1A 4 More on number
Quick reference
Core activity 4.1: Addition of decimals (Learner’s Book p14)
Learners revise previous learning on adding decimal numbers. They extend their
knowledge to add decimals including with different numbers of decimal places.
Core activity 4.2: Division (1) (Learner’s Book p17)
Learners revise division methods when there is a remainder by dividing two- and
three-digit numbers by single-digit numbers.
Core activity 4.3: Number sequences (Learner’s Book p18)
Learners consolidate previous learning using the vocabulary related to sequences
with precision. They work increasingly with sequences involving fractions and
decimals.
Prior learning Objectives* – please note that listed objectives might only
as a whole
This chapter builds on
work in Stage 5 where 1A: Numbers and the number syste
learners worked on 6Nn15 – Recognise and extend number seque
number sequences and
continued to develop and 1A: Calculation (Mental strategies)
re ne mental and written 6Nc1 – Recall addition/subtraction facts for n
strategies for the four
operations: addition, 0.4 + 0.6.
subtraction, multiplication 6Nc10 – Divide two-digit numbers by single-dig
and division.
1A: Calculation (Addition and subtra
6Nc11 – Add two and three-digit numbers with
1A: Problem solving (Using techniqu
6Pt1 – Choose appropriate / eff i cient menta
multiplication or division.
6Pt3 – Check addition with a different order w
1A: Problem solving (Using underst
6Ps1 – Explain why they choose a particular
– Make sense of and solve word problems an
Vocabulary
sequence step term rule
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Add it ion o f deci mals Div ision (1) Number sequences Vo c abula r y
Let’s investigate Let’s investigate Let’s investigate se que nce : a n ordered Cho o se different
Arran ge the num ber s 0 . 1, 0. 2 , 0. 3, 0 .4 , 0. 5 an d 0 .6 in the A bd u l was as ked h ow o ld he wa s. set of numbers, sha pe s tha t ha ve a ru le ‘ad d 5 ’.
circle s s o the s um alo n g ea ch s ide of the tr ia n g le is 1 . 2. star ting numbers to ma ke seq ue nces
or o the r mathema tica l
Try us in g n um bers o n
cards or sm all piece sooff If my a g e is d iv id e d by Is it p o s sib le to ma ke a se q ue nce where objects arranged
paper, tha t y ou c an 2 o r 3 or 4 th ere is 1 the ru le is ‘ad d 5 ’ a nd the term s are: according to a ru le.
move aro un d. lef t o ver. I f my a g e is For example, 3,
r d iv id e d by 7 the re is 7. ● m u ltiples o f 5 ? 6, 9 , 12 , 1 5 …
d L is t the m ultiple s off ● m u ltip le s of 1 0 ? 11,4, 9 , 1 6, 2 5 …
s no re m ainder.
● a ll o dd ? ssttep:the ‘ju mp s ize ’.
Ho w o ld is A b du l? FFor exam ple,in the
● inc lu de 2 4 a n d 3 9 ? You will ne ed to try sequence
60 110 160 210
● are n ot w h o le num ber s ? different s tartin g number s
+50 +50
. +50 the step is ’ 50 ’.
1 Vincen t wants to p ut 75 photo graphs in an alb um. 1 Here is the beginn ing of a sequence of
A full page ho lds 6 pho tographs. What is the sma lles t n umber of pages
1 The ans wers to the following q uestio ns are in the gr id. Fin d w hich Vincen t use s? num be rs: term: one of the
answer goes w ith which q uestion .
Which number is n ot one of the answers? 8, 16, 24, 32, 40 . .. numbers in a
The seque nce continues in the same way .
8.28 4.3 2.05 2 Which number on the grid can be 67 72 51 Will 8 8 be in the seque nce? Ex plain how sequence.
7.8 5. 4 1 12.18 div ided by 8 w ith a remainder of 1? 42 73 64
13.95 4.98 12.21 rule: a ru le tells y ou
how thin gs or numbers y ou know.
are connected. For
60 20 69 2 A seq uence starts at 20 0 an d 30 is example, the numbers
subtracted each time. 3, 7, 11 , 15 , 1 9 … are
(a) 4.61 0. 8 ( b) 0. 45 1. 6 (c) 3. 7 4. 58 (d) 6 .1 7 .85 3 Complete these calc ulatio ns:
(e) 4.3 0. 68 (f) 7.5 4.6 8 (g) 4. 25 7.96 ( h) 3 .45 0. 85 200, 170 , 14 0 ... connected by the r ule
2 K iki ha s tw o p ieces of rope. One piece is 93 .7 metres lo ng and the o ther p iece is 1 25. 9 (a) 78 4 ( b) 68 7 (c) 98 6 ‘ad d 4 to the previous
metres long. What is the total leng th of her rope? num be r’.
41 ÷ 4
4 Copy the grid. Sha de the squares 14 ÷ 4 What are the rs t two numbers in the seque nce that
that have a remainder in the 55 ÷ 6
answer. 34 ÷ 7 47 ÷ 9 48 ÷ 5 are less than zero?
60 ÷ 8 25 ÷ 5 31 ÷ 3
3 Fin d the sum of all the numbers le ss than 5. 5 in this lis t. 5. 05 What letter have y ou made ?
5.5 5 5.1 5 5.5
5 Compl1e4te7 these calc ulatio ns: 27 ÷ 6 50 ÷ 7
48 ÷6 54 ÷ 9
(a) 132 ÷ 6 (b) 146 ÷ 9
(c) ÷ 2 (d) 1 07 ÷ 4 54 ÷ 6 4 9 ÷ 7 18
(e) 156 ÷ 8 (f) 14 8 ÷ 9
14
17
y be partially covered within any given chapter but are covered fully across the book when taken
em
ences.
numbers to 20 and pairs of one-place decimals with a total of 1, e.g.
git numbers, including leaving a remainder.
action)
h the same or different numbers of digits/decimal places.
ues and skills in solving mathematical problems)
al or written strategies to carry out a calculation involving addition, subtraction,
when adding a long list of numbers; check when subtracting by using the inverse.
tanding and strategies in solving problems)
method to perform a calculation and show working. 6Ps6
nd represent them.
*for NRICH activities mapped to the Cambridge Primary objectives,
please visit www.cie.org.uk/cambridgeprimarymaths
Unit 1A 27
Core activity 4.1: Addition of
decimals
Resources: (Optional: 0–9 digit cards photocopy master (CD-ROM).)
Start by challenging the learners to solve the following number puzzle:
“Complete the diagram (on the right) so that each line of numbers totals 1.”
Get feedback from the class about how learners solved the puzzle. Suggestions might
completing the bottom line first as a good starting place: they could add together the
numbers, then subtract them from 1, or use number pairs to 1 (for example 0.1 + 0.4
= 0.5; learners know that 5 and 5 is a number pair to 10 and therefore that 0.5 and 0.5
number pair to 1, so the third number must be 0.5). As they now have two numbers on
the other lines, they can add and subtract from 1 (or use number pairs to 1) as before.
As a class, practise some decimal additions where both numbers have one decimal pla
“What is 0.3 + 0.7?” (Answer: 1)
“What is 1 − 0.9?” (Answer:
(Again, number pairs c0a.n1)be useful here).
Move on to decimal addition where the numbers have different numbers of digits and
decimal places, for example ask:
“How could we work out 0.7 + 0.51?” (Answer: 1.21)
Gather information from the learners on what we need to think about when we are ad
numbers with different numbers of decimal places. Make sure this includes the impor
place value: tenths must be added to tenths, hundredths must be added to hundredths
Learners may suggest a variety of methods including:
partitioning (in this case into tenths and hundredths)
0.51 = 0.5 + 0.01
0.7 + 0.5 = 1.2
1.2 + 0.01 = 1.21
28 Unit 1A 4 More on number
LB: p14
ht include 0.2
e two existing
5 is a 0.1 0.4
on both of
. Opportunities for display!
ace, e.g. Posters with different addition methods shown for a
given sum.
d
Addition and subtraction strategies from Stage 4 that
dding could be adapted for adding decimal numbers:
rtance of Counting on/back in hundreds, tens and ones. Using
and so on. near doubles and compensating.
Using number pairs of 10 or 20. Partitioning
into hundreds, tens and units.
Rearranging the order of the addition, e.g. largest to
smallest numbers; or adding the 20 to 30 rst to make
50, then doubling 50.
Adding or subtracting near multiples of 10 to or from
a three-digit number.
Adding three numbers where the sum of two of the
numbers is a near multiple of 10.
Subtraction by finding the difference.
using a number line
+0.1 +0.1 +0.1 +0.1 +0.1 +0.1 +0.1
0.51 0.61 0.71 0.81 0.91 1.01 1.11
using a vertical addition
0.70
+ 0.51
1.20 (+ 0.5)
1.21 (+ 0.01)
using a standard written method:
0.70
+ 0.51
1.21
1
When using either ‘vertical’ method, encourage learners to write 0.7 as 0.70 so t
numbers have the same number of decimal places.
Practise the methods discussed by asking learners to choose the best method to a
following:
2.45 + 4.3 (Answer: 6.75)
34.61 + 1.92 (Answer: 36.53)
82.03 + 230.8 (Answer: 312.83)
Gather answers from the class and ask learners which method they chose. Leane
you if they got the answer wrong in order to identify where it went wrong. Did o
calculate the answer using a different method?
1
1.21
that all In this standard written method, the learners work from
answer the right to left, starting at the hundredths. They add
vertically down the place value column and write the
ers should also tell answer below. In the tenths column 7 + 5 = 12, so they
other learners write ‘2’ down and carry the ‘1’ (a unit) over to the next
column to the left.
Learners should use whatever method works best for
them. Support learners by asking them to consider
whether their method is:
Checkable
Accurate
Reliable
Efficient.
Core activity 4.1: Addition of decimals 29
Summary
Learners add two- and three-digit numbers with the same or different numbers of dec
places using an appropriate mental or written strategy.
Notes on the Learner’s Book
Addition (p14): a variety of questions focusing on the addition of decimals in and ou
context. Question 5, 6, 7, 9 and 10 ask the learners to solve puzzles by applying what
know about adding decimals.
More activities
Add the cards
(pYaoirus)will need 0–9 digit cards photocopy master (CD-ROM).
Each player will need a set of 0–9 digit cards and two decimal points. Each player sh
deals out six digit cards together with the two decimal points. Arrange the cards like
•
+ •
Complete the calculation. The winner of the round is the player with the highest tota
can vary the game by choosing different arrangements for the cards, for example:
• •
+ •
+ •
30 Unit 1A 4 More on number
cimal Check up!
ut of “Add 1.46 and 0.9. Explain your method.”
t they “Ahmed has made a mistake in the calculation:
0.7 + 0.41 = 0.48
How would you help him avoid making the same
mistake again?”
huffles their cards and then
this:
al. Play more rounds. You
Blank page 31
Core activity 4.2: Division (1)
Resources: (Optional: 0–9 digit cards photocopy master (CD-ROM).)
Learners work in pairs to solve the three word problems in any way they like:
1. Three boys share 56 marbles. How many marbles does each boy get and how many
2. 72 cubes are arranged in groups of five. How many groups are there and how many a
3. Zina needs 172 stickers. They are sold in packs of six. How many packs must she bu
(Answer: 29. She will have 2 extra)
Review work done ensuring that the following points are covered:
1. Division can be thought of as sharing or grouping. 12 cubes in
groups of four.
12 flowers shared
between four people.
2. There are a number of ways of performing a division calculation, for example, 15
These include:
using a number line to count back from 159:
7 7 70 70
0 5 12 19 89 159
using a number line to count on from 0:
+70 +70 +7 +7
0 70 140 147 154 159
32 Unit 1A 4 More on number
LB: p17
are left over? (Answer: 18 r2)
are left over? (Answer: 14
uy? How many re2x)tra stickers will she have?
59 ÷ 7. (Answer: 22 r5)
using repeated subtraction:
159 (10 × 7)
70− (10 × 7)
(2 × 7)
89
70−
19
14−
5
using short division:
2 2r5
7 1519
3. Remainders can be thought of as ‘a number left over’ but in word problems th
must decide if they can keep the answer as a remainder or if they need to rou
is 28 packs with a remainder of 4, so she must buy 29 packs.
4. Always use the most appropriate and efficient way to perform each calculatio
(Is their method Checkable, Accurate, Reliable and Efficient?)
Summary
Learners confidently divide a two- or three- digit number by a single-digit num
When dealing with contextual problems, learners treat any remainder appropri
rounding up or down to the nearest whole number.
Notes on the Learner’s Book
Division (1) (p17): the investigation is set in a context of division but is really ab
might provide an opportunity to remind learners why it is important to aim for re
division) facts. The five questions provide practice of division, focusing on rem
More activities
Divide the cards
(pairs) need 0–9 digit cards photocopy master (CD-ROM).
You will
Each player needs a set of 0–9 digit cards. Shuffle the cards and deal four cards
arrange their cards in to this layout:
Each player works out the answer. The winner of the round is the player with the
he remainder must be dealt with in the context of the problem, and the learner
und the answer up or down. For example, for puzzle 3, Zina’s stickers, 172 ÷ 6
on. (Teachers may need to discuss this with individuals, groups or the whole class.)
mber in and out of context. Check up!
iately; as a remainder or by
Ask learners questions such as:
bout using table facts, so it “Write a word problem for 15 ÷ 4. What is
ecall of multiplication (and
mainders. an appropriate answer to your problem?”
“What method would you use to divide 113
by 7? Explain why you chose this method.”
to each player. The players choose how to ÷
e smallest answer.
Core activity 4.2: Division (1)
33
Core activity 4.3: Number sequences
Resources: There are no specific resources required for this activity.
Ensure that learners are confident in finding the rule for number sequences by carryi
series of activities.
Write the numbers 20.1, 20.3 and 20.5 for the whole class to see. Say, “These are
consecutive terms in a sequence.” Ask learners what you mean by the words ‘term
‘sequence’, and remind them what we mean by ‘consecutive’ if you need to.
Continue the sequence forwards (20.7, 20.9, 21.1 . . .) and backwards (19.9, 19.7, 19
“What is the step size?” (Answer: the ‘jump’ is 0.2)
“What is the rule?” (Answer: add 0.2)
Ask learners what you mean by ‘step’ and ‘rule’. Repeat
for other sequences, for example:
141, 121, 143, 2 . . .
1.25, 1.5, 1.75 . . .
Ask, “If I start at 3, and my steps are 0.25 what will the 5th term of my sequence be?
Allow thinking time, then ask learners to share their strategies (write the sequence ou
3.25, 3.5, 3.75, 4 . . . ).
Ask learners to suggest a start number and step size, then nd the sequence as a class
Ask learners to work in pairs to complete the following sequences:
10 25 70 (add 15; 10, 25, 40, 55, 70, 85)
(add 2; –10, –8, –6, –4,–2, 0)
6 4 2
0.9 1.1 1.3 (add 0.1; 0.8, 0.9, 1.0, 1.1, 1.2, 1.3)
Review the work done and then ask questions in a different format, for example:
“These numbers form part of a sequence 1.4, 1.7, 2 . . .
If 1.7 is the middle term in a sequence of fi ve numbers, what are the start and fin
(Answer: 1.1 and 2.3)
If 1.4 is the third term what would the first term be? (Answer: 0.8)
If 1.4 is the fifth term what would the tenth term be?” (Answer: 2.9)
34 Unit 1A 4 More on number
ing out a LB: p18
e three
m’ and Vocabulary
9.5 . . .)
consecutive: numbers increase from smallest to largest
?” one after the other, without any gaps. For example, 1, 2,
ut: 3, 3, 4, 5. . .
s. sequence: an ordered set of numbers, shapes or other
mathematical objects arranged according to a rule.
For example,
3, 6, 9, 12, 15 . . .
1, 4, 9, 16, 25 . . .
∆∆
step: the ‘jump size’. For example, in this sequence
the step is +50,
60 + 50 110 + 50 160 +50 210 + 50
term: one of the numbers in a sequence.
rule: tells you how things or numbers are connected.
For example, the numbers 3, 7, 11, 15, 19 . . . are
connected by the rule ‘add 4 to the previous number’.
nish numbers?
Summary
Learners revise work on sequences using ascending and descending sequence
positive and negative numbers, fractions and decimals.
They use the language (sequence, step, term, rule) with precision.
Notes on the Learner’s Book
Number sequences (p18): learners nd missing numbers in sequences or continu
might be given the rule or have to work out the rule. Questions 4 to 7 use the voc
introduced in the unit (step, term, rule).
More activities
Generating sequences (small groups or whole class)
The rst player is given a starting number and the rest of the group take turns to
player. Start with a low number and a simple rule, for example, start at 5 and add
Games Book (ISBN 9781107667815)
Sequence trail (p8) is a game for individuals or pairs. It gives practice in nding
Answers (start anywhere in the loop):
60 35 6 65 1210 1025 1046 8 22 17 120 12 15 2
es involving Check
ue sequences. They up“!Complete these sequences:
cabulary
rst term 4, rule add 5
rst term 0.5, rule subtract 2.”
“A sequence starts at 100 and 40 is subtracted each
time. What is the rst term less than zero?”
continue the sequence, following a given rule with the leader choosing the next
d on 2. Extend to include negative numbers, fractions and decimals.
missing terms in sequences.
7 162 3 1027
Core activity 4.3: Number sequences 35
1B 5 Length
Quick reference
Core activity 5.1: Working with length (Learner’s Book
Lp2e0ar)ners select and use standard units of length. They convert between km, m, c
and mm. They use measuring instruments with different scales.
Core activity 5.2: Drawing lines (Learner’s Book p22)
Learners practise drawing lines accurately to the nearest millimetre. They are rem
the importance of using a sharpened pencil for greater accuracy.
Prior learning Objectives* – please note
• Read, choose, use and record standard across the b
units to estimate and measure length,
mass and capacity to a suitable degree of 1B: Measure (Le
6Ml1 – Select and use st
accuracy. 6Ml2 – Convert between
• Convert larger to smaller metric (units
to three places, e
decimals to one place) e.g. 2.6 kg to 2600 g. 6Ml3 – Interpret readings
• Order measurements in mixed units. 6Ml4 – Draw and measur
• Round measurements to the nearest whole
2A: Numbers an
unit. 6Nn16 – Recognise and u
• Interpret a reading that lies between two
1A: Problem solv
unnumbered divisions on a scale. 6Pt2 – Understand every
• Compare readings on different scales.
• Draw and measure lines to nearest and use these to
6Pt5 – Estimate and app
centimetre and millmetre.
1B: Problem solv
6Ps4 – Use ordered lists
*for NRICH activities mapped to the
Vocabulary
millimetre • centimetre • metre • kilometre
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Measure Drawing length
Measuring length Vocabulary 1 Accurately draw straight lines that measure:
Let’s investigate millimetre (mm): a (a) 9.6 cm ● Your pencil should be sharp.
(b) 122 mm ● Check the scale on your ruler. If
Nicola needs to put up bunting around a whole room unit for measuring (c) 0.129 m
(d) 5.1 cm necessary convert the length into
for a party. The room is 4 m long and 3 m wide. lengt h. (e) 26 mm the units shown on your ruler.
She has lots of 70 cm lengths of bunting. Every time centimetre (cm): a she (f) 0.088 m ● Find ‘0’ and the point on the
scale you need to make the correct
cm ties two pieces together she needs to use 50 mm unit formeasuring of each
minded of
piece of string for the knot. How many pieces length.There are 10
of 70 cm long bunting does she need to go right mm in 1 cm. length before starting to draw the
around the room? metre (m): a unit for 2 Curves and patterns, such as those below, can bleinem. ade by careful
measuring length. There measuring and drawing straight lines. Use your ruler to check that
are 100 cm in 1 m. all the lines drawn on the designs are straight.
First work out the kilometre (km): a unit for
perimeter of the or omm. . measuring length. There
Choose to do the are 1000 m in
calculation in mm,cm
or m and make all the 1 km.
measurements have the
same unit.You could
take,or imagine,three
or four pieces of
1 Eric has lost his umbrella.At thsetrLinosgt aPnrodperttiye Othfemce he looks at the list of umbrellas
that have been handed in.The ptoegrseothnerwho has lled in the Lost Property log seems to
have confused the units of lentgothb.etter understand
the problem.
Object Date Handed in Colour
Length
umbrella 12 September
umbrella 25 October Black 218 m
flowers) 84.9 m umbrella Blue (with
Red 26 October
umbrella 5 November
umbrella 19 November 895 cm
umbrella 20 November Black 97.2mm
Pink 527 cm
Silver 1.05 cm
22
20
e that listed objectives might only be partially covered within any given chapter but are covered fully
book when taken as a whole
ength, mass and capacity)
tandard units of measure. Read and write to two and three decimal places.
units of measurement (kg and g, l and ml, km, m, cm and mm), using decimals
e.g. recognising that 1.245 m is 1 m 24.5 cm.
s on different scales, on a range of measuring instruments.
re lines to nearest centimetre and millimetre.
nd the number system
use decimals with up to three places in the context of measurement.
ving (Using techniques and skills in solving mathematical problems)
yday systems of measurement in length, weight, capacity, temperature and time
perform simple calculations.
proximate when calculating, e.g. use rounding, and check working.
ving (Using understanding and strategies in solving problems)
or tables to help solve problems systematically.
e Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 1B 37
Core activity 5.1: Working with length
Resources: Measuring length poster photocopy master (p44). Car insurance
group resource sheet photocopy master (p46). Measuring curved lines resource
pieces of paper, or sticky notes. String. Pens. Dice. (Optional: four cones (or other l
Units of length
In small groups, ask learners to list, or draw a diagram such as a cluster/cloud diagram,
what they know about length and the equipment and units used for measuring and comm
length. Display the groups’ lists alongside the Measuring length poster. Encourage learn
to the poster and their lists during the following activities.
[Note: the poster only shows metric measures of length but some learners may be fam
with imperial measures. At this stage, don’t try to convert between the two systems b
they know the following relationships: 12 inches = one foot (the length of a standard
classroom ruler), three feet = one yard (one yard is a little bit less than a metre) and 1
= one mile (one mile is about 1.6 km).]
Tell the learners that people often need to ll in some details about their car for the in
company, or for taking it on a ferry. Show them the Car insurance lengths resource
sheet. Look at the first example together. Ask learners to briefly discuss in pairs whic
of information are unrealistic . Tell learners that some of the information has been given
the correct numbers, but the incorrect units. Ask them to say what the units should be
tape measure to demonstrate the difference between values in metres, centimetres and
millimetres, and the importance for using the correct units. Learners should correct th
example themselves.
(Answers: Ciorda; units of length and height should be m, distance units should
Mutsui; length should be 3.97 m, height units should be m, distance units shoul
Get permission from members of staff for learners to measure the length and height
cars and, if possible, nd out the distance travelled and the average fuel consumption
necessary use an internet search or a conversion chart to convert miles into kilometre
close approximation, multiply the miles by 1.6 to get the kilometres.) Before
38 Unit 1B 5 Length
LB: p20
lengths resource sheet photocopy master (p45). Measuring straight lines
sheet photocopy master (p47). Tape-measures, metre sticks, rulers. Small
large place markers).)
, to show Vocabulary
municating
ners to refer millimetre (mm): a unit for measuring length.
centimetre (cm): a unit for measuring length.
miliar There are 10 mm in 1 cm.
but see if metre (m): a unit for measuring length.
d There are 100 cm in 1 m.
1760 yards kilometre (km): a unit for measuring length.
There are 1000 m in 1 km.
nsurance
Opportunities for display!
ch pieces Display the learners’ diagrams/lists about lengths and
measuring equipment.
n with
e. Use a Look out for!
d Learners who don’t understand the difference
he second between measuring in a unit and measuring to the
nearest whole unit. Give an example, such as: a
d be km. measurement given in metres could be measured to
ld be km.) the nearest metre (2 m), the nearest centimetre
(2.45 m), or the nearest millimetre (2.453 m). In
of their the case of a car, measuring to the nearest metre
n. (If would usually not be accurate enough and measuring
es or, for a to the nearest millimetre would be unnecessarily too
accurate.
learners measure the cars, ask them to explain and discuss how accurate they thin
measurements need to be, e.g. to the nearest metre, centimetre or millimetre. Lea
the blank table to complete the information about the car they have measured.
Measuring Length
Tell learners that their challenge is to increase their accuracy in measuring and d
the nearest millimetre, which they started to do in Stage 5.
Give groups, of approximately six learners, the Measuring straight lines group resou
each member of the group to secretly measure line A. They should write their meas
nearest millimetre on a small piece of paper or sticky note. Once all the members o
measured the line they should compare their measurements and reach an agreeme
length of the line, to the nearest millimetre. Ask the members of the group who have
line most accurately to support less accurate members to measure the line again, w
learners:
starting their measurement from the end of the ruler, rather than the start (0) of th
moving the ruler as they measure
reading the scale incorrectly
rounding incorrectly, to the wrong division.
Groups should carry out the same activity with the other lines.
Ask learners to ref l ect on whether they think that the group activity has improve
measuring, and on how they have improved their measuring technique.
Draw a large, simple curve on the board. Demonstrate to learners how to measur
piece of string and a partner (one of the learners or an additional adult). Hold th
string at the start of the line and lay the string over the line until it reaches the en
Mark the string with a pen where it meets the end of the line. Measure the string
the marked point using a ruler or metre stick. Tell learners that when they measu
make sure that they measure the piece of string that they used to measure the lin
end of the string.
Give pairs of learners the Measuring curved lines resource sheet, some string and
to work together to measure each line.
Discuss together successful measuring techniques and advice for others trying to
accuracy of their measuring.
nk their Use observations of this activity to inform teaching in
arners can use the next activity, where learners will learn and practise
measuring with greater accuracy to the nearest
drawing lines to millimetre.
urce sheet. Ask Look out for!
surement to the Learners who make some of the common mistakes
of the group have listed on the left. Whilst encouraging learners to self
ent about the true and peer diagnose problems with measuring, it could
e measured the be useful to show some individuals what has gone
watching out for wrong, for example, have two rulers that have
he scale different ‘gaps’ at the end.
ed their
re the line using a
he end of the
nd of the line.
g from the start to
ure a curve to
ne, and not the
a pen. Ask them
o improve the
Core activity 5.1: Working with length 39
Summary
L earners have selected and used standard units of length. They
h ave converted between km, m, cm and mm.
T hey have used measuring instruments with different scales.
Learners have improved their accuracy in measuring lines to the nearest millimetre
Notes on the Learner’s Book
Length (measuring) (p20): learners correct measurements written in the wrong units
lengths. They estimate the lengths of lines, to the nearest cm, and measure them to th
mm.
More activities
Circuit (whole class or small groups)
You will need four cones (or other large place markers). Tape-measure.
Learners place four cones in an outside space to mark out a running circuit. Ask learn
times they would need to run around the circuit to complete a 1 km run. Ask them to
Unit conversion (individual)
Ask learners to work out how many millimetres there are in a kilometre. Challenge th
Games Book (ISBN 9781107667815)
The ordering lengths game (p59) is a game for two to four players. Learners race to o
40 Unit 1B 5 Length
e. Check up!
and order Ask learners to measure the length of the classroom
he nearest and to give the measurement in kilometres (to the
nearest metre), metres (to the nearest centimetre),
centimetres (to the nearest millimetre) and in
millimetres. Ask them to suggest which units they
think would be best for giving to someone laying a
new floor for the classroom, and why.
ners to measure the length of one complete circuit and calculate how many
o mark where the start and finishing lines would be on the circuit.
hem to write 1 mm in kilometres.
order lengths given in km, m, cm and mm.
Blank page 41
Core activity 5.2: Drawing
lines
Resources: Dice.
Drawing lines
Tell learners that they will be trying to improve the accuracy of their line drawing. Rem
that when a pencil is sharpened it has a tip that is less than one millimetre in width, wh
it could be more than two millimetres wide. Explain that the objective for this activity
learners to draw lines accurately to the nearest millimetre. If the learners’ pencils tips
than a millimetre they will not be able to draw the lines as accurately.
Tell the learners that they are going to draw a line that is 43 mm long, ask the learner
many centimetres that is. (Answer: 4.3 cm) All the learners will draw the line on plai
Tell the learners to pass their line to a partner for them to check that the line measures 43
Ask learners what advice they can remember that helps them to accurately draw a line t
nearest millimetre. Ask the learners to apply this advice to draw a line of 38 mm/3.8 cm,
partner will measure. Encourage learners to reflect on their accuracy and whether they n
support to improve their accurate drawing.
Remind learners that they are measuring and drawing lines to the nearest mm, not exac
length as they should understand the continuous nature of measure. Ask learners to
mark a 1 mm subdivision between 3 mm and 4 mm marks on a ruler with a sharp pen
2
them what measurements would round, to the nearest half millimetre, to 3.5 mm. Discu
with learners what the range of measurements would be that would round to 3.5 mm (
mm to 3.74 mm).
42 Unit 1B 5 Length
LB: p22
mind learners Look out for!
hen it is blunt
is for the Learners who have difficulty drawing to the nearest
are wider
millimetre. Gather these learners in a group and give
rs how
in paper. instructions verbally to help them understand the
3 mm. process of accurately drawing lines, and avoiding
to the common mistakes:
, which their 1. “Check whether your ruler measures in centimetres
need further
or millimetres.”
ctly that 2. “Find ‘0’ on the ruler.”
3. “Find ‘4.3’ on the ruler if it measures in
ncil. Ask 2
centimetres, or 43 if it measures in millimetres.”
cuss 4. “Place the ruler on the paper where you wish to
(3.25
draw the line.”
5. “Hold the ruler down firmly with the hand you do
not write with.”
6. “Mark a dot on the paper next to the ruler at the
positions ‘0’ and ‘43’ or ‘4.3’.”
7. “Still pressing firmly on the ruler with the non-
writing hand, put the tip of your pencil on the
dot by the ‘0’ then run the pencil in one smooth
movement along the ruler, stopping exactly on the
other dot.”
Give pairs of learners two dice. They throw the dice and record the two 2-digit numb
the numbers shown on the dice, for example, if a 1 and a 4 are thrown the 2-digit n
and 41. Each partner draws one line to match one of the 2-digit numbers made in m
Partners check the length of each other’s lines. They calculate the difference betwe
the two lines in centimetres, then mark the length of the shorter line on the longer li
the remainder of the line to check the accuracy of their drawing, measuring and cal
Ask learners to create a picture or pattern using one each of these lines:
16 mm
25 mm
39 mm
40 mm
51 mm
73 mm
100 mm
Summary
Learners will have improved their accuracy in drawing lines to the nearest millim
Notes on the Learner’s Book
Length (drawing) (p22): learners draw lines to the nearest mm, converting from
of length. Learners use careful drawing of straight lines to produce interesting an
patterns.
More activities
Spiral (individual)
Learners can make a spiral pattern by drawing a 4 mm line, rotating the ruler slig
then continuing by drawing a line 4 mm longer each time the ruler is rotated.
Games Book (ISBN 9781107667815)
The length competition game (p59) is a game for three players. Players compete
bers made by Opportunities for display!
numbers are 14 Display the instructions in ‘Look out for!’ as a poster
millimetres. for learners to refer to when they are drawing lines.
een the lengths of
ine and measure Opportunities for display!
lculation. Display the pictures and patterns made with the
lines. Ask learners to identify which line is which.
metre. Check up!
other units Ask learners to measure the length of an object, less
nd colourful than 20 cm, to the nearest mm. They should draw a line
of the same length then place the object next to their
line to check their accuracy in measuring and drawing.
If their line does not match the length of the object, ask
them to nd out whether their measuring, drawing, or
both, were not accurate.
ghtly and adding an 8 mm line to the end of the original line at an angle, and
to draw the most accurate lines, to the nearest millimetre.
Core activity 5.2: Drawing lines 43
Measuring len
Some of the units length is measured in are kilometres, me
There are 1000 metres (m) in 1 kilometre (km).
There are 100 centimetres (cm) in 1 metre (m).
There are 10 millimetres (mm) in 1 centimetre (cm).
There are 1000 millimetres (mm) in 1 metre (m).
You can use decimals to show part of a whole unit.
Examples:
1.69 km = 1690 m 2.85 m = 285 cm 1.23
0.78 m = 78 cm = 780 mm
A tape measure for measuring around curves. A ruler
© l Nata-Lia/Shutterstock; r SmileStudio/Shutterstock
Instructions on page 38
ngth poster
etres, centimetres and millimetres.
35 m = 123.5 cm 3.9 cm = 39 mm
for measuring straight lines.
Original Material © Cambridge University Press, 2014
Car insurance lengths resource sheet
Make of car Ciorda
Type of car Hatchback
Number of seats 5
Length of car 4.272 mm
Height of car 1.5 km
Colour Silver
Distance driven 30 000 cm
Average fuel consumption 7.9 litres to 100 km
Make of car Mutsui
Type of car Convertible
Number of seats 2
Length of car 397 km
Height of car 1.3 cm
Colour White
Distance driven 58 000 mm
Average fuel consumption 9.4 litres to 100 km
Make of car
Type of car
Number of seats
Length of car
Height of car
Colour
Distance driven
Average fuel consumption
Instructions on page 38 Original Material © Cambridge University Press, 2014
Measuring straight lines group resource sheet
A C
B
D
E
F
G Original Material © Cambridge University Press, 2014
Instructions on page 39
Measuring curved lines resource sheet
A
B
C
D
Instructions on page 39 Original Material © Cambridge University Press, 2014
48 Blank page
1B 6 Time (1)
Quick reference
Core activity 6.1 Timetables (Learner’s Book p24)
Learners tell the time, compare times and calculate time intervals on
24-hour digital clocks and analogue clocks.
Core activity 6.2 Calendars (Learner’s Book p26)
Learners use a calendar and their understanding of days, weeks,
months and years to calculate the solutions to problems.
Prior learning Objectives* – please note th
across the boo
Recognise and use the units for time
(seconds, minutes, hours, days, months 1B: Measure and pr
and years). 6Mt1 – Recognise and unde
Tell and compare the time using digital and
analogue clocks using the 24-hour clock. months, years, decad
Read timetables using the 24-hour clock. 6Mt2 – Tell the time using dig
Calculate time intervals in seconds, 6Mt3 – Compare times on di
minutes and hours using digital or 6Mt4 – Read and use timeta
analogue formats. 6Mt5 – Calculate time interva
Use a calendar to calculate time intervals 6Mt6 – Use a calendar to ca
in days and weeks (using knowledge of 6Mt7 – Calculate time interva
days in calendar months).
Calculate time intervals in months or 1A: Problem solving
years. 6Pt2 – Understand everyday
use these to perform
1A: Problem solving
6Ps1 – Explain why they cho
*for NRICH activities mapped to the C
Vocabulary
12-hour clock 24-hour clock analogue digital am pm second
minute hour day week fortnight month year decade century
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Telling the time and timetables Time intervals and calendars
Let’s investigate
Let’s investigate
Dylan has a recorded a song which he listens to You could work outthe e I have been You could use a calculatoro
over and over again. The song is three minutes and times that the songwi ill alive for 525 tto convert the time into
45 seconds long. When the song stops there is a start playing betweelln one 600 minutes. hours, days and then years.
20 second silent gap before the song starts again. o’clock and half past Use your knowledge of
one. Is this likely to be true? Why? people and the world to
He starts the song playing at one o’clock. give your reasoning.
Is the song playing at half past one or is it the silent gap?
1 These children are talking about what time they arrived at a party one afternoon. 1 Write these sentences and ll in the missing numbers and words. There are 100
I arrived at
I arrived I was at the years in a .
party from twenty 2:40 pm.
at quarter There are years in a decade. There are
to three this
past two. months in one year.
afternoon.
I got here There are days in one week. There are
at 15:45.
hours in one day.
JASON KYLE LINA MIA There are 60 in one hour. There are
60 seconds in one .
I got here at I was at the 2 (a) Copy and complete the table with equivalent times.
party from
12 minutes Days Hours Minutes Seconds
to three. 14:50.
NAOMI OMAR 1 1440 86 400
(a) Who arrived rst, second, third, fourth, fth and sixth? The clock 2 48
3 259 200
on the wall at the party showed this time: 11 12 1 4 345 600
(b) How long had each child been at the party? 2
10 3
9 5 7200
4
87 6 6 144 518 400
5 7 10 080 604 800
(b) Explain how you can use the table to nd out how many
seconds there are in one week.
24
26
hat listed objectives might only be partially covered within any given chapter but are covered fully
ok when taken as a whole
roblem solving (time)
erstand the units for measuring time: seconds, minutes, hours, days, weeks,
des and centuries; convert one unit of time into another.
gital and analogue clocks using the 24-hour clock system.
igital and analogue clocks (e.g. realise quarter to four is later than 3:40).
ables using the 24-hour clock system.
als using digital and analogue times.
alculate time intervals in days, weeks or months.
als in days, months or years.
g (Using techniques and skills in solving mathematical problems)
y systems of measurement in length, weight, capacity, temperature and time and
m simple calculations.
g (Using understanding and strategies in solving problems)
ose a particular method to perform a calculation and show working.
Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 1B 49
Core activity 6.1: Timetables
Resources: Analogue teaching clock with moveable hour and minute hands (alte
clock. Ordering Times photocopy master (p57). Practise and consolidation of tellin
(Camford MetraBus timetable photocopy master (p58)).
Tell learners that they are going to check that they can tell the time accurately on ana
digital clocks. Show them 23 minutes past 9 on an analogue teaching clock (this co
clock projected from the computer). Ask them to write down the time as a
24-hour digital time, both for if the time was in the morning and for if the time was i
afternoon. (Answer: 09:23 and 21:23.) Ask learners to check that they have written
times as other learners, and to say the time out loud. Repeat with 13 minutes to 5.
(Answer: 04:47 and 16:47.)
Display the time 23:51 on a 24-hour digital clock. Ask learners to describe to their partne
analogue clock would look like at this time.
Ask learners to reflect on how easy or hard they found these activities, and whether th
need further practise and support in consolidating reading times on analogue or digita
clocks.
Tell learners that it is important to understand how the different ways of describing the tim
compared. On the Ordering Times photocopy master, learners are asked to cut out the c
order them from 00:00 to 23:59. Learners should talk about and compare the times show
cards in pairs or small groups.
Remind learners that they can calculate time differences using a time line. Demons
find the difference between two times using a time line, e.g. finding the difference be
and 17:24.
Either count up to the next whole hour, count the hours in between, then add on extra
minutes.
Or, count up in hours from the earlier time and then add on the extra minutes.
50 Unit 1B 6 Time
(1)
LB: p24
ternatively use the Analogue clock photocopy master (CD-ROM)). Digital
ng the time resource sheet (CD-ROM). Local bus and/or train timetables
alogue and Vocabulary
ould be a
in the 12-hour clock: one day is divided into two twelve hour
the same periods.
24-hour clock: one day is divided into one twenty-four
er what an hour period.
analogue: a time shown with hands on a clock.
hey digital: a time shown on a clock with numerals.
al am: ante meridiem, a time between midnight and
midday.
mes can be
cards and pm: post meridiem, a time between midday and
wn on the midnight.
strate how to 41 mins 4 hours 24 mins 5 hours and 5 minutes
etween 12:19 12:19 13:00 17:00 17:24
a 5 hours 5 mins = 5 hours and 5 minutes
17:19 17:24
12:19
Both methods achieve the same solution. In this example the second method app
most efficient, but learners should be encouraged to choose a method that best su
in the calculation.
Ask learners to shuffle the cards from the Ordering Times sheet and deal them into
should find the difference between each pair of times. Comparing methods and solu
partner or small group.
Remind learners that timetables are types of two way tables that provide informat
(and sometimes also where) an event will occur. Timetables can have times writt
or 24-hour clock notation.
Preferably give learners a local bus or train timetable, otherwise use the Camford
timetable photocopy master. Tell them that this is a copy of a real bus timetable.
find some times and places on the timetable as they are called out, to help them
themselves with the timetable.
Ask learners to write questions that can be answered using the timetable to give to
Provide questions stems (as below) and encourage learners to think of their own t
that can be answered from the timetable.
Question stems:
How long does the bus take to travel from . . . to . . . ?
If you left . . . at . . . , what time should you arrive at . . . ?
If you arrived at . . . , how long would you have to wait for a bus to . . . ?
If you had to be at . . . by . . . , what time would you need to catch the bus at . . .
If the . . . bus from . . . was delayed by 35 minutes because of a traffic jam, what
reach . . . ?
Learners should answer their partner’s questions, and discuss their methods and so
partner.
pears the Look out for!
uits the times Learners who might have a stronger or weaker ability
to tell the time than their attainment in other areas of
o pairs. Learners mathematics would suggest. Ensure that those with a
utions with their weaker ability, or less experience, have an
opportunity to practise telling the time and talk about
ation about when the times on clocks and how the time is read. The
ten in 12-hour Practise and consolidation of telling the time
resource sheet (CD-ROM)’ should be used in a
d MetraBus situation where learners can manipulate real clocks to
Ask learners to show the times and talk to others about their methods
familiarise and solutions.
o another learner. Opportunities for display!
types of questions Display a copy of the timetable with some of the
learner’s questions so that a wider group of learners
? can try to answer each others’ questions.
t time would it
olutions with their
Core activity 6.1: Timetables 51
Summary
Learners will have consolidated telling the time.
They will have compared times and calculated time intervals on 24-hour digital clo
analogue clocks.
They will have read and used timetables using 24-hour clock.
Notes on the Learner’s Book
Telling the time and timetables (p24): learners order times and work out time interval
hours and minutes. They use a timetable to plan sporting events for a group of childre
More activities
Timetable (individual/small groups)
Learners draw a map of an imaginary small country, add bus and train routes and dra
inhabitants of the country and write their own questions to be solved by other learner
Clock race (groups)
You will need analogue clocks with moveable hour and minute hands (alternatively
In small groups, each learner can have their own analogue clock and race to move the
Games Book (ISBN 9781107667815)
Earlier or later times (p64) is a game for two players. Players predict whether a card
on analogue or 24-hour digital clocks. Learners calculate the time difference shown o
52 Unit 1B 6 Time
(1)
ocks and Check up!
ls in Ask learners to show on an analogue clock the times
en. that different buses arrive at different stops on the
Camford MetraBus timetable resource sheet or local
timetable.
aw up timetables for the buses and trains. Learners plan journeys for
rs using their timetables.
use the Analogue clock photocopy master (CD-ROM)).
e hands to a time specified by one of the learners.
will show an earlier or later time than a given time. Times are shown either
on two cards.
Blank page 53
Core activity 6.2: Calendars
Resources: Keeping healthy photocopy master (p59). Calendars for the current
Ask groups of learners to make a list of as much of the vocabulary and facts they know
in 10 minutes.
Pick out some of the vocabulary and facts the learners have listed that were not part o
the previous Core Activity. Ask the groups about the vocabulary and fact. Make a clas
the units used to measure time that the groups have included in their lists. Ask learner
know any other units for measuring time and add those to the list. Ensure the vocabu
to the right is included and discussed.
Ask learners to describe how they would calculate how many seconds are in one hou
many hours there are in a week. Show the learner how you would make jottings to wo
two step calculations. Ask learners if any of them would use different methods or jot
ask two or three learners to show how they would find the solutions.
Show learners the Keeping healthy photocopy master. Tell them that ‘Tia’ has made a H
Living poster and ask them to read the information on the poster. Ask learners to work in
solve some of the following problems, learners should discuss and choose methods:
How much time should be spent brushing teeth in one week?
Approximately how many times does a child’s heart beat in one hour?
How many hours should you brush your teeth for in the month of June?
Approximately how many days should a child sleep for in one year?
Show the learners calendars for the current year. Ask them to find out the day of the
different dates and other information from the calendar to help them become familiar
e.g:
W hat day of the week is 2nd March?
H ow many Wednesdays are there in August?
W hat is the date of the 3rd Thursday in December?
54 Unit 1B 6 Time
(1)