs to decorate the rooms. She He is 2 inches lo ng a nd inch wide.
2
kno ws that s he w ill need 8 p ints of pain t for every 400
square feet of wall, b ut the pa int tin s come in litres. Draw the other members of his family :
What tins s hou ld she b uy for each of these rooms: 1
(a) baby sister, 1 inch long, inch w ide
(a) hallway 400 sq uare feet in Lemon Yellow 12 wi de
(b) older brother, 3 inch2es long, 1 inch
(b) bathroom 20 0 sq uare feet in Ice Blue 1
(c) bedroom 700 square feet in Coral Pin k (c) parent, 4 inches long, 1 inches w ide
2
(d) parent 5 inches long, 2 inches wide.
10 8
11 0
listed objectives might only be partially covered within any given chapter but are covered fully across
ken as a whole
, mass and capacity)
ard units of measure. Read and write to two and three decimal places.
s of measurement (kg and g, l and ml, km, m, cm and mm), using decimals to
ognising that 1.245 m is 1 m 245 mm.
different scales, on a range of measuring instruments.
nes to nearest centimetre and millimetre.
till in common use, e.g. the mile, and approximate metric equivalents.
blem solving
ecimals with up to three places in the context of measurement.
(Using techniques and skills in solving mathematical problems)
systems of measurement in length, weight, capacity, temperature and time and
simple calculations.
mate when calculating, e.g. use rounding, and check working.
mbridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 3B 259
Core activity 30.1: Capacity and mass
Resources: Measurement units puzzle photocopy master (p267). Non-metric meas
Rulers marked in centimetres. Empty containers marked with capacity, some marke
Pounds and kilograms photocopy master (p270). A bag weighing 1 kg (ideally cont
(Optional: an unmarked container and measuring jugs labeled in metric and imperia
measures.)
Explain that, during this session, learners will be exploring many different units of m
and that they will be making conversion tables and graphs to help them convert betw
systems of measurement.
Give learners the Measurement units puzzle sheet. Tell them that hidden in the grid are
used as units of measurement. They should work with a partner to try to remember diffe
measurement they have used or heard of and try to find them in the grid. Remind learne
units of measurement use another unit as a stem for the word, e.g. centimetre and metre
should check that words they find are not part of a longer word. This activity should enco
learners to discuss and use the vocabulary.
(Answer: the 16 words in the wordsearch are: litre, millilitre, pint, gallon, gram,
pound, ounce, centimetre, millimetre, metre, kilometre, mile, inch, foot, yard.)
Give learners the Non-metric measures sheet. Tell them that the ‘gallons’, ‘quarts’, ‘p
‘cups’ are all measures for liquids. Explain that, where the metric system uses multip
100 and 1000 for the units of measurement, the imperial and US systems use differen
quantities. In pairs learners should look at the two diagrams and discuss what the diagr
to illustrate about these different measures.
As a whole group, talk about the relative amounts and how the two diagrams show th
learners to choose one of the diagrams to help them answer questions such as:
In the USA, how many:
quarts are there in a gallon
cups are there in a quart
pints are there in a gallon
cups are there in a gallon?
(Answers: 4, 4, 8, 16)
260 Unit 3B 30 Metric and imperial measures
LB: p108
sures photocopy master (p269). Grid paper for drawing line graphs.
ed in imperial and some marked in metric units (or pictures of these).
taining potatoes). A bag weighing 1 lb (ideally containing potatoes).
al units; a recipe book with ingredient quantities in imperial
measurement Vocabulary
ween different
gallon: an imperial measure of capacity or liquid
16 words volume.
erent units of quart: an imperial measure of capacity or liquid
ers that some volume, there are four quarts in a gallon.
e, so they pint: an imperial measure of capacity or liquid volume,
ourage there are two pints in a quart.
pounds: an imperial measure of mass.
, kilogram, ounces: an imperial measure of mass, there are 16
ounces in a pound.
pints’ and
ples of 10, Look out for!
nt Learners who are unsure that a word, they think they
have found, is a unit of measure. Provide learners with
rams are trying a mathematics dictionary (either paper or electronic)
for them to look up words.
hese. Tell
Remind learners that a US cup measurement is equivalent to 240 ml of liquid. A
this information, and the diagrams on the resource sheet, to help them calculate t
equivalent amount in millilitres or litres of a US pint, a US quart and a US gallo
ml, 960 ml 3.84 l). Remind learners of the tables and line graphs they used in
186 unit 2Ci) to compare cups and millilitres. Ask learners to construct their o
graph on paper showing the conversion between litres and US pints.
Explain that another system of measurement is the imperial system, which uses
‘pint’, ‘quart’ and ‘gallon’, and the relationships are the same as on the Non-met
but they have a different value in litres. Tell learners that one imperial pint is equ
litres. Ask them to draw a new table comparing imperial pints to litres and then a
information to the line graph alongside the US pints to litres. They should draw
different colour and add a key.
Show learners some examples of containers with their capacities labelled in the dif
Learners should write five questions about the information in their graphs and then ans
questions, e.g. “What is the approximate difference in imperial and US pints that eq
Show learners the Pounds and kilograms sheet. Ask learners whether, at this stall,
better value to buy the potatoes by the kilogram or the pound, or whether the value
Pass around the 1 kg and 1 lb bags so that learners can compare the difference in m
Ask them if they agree that one pound is equal to approximately 1 kg. Ask
2
weigh the 1 lb bag in kilograms (they should find that it has a mass of approximat
kg). Learners should discuss in pairs, and then with the whole group, how they can
information to decide which is the better value on the resource sheet. (Answer: $4
Summary
Learners have learnt the vocabulary associated with imperial units in common us
converted to the metric equivalents.
Notes on the Learner’s Book
Metric and imperial measures (1) (p108): learners convert between pints and litr
conversion table in the context of painting walls. They convert between pounds a
using a line graph.
Ask them to use Look out for!
the
on (Answers: 480 Learners who cannot work out a suitable scale for the
Chapter 20 (page graph. Suggest that they use the horizontal scale on
own table and line the graph for pints, divisions marked and labelled at
one pint intervals, and the vertical scale for litres.
the same words, Ensure that learners understand the need for:
tric measures sheet table and graph headings
uivalent to 0.568 axis labels
add this using appropriate tools, e.g. ruler and sharp
the line in a
pencil, to assist accuracy.
fferent systems.
swer their partner’s
qual 3 litres?”
they think it is
e is the same.
mass.
k two learners to
tely 0.455
n use this
4 per kilogram.)
se and Check up!
res using a Give learners a selection of food and drink packaging.
and kilograms Ask learners to use the conversion tables and line graphs
they have draw to convert the measurement on the
packaging from metric to imperial, or vice versa.
Core activity 30.1: Capacity and mass 261
More activities
My wordsearch (individual or pairs)
Learners can design and make their own wordsearch (or other) puzzle using metric a
Capacity scale (individual or pairs)
You will need an unmarked container and measuring jugs labeled in metric and imp
Learners can measure liquids and label an unmarked container so that it can be used
Recipe (individual)
You will need a recipe book with ingredient quantities in imperial measures.
Learners can find a recipe that is written using imperial measures and convert it to m
Games Book (ISBN 9781107667815)
Gallon Man game (p78) is a game for two to four players. Players use a spinner to co
Gallon Man is the winner.
262 Unit 3B 30 Metric and imperial measures
and imperial measures vocabulary. Swap it with a partner and try to solve it.
perial units.
to measure metric and imperial quantities.
metric measurements.
ollect pieces of a ‘Gallon Man’. The first player to complete their
Blank page 263
Core activity 30.2: Distance
Resources: Miles and kilometres photocopy master (p271). Paper strips (at least 3
Map of south America. Grid paper for drawing line graphs. Calculators.
Tell learners that an inch is a measurement 2.54 cm in length. [In everyday life 2.5 cm
adequate approximation, but the learners will be converting inches to centimetres to t
places, then drawing and measuring the lengths to the nearest mm.]
Give each learner a strip of paper at least 35 cm long. Ask them to measure with a ce
and cut the strip so that it is 12 inches long. They should then mark on divisions at in
inch. Encourage learners to think of their own strategy to complete this activity, or su
draw a table for converting up to 12 inches into centimetres.
Explain to learners that 12 inches equals one foot, so their paper strips are one foot lo
learners to find objects around the classroom that are approximately one foot long.
Have groups of eight children join their strips of paper together (without overlapping) to cr
eight-foot tape measure. Ask learners to use their tape measures to measure the height o
member of their group to the nearest half inch and then convert the measurements into c
Tell learners that some countries measure road distances in miles and some in kilome
Discuss any countries that they know that use each of these measurements. Tell learn
there are approximately 8 km to every 5 miles and ask them to draw and complete thi
showing comparison between miles and kilometres, using their understanding of rati
miles kilometres
5 8
10
20 80
100
Show learners the Miles and kilometres sheet. Explain how the table is read by find
distance between two cities where the relevant column and row meet. Show the learn
location of the cities on a map of South America. Check that learners understand how
is read by asking them to find the distance in kilometres between:
264 Unit 3B 30 Metric and imperial measures
LB: p110
35 cm long). Rulers marked in centimetres. Scissors. Sticky tape.
m is usually an Vocabulary
two decimal
miles: an imperial measure of length or distance.
entimetre ruler yards: an imperial measure of length or distance, there
ntervals of one are 1760 yards in a mile.
uggest that they feet: an imperial measure of length, there are three
feet in a yard.
ong. Ask inches: an imperial measure of length, there are 12
inches in a foot.
reate an
of each Look out for!
centimetres. Learners who need a greater challenge. Ask them to
work out at what length an approximation of
etres. 1 inch = 2.5 cm will the measurement be more than 1
ners that cm away from the true measurement (where
is table 1 inch = 2.54 cm).
io.
ding the
ners the
w the table
Quito and Lima (1807 km)
Caracas and Buenos Aires (7405 km)
Asuncion and Rio de Janeiro (1801 km)
Give learners an opportunity to discuss how they might work out these distances in
Discuss as a whole group any strategies that they have thought of. Suggest that le
the following methods of f i nding the approximate number of miles that is equi
journey from Asuncion to Rio de Janeiro:
extend the table (made earlier in the session) to include 1800 km (and helpful
between)
draw a line graph using the measurements in the table, and extend to include 1
divide 1800 km by 8, then multiply by 5
multiply 1800 km by 0.625 using a calculator. (Answer: approximately 112
All learners should draw a line graph to show the conversion between kilom
miles on paper.
In pairs ask learners to work out a route around South America that would visit all th
give the total distance in kilometres and miles. Pairs should compare their routes w
investigate which might be the shortest and longest routes. Instruct learners to crea
their conversion tables and graphs between metric and imperial measures.
Summary
Learners have learnt the vocabulary associated with imperial units of length i
and converted to the metric equivalents.
Learners have measured lines with increasing accuracy.
Notes on the Learner’s Book
Metric and imperial measures (2) (p110): learners draw lengths in inches and or
given in inches, centimetres and millimetres. They use a table to find distances in
then convert the distances into miles. For Q3, help learners familiarise themselve
information in the picture by discussing the answers to the question.
n miles. Opportunities for display!
Display learners’ booklets of conversion tables and
earners use one of graphs.
ivalent to the
l values in
1800 km
25 miles.)
metres and
he cities listed and
with others and
ate a booklet of
in common use Check up!
rder lengths Give learners the distances between local towns and
n kilometres and villages in kilometres. Ask learners to draw a scale map of
es with the the position of local towns and villages, using a scale of 1
inch to 1 mile.
Core activity 30.2: Distance 265
More activities
Fibonacci (individual)
Learners can investigate the approximate link between the ratio of miles to kilometre
kilometres etc. Numbers that are not in the sequence can also be partitioned into Fibo
+ 8 + 3, all Fibonacci numbers. The next numbers are 144, 13, and 5, which add up to
Local distance (individual)
Learners can find out distances to local towns in both kilometres and miles.
266 Unit 3B 30 Metric and imperial measures
es and the Fibonacci sequence, e.g. 5 miles equals 8 km, 8 miles equals 13
onacci numbers for converting, e.g. 100 can be partitioned into 89
o 162. (100 miles is equivalent to 160.934 km).
Measurement units puzzle
There are 16 words hidden in this wordsearch that are used as units of
measurement. Find the words and write them in the table below.
J U T FWE Y AR D T OO F P
A ZQ T LV L VE R T I L B P
CENT I ME TR EDS NEV
K I L OME T R E C NUO CM
OKOUX J GYFMZXK I H
S WW E M E R T E M I L L I M
N PDU I E P E J D I E QK S
B FK I LOGRAME T R E F
DKBNLAGO TB I RUHA
OHOU I HTAANHC S V I
A E XWL E C O L O I YMT E
QVHQ I J A EML S PMGA
PVH I TXDX SEOYNGB
HE S F RR F RNHDNUO P
BWK Q E BM C O X UMA R G
Unit of measurement words:
mass/weight capacity/liquid volume length/distance
Instructions on page 260 Original Material © Cambridge University Press, 2014
Answers to measurement units puzzle
J U T FWE YAR D T OO F P
AZQT LVLVERT I LBP
C E NT I ME T R ED S NE V
K I L OME T R E CNUOCM
OKOUX J GYFMZ XK I H
S WW E M E R T E M I L L I M
N PDU I E P E J D I EQKS
B F K I L OG R AME T R E F
DKBN LAGOT B I RUHA
OHOU I HTAANHC S V I
A E XWL E C O L O I YM T E
QVHQ I J AEML S PMGA
P VH I TXDX SEOYNGB
HE S F RR FRNH NUO P
BWKQ E BMC O XDMA R G
U
LITRE, MILLILITRE, PINT, GALLON, GRAM, KILOGRAM, POUND,
OUNCE, CENTIMETRE, MILLIMETRE, METRE, KILOMETRE,
MILE, INCH, FOOT, YARD
Instructions on page 260 Original Material © Cambridge University Press, 2014
Non-metric measures
Mr.
Gallon Man
Instructions on page 260 Original Material © Cambridge University Press, 2014
Pounds and kilograms
Instructions on page 261 Original Material © Cambridge University Press, 2014
Miles and kilometres
Asuncion
Buenos 1345 km
Aires
Caracas 7405 km 6036 km
Lima 5665 km 4189 km 3612 km
Montevideo 4760 km 7372 km 960 km 1458 km
Rio de 2384 km 5258 km 6544 km 2698 km 1801 km
Janeiro
Quito 7051 km 6560 km 1807 km 7465 km 5991 km 5414 km
Santiago 3753 km 2103 km 3436 km 8138 km 1550 km 1523 km 2143 km
Instructions on page 264 Original Material © Cambridge University Press, 2014
272 Blank page
3B 31 Time (3)
Quick reference
Core activity 31.1: Time zones (Learner’s Book p112)
Learners read and use a timetable, using the 24-hour clock system, and calculate
intervals. They learn how the time is different in different time zones around the
Core activity 31.2: Leap years (Learner’s Book p114)
Learners investigate how calendars relate to the orbit of the Earth around the Sun
use of leap years to adjust the calendar to match the cycle. Learners calculate tim
intervals in days, weeks and months, using their knowledge of calendars and lea
Prior learning Objectives* – please note th
across the boo
• Recognise and use the units for time:
seconds, minutes, hours, days, months 3B: Measure (time)
and years. 6Mt4 – Read and use timeta
– Calculate time intervals usi
• Tell and compare the time using digital and 6Mt6 – Use a calendar to cal
6Mt8 – Appreciate how the ti
analogue clocks using the 24-hour clock.
• Read timetables using the 24-hour clock. 2B: Measure (time)
• Calculate time intervals in seconds, 6Mt7 – Calculate time interva
minutes and hours using digital or 3B: Problem solvin
analogue formats. 6Pt2 – Understand everyday
• Use a calendar to calculate time intervals
in days and weeks using knowledge of use these to perform
days in calendar months.
• Calculate time intervals in months or 3B: Problem solving
years. 6Ps2 – Deduce new informa
has on another.
6Ps4 – Use ordered lists or t
*for NRICH activities mapped to the C
Vocabulary
time zones • universal time • longitude • leap year • orbit
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Time zones (2) Vocab ulary It’s a date
Let’s investigate time zones : regions
T he se ch ildren ha ve d ifferen t b ir th m o nth s, b u t were all o n th e ear th s urface b or n in
th e s ame y e ar bef ore May . Fin d o u t w ho wa s tha t share a c om m on bo rn in e ac h
mo n th . tim e .
1 Me en a was b or n bef ore J es s .
2 J es s wa s bo rn tw o m on ths af ter A da m. You c ou ld write th e n ame s o n
e time 3 Ad am wa s bo rn af ter J o sh b u t before M ee n a. separa te p iec es of pa pe r a nd the n
world. rearrange th em a ga ins t th e
n, and the mo n th s un til a ll three
me
ap years. 1 Lima Sa o Paulo statemenCtas paereTotrwuen.
(05 :5 19)81202122023111224113 114612543 (0 7:5918)120212127932110128461171253111641254 3 9(811220122:52012)31112142 13 111645243
19 18 17 19 18 17
7 6 5 7 6 5
This is a page from the ca lendar for 197 6.
1 1 12 1 To ky1o022(2193:5214)1113112429121 11 12 1 Januar y 1976
0222 3 24 13 142
Karachi 1 142 1 02125A2 d33e2la4i d1e3 M on day Tue sday W e d ne sda y Th ur sda y Fr ida y Sa t ur da y S un day
1 9 2 15 3 (2 0 :2 1) – – –1 234
5 6
(15 :2 1) 12 13
21 7316 19 20
9 8 20 19 15 5 4 8 2019 16 4 8 2019 168175 16 4 26 27
7 181 7 168157 7
6 78 9 10 11
14 15 16 17 18
21 22 23 24 25
This is a table to s how the time difference between cities. The table sho ws tha t there is 28 29 30 31 –
a 14 ho ur time d ifference between Lima and Toky o.
Li ma Use the cale ndar above an d what y ou kno w ab ou t y ears, months, weeks a nd day s
to wor k out the day of the wee k of o n:
Sao Pa ulo
Ca pe Tow n (a) 1st March 19 76
(b) 15th May 197 6
14 hours Kar ac hi (c) 1st December 19 75 Reme m ber to workk
(d) 22n d J uly 197 6 o ut w he ther the year
To ky o (e) 31st December 1 976
ar is a le ap y ear.
Ade lai de
(f) 1 st March 197 7
Copy and complete this table show ing the time difference between the different
cities u sing the cloc ks above.
11 2 11 4
hat listed objectives might only be partially covered within any given chapter but are covered fully
ok when taken as a whole
ables using the 24-hour clock system. 6Mt5
ing digital and analogue times.
lculate time intervals in days, weeks or months.
ime is different in different time zones around the world.
als in days, months or years.
ng (Using techniques and skills in solving mathematical problems)
y systems of measurement in length, weight, capacity, temperature and time and
simple calculations.
g (Using understanding and strategies in solving problems)
ation from existing information and realise the effect that one piece of information
tables to help solve problems systematically.
Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 3B 273
Core activity 31.1 Time zones (2)
Resources: Time Zone map photocopy master (p280). Flight timetable photocopy
the cards with a destination on them and place in an envelope (one set for each gro
with flight timetables.)
Note: some of these activities involve a lot of calculations. It may be best to specify l
destinations for each of the groups (or the same destination for each group for compa
Hold up a globe and rotate it slowly. Remind learners that, because the Earth rotates,
different time zones around the world. Remind them that the time differences are roug
measured from Universal Time (also known as Greenwich Mean Time), a line of lon
passing through Greenwich, England, and also passing through France, Spain, Algeri
Burkina and Ghana.
Ask pairs of learners to find the Hawaiian Islands (US) and the Line Islands (Kiribati) on
globe. They should use the internet to find out the current time and date in these two loc
pairs of learners to discuss what is surprising about the time in the two locations, and w
think of any reason for one location being one day ahead of the other, although they are
same longitude.
Explain that, although the Earth can be split into equal-sized time zones (show the Ti
countries often choose a time for other geographic, political or business reasons. The
gives an indication of the time differences but may not be accurate.
Ask learners to choose and investigate the time zones of one of the following countries
than two zones on the Time Zone map:
China
Russia
United States of America
Canada
Australia
The Antarctic.
274 Unit 3B 31 Time (3)
LB: p112
y master (p281). Travel agent customers photocopy master (p282) – cut out
oup). Globe. World atlases. (Optional: flight timetables or holiday brochures
locations and Vocabulary
arison).
time zones: regions on the earth surface that share
there are a common time (in relation to when the sun is in the
ghly sky).
ngitude universal time: the time to which different time
ia, Mali, zones are compared. It is the time at longitude zero.
longitude: imaginary lines from pole to pole on the
n a map or Earth’s surface to help navigate and identify time
cations. Ask zones.
whether they can
e both at the Opportunities for display!
Learners can create a display of what they have
ime Zone map), found out about how different countries use time
e Time Zone map zones around the world.
that cover more
Give pairs, or small groups, of learners the Flight timetable sheet. Ask them to calc
different planes will land, using the time in Glasgow in the summer, then convert the
time where the flight ends (local time). Learners should ideally find internet resourc
correct time differences, or they could use the Time Zone map for approximate time
Give groups of learners an envelope with the cards from fro the Travel agent custom
learners that each speech bubble represents a customer who would like to fly from
Ask them to take one piece of paper at a time out of the envelope and discuss whic
recommend to the customer. For some customers only one flight matches their requ
will be more than one flight to choose from, or none that match it well, but the group
agree the best flight to recommend. Give the groups the three blank speech bubble
requests for another group so discuss. Groups should try to fulfill the requests of an
flight timetable.
Display the following worded problems involving time. Explain that all the times
learners will need to find out the time differences between the places:
How long was the flight? Casablanca, Morocco, to Jeddah in Saudi Arabia lea
Monday and arriving at 03:25 Tuesday.
How long was the flight? Ulaanbaatar, Mongolia to Moscow, Russia leaving
and arriving the same day at 11:55.
You decide to visit a friend in Auckland, New Zealand, travelling from Santia
flight leaves at 23:55 on Tuesday and arrives at 04:05 on Thursday. How long
Summary
Learners have read and used a timetable using the 24-hour clock system and t
calculated time intervals.
They will have learnt how the time is different in different time zones around
Notes on the Learner’s Book
Time zones (p112): learners calculate the time differences between different citie
clocks and enter the information into a table. They calculate the length in time of
cities using departure and arrival times.