Table square
× 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100
Instructions on page 132 Original Material © Cambridge University Press, 2014
2A 15 Multiplication and division
Quick reference
Core activity 15.1: Divisibility rules (Learner’s Book p)
Learners extend their understanding of multiples to look at tests of
divisibility for 2, 4, 5, 10, 25 and 100.
Core activity 15.2: Multiplication (Learner’s Book p)
Learners become increasingly prof icient with calculation, estimating first
and then choosing an appropriate, efficient calculation for multiplication.
Core activity 15.3: Division (2) (Learner’s Book p)
Learners become increasingly proficient with calculation, estimating rst and th
Prior learning Objectives* – please note that listed objectives
taken as a whole
This chapter builds on
previous stages where 2A: Numbers and the number sy
learners have worked with 6Nn2 – Know what each digit represents in
multiples and developed 6Nn4 – Multiply and divide any whole numb
written methods for
multiplication and division. 2A: Calculation (Mental strategies
6Nc3 – Know and apply tests of divisibility
6Nc10 – Divide two-digit numbers by single-
2A: Calculation (Multiplication and
6Nc18 – Multiply two, three or four digit num
two-digit numbers.
6Nc19 – Divide three-digit numbers by singl
numbers by two-digit numbers (no
6Pt5 – 2A: Problem solving (Using techn
Estimate and approximate when ca
6Ps1 – 2A: Problem solving (Using unde
6Ps9 – Explain why they choose a particul
Make, test and refine hypotheses, e
Vocabulary
divisible divisibility
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
n (2)
Div isib ility ru les Mult iplicat ion Vocab ulary Div ision (2)
Let’s investigate Let’s investigate consecutive: next Let’s investigate Exa mp le:
Fin d the s ma lles t n um ber to each other. For ● Ch o os e a three- digit n um ber w ith a ll the d ig its the sa me. 6 66
th at is d iv isib le by 2 , 3, 4 a nd 5 . Ma ke lis ts of the Two con secutive n umbers mu ltiply example, 7 and 8 are ● A dd the d igits. 66 6
multiple s or s ha d emthe consecutive wh ole ● Div ide y o ur or ig ina l n um ber by y ou r a d ditio n a ns wer. 6 66 1 8
hem in o n a h u ndre d to gether to ma ke 65 0. 20 20 400 num be rs. ● Rec ord the re s ult. 18
W ha t are the two n um bers ? 30 30 900 37
sq uare. Rep ea t with differe nt s tar tin g nu mber s. W ha t d o y ou n o tice ?
Vocabulary Ma ke u p so me more p u zzle s like th is
an d swa p them w ith a par tner .
div isible : can be div ided w ithou t a remainder. For example, 1 4 is
div isible by 2. 1 Wor k o ut the se multip lications u sin g the grid meth od. 1 Estimate rst and then wor k o ut these calc ulatio ns:
(a) 164 5 (b) 327 8 (a) 104 4 ( b) 16 8 7 (c) 3 42 6
Nu mbe r Te st o f div is ibilit y (d) 42 3 9 (e) 4 72 8 (f) 30 5 5
2 T he u n its d ig it is d iv is ib le by 2 10 0 6 0 4 300 20 7
5 8
4 T he n u m ber m a de by th e la s t tw o d ig its is d iv is i b le by 4 2 Wor k o ut the se d iv ision calcu lation s.T hey all have a remainder.
(a) 351 6 ( b) 50 9 9 (c) 3 98 8
5 T he u n its d ig it is 5 or 0 2 (a) Estimate the answer to 86 7 (d) 37 5 4 (e) 4 36 7 (f) 29 6 3
(b) Calculate 86 7
1 0 T he u n its d ig it is 0
25 The la st tw o digits are 00, 25, 50 or 75 3 What is the m iss in g d ig it?
3 Wor k ou t the following calc ulation s: ? 7 9 33 3
1 0 0 T he la st tw o d ig its ar e 0 0 (a) 2 9 8 (b) 4 1 8 (c) (d)
2
59 6 2 09
6
43 4 Give the answers to these calcu lation s inclu ding a remainder.
1 Which of these numbers w ill d ivide exactly by 2? Ex plain (a) 254 9 ( b) 34 5 6 (c) 3 96 7
how y ou kn ow.
34 37 2 9 48 260 2 16 2 37 0 What do y ou no tice a bou t the ans wers to (a) a nd (c) and the answers to (b) and e the answers to these calcu lations inclu ding a remainder.
(d)?
2 Which of these numbers w ill d ivide exactly by 4? Ex plain 5 G(aiv) 964 5 ( b) 30 5 2 (c) 2 31 4
how y ou kn ow. Exp lain why this hap pened.
74 37 9 2 84 260 2 16 2 37 2 6 Find the mis sin g number?
3 Complete this three-digit n umber so that it is divis ib le by 4. 4 Calculate: ( b) 57 6 1 (c) 4 8 56 ? 5 22
(a) 32 8 3 (e) 4 7 34 (f) 36 54
2 ? ? a number divisible by 4. (d) 24 92 7 How many groups of e igh t can be made from 100 ?
8 (a) Divide 1 12 by 7. (b) Divide 7 into 22 4. (c) Share 20 7 between 9 .
62 64
60
hen choosing an appropriate, efficient calculation for division.
might only be partially covered within any given chapter but are covered fully across the book when
ystem
n whole numbers up to a million (part).
ber from 1 to 10 000 by 10, 100 or 1000.
s)
by 2, 4, 5, 10, 25 and 100.
-digit numbers, including leaving a remainder.
d division)
mbers (including money) by a single digit number and two- or three-digit numbers by
le-digit numbers, including those leaving a remainder and divide three-digit
remainder) including sums of money.
niques and skills in solving mathematical problems)
alculating e.g. use rounding and check working.
erstanding and strategies in solving problems)
lar method to perform a calculation and show working.
explain ad justify methods, reasoning, strategies, results or conclusions orally.
*for NRICH activities mapped to the Cambridge Primary objectives,
please visit www.cie.org.uk/cambridgeprimarymaths
Unit 2A 137
Core activity 15.1: Divisibility rules
Resources: Activity sheet Table patterns photocopy master (p146).
“If I am counting in tens from zero, will I say 146? How do you know?”
(Answer: no, because the units digit must be zero and in 146 it is 6.)
Explain that we are going to build up and display a set of divisibility rules.
“How can we test whether a number is divisible by 100?”
(Answer: the last two digits are 00.)
Display this rule.
Work in pairs to investigate the patterns made by the units digits of the 2, 3, 4 and 5 time
using the activity sheet Table patterns. For each table list the units digits in order in the b
they start to repeat. To help learners do this they could cross the units digits on the circle
them in order.
Review the learners’ results to arrive at these conclusions:
multiples of 2 end in 0, 2, 4, 6 or 8
multiples of 3 can end in any digit
multiples of 4 end in 0, 2, 4, 6 or 8
multiples of 5 end in 5 or 0.
Say, “We can use these ideas to support us in nding divisibility rules. All numbers tha
2, 4, 6 or 8 are divisible by 2 (they are even numbers) and all numbers that end in
divisible by 5.” Add these rules to the display.
Continue by asking which of these numbers will divide exactly by 4:
134 (×) 204 ( ) 154 (×) 124 ( ) 244 ( ) 214 (×)
“What can you say about the last two digits of the multiples of 4?”
(Answer: they make a number that is divisible by 4.)
e.g. 134; 34 is not divisible by 4 so neither is 134. 124;
24 is divisible by 4 so 124 is as well.
Add the rule to the display.
138 Unit 2A 15 Multiplication and division (2)
LB: p60
es table Vocabulary
boxes until
e and join divisible: can be divided without a remainder.
Example: 14 is divisible by 2.
at end in 0,
n 0 or 5 are number Test of divisibility
2 The units digit is divisible by 2
4 The number made by the last two digits is
divisible by 4
5 The units digit is 5 or 0
10 The units digit is 0
25 The last two digits are 00, 25, 50 or 75
100 The last two digits are 00
Give learners examples of even numbers that are not
multiples of 4, such as 6 and 22. Learners could
investigate the pattern of even numbers that are also
multiples of 4. Share the generalisation: All multiples
of 4 are even, but not all even numbers are multiples
of 4.
Opportunities for display!
Display the rules of divisibility with examples.
Which of these numbers will divide exactly by 25? )
125 ( ) 155 (×) 175 ( ) 250 ( ) 235 (×) 400 (
What can you say about the last two digits of the multiples of 25?
(Answer: they are 00, 25, 50 or 75.)
Add the rule to the display.
Summary
Learners use rules to test for divisibility.
Learners relate this work to multiples so they can say, for example, 64 is a mu
2 AND 64 is divisible by 2.
Notes on the Learner’s Book
Divisibility rules (p60): the investigation challenges learners to nd a number tha
divisible by 2, 3, 4 and 5. Learners may realise that this number is a multiple of 2
and 5 and relates to the number orchestra activity met earlier in the course.
The rules of divisibility are given as a reference and then learners work through
More activities
Make a poster (individual)
Design a poster to show the divisibility rules. Extend to nd other rules, for exam
ultiple of Check up!
at is “E xplain the divisibility rules for 2 and 4.”
2, 3, 4 “Are these statements true or false? Explain how you
the examples.
know.
All numbers that are divisible by 2 are also divisible
by 4.
All numbers that are divisible by 4 are also divisible
by 2.”
mple a test of divisibility for 3 and 8.
Core activity 15.1: Divisibility rules 139
Core activity 15.2: Multiplication
Resources: Activity sheet Find the error photocopy master (p147). (Optional: 0–9
Ask learners to work in pairs using the Find the error photocopy master. They should
what error has been made and any useful ways to avoid making similar errors.
Review the work done:
1. error in addition – added 2000 instead of 2400
2. addition error – failed to add the ‘carry 5’ in the hundreds column
3. 300 × 3 = 900, not 90
4. place value error – has worked out 22 × 1 instead 22 × 10.
Ask how these errors might be avoided. Take answers and discuss.
Depending on the responses learners give, decide how much or little of the foll
needs covering.
Write on the board the example: 6435 × 6
Tell learners that they should estimate before calculating: 6435
is between 6000 and 7000
6000 × 6 = 36 000
7000 × 6 = 42 000
so the answer must lie between 36 000 and 42 000
Talk through the various methods the learners could use to calculate the answer exac
learners for the advantages and disadvantages of using each method.
Grid method
6435 × 6 30 5
× 6000 400 180 30
6 36000 2400
3600 + 2400 + 180 + 30 = 38610
140 Unit 2A 15 Multiplication and division (2)
LB: p62
9 spinner (CD-ROM).)
d discuss
Look out for!
Learners who make errors when doing calculations of
the type 300 × 3 or 20 × 20. Revise multiplying
multiples of 10 and 100 by single digits and other
multiples of 10 remembering to estimate the answer
first.
lowing
Encourage learners to estimate before calculating.
Learners should use the method that they feel
comfortable with. Do not encourage the use of a
compact method before it is understood.
ctly. Ask
Expanded method Compact method
6435
6× 6435
6×
30 6 ×
180 6 × 38610
2400 6 ×
2 23
36000 6 ×
38610
Ask learners to choose a method discussed to work out 6848 × 7. Remind them t
advantages of that method are.
Extend to long multiplication by considering the example 435 × 16. Talk learner
435 × 16
× 400 30 5
10 4000 300 50
6 2400 180 30
4350 + 2610 = 6960
435
16×
4350
2610
6960
Ask learners to choose a method discussed to work out 363 × 39. Again, they sh
advantages of that method are.
to estimate first! Ask them why they chose their method and what the
rs through the different methods.
hould estimate first. Ask them why they chose their method and what the
Core activity 15.2: Multiplication 141
Summary
Learners become increasingly prof icient with calculation, estimating first and then c
appropriate, efficient calculation strategy.
Notes on the Learner’s Book
Multiplication (p62): questions 1 to 4 are practice calculations with different method
multiplication. Question 5 requires some thought, hopefully learners will quickly not
units digit of one of the numbers must be zero, then there are few possible calculation
Question 6 revises the use of the word product, question 7 is an easy calculation if le
multiply 5 by 6 rst and question 8 is easy to solve by division despite the multiplica
other questions require more thought and questions 10 and 13 may take some time.
Teachers may ask learners to work in groups to try different possibilities.
More activities
Closest to 2500 (pairs)
You will need 0–9 spinner (CD-ROM).
Players spin the spinner four times and place the digits in a grid.
×
Each player works out their answer. The player closest to 2500 wins the round.
142 Unit 2A 15 Multiplication and division (2)
choosing an Check up!
“W hat calculation strategy would you use for these
ds of
tice that the calculations?”
ons to try. 24 × 10 24 × 17 32 × 6
earners
ation sign. The “Explain your method.”
“Identify the error in this calculation.”
2013
7×
14791
2
Blank page 143
Core activity 15.3: Division
(2)
Resources: Museum poster photocopy master (p148). (Optional: a set of 0–9 digit
Display the information from the Museum poster.
Ask learners to work with a partner to decide which speech bubble they agree with.
Allow time then discuss findings. (Answer: 670 (4020 ÷ 6))
Discuss how the other answers may have been obtained:
574 (4020 ÷ 7 then rounded to the nearest whole number)
67 (omission of zero in answer)
70 (ignore one zero and work out 420 ÷ 6)
700 (confuse zeros: 420 ÷ 6, but then insert zero in answer)
Ask learners how they would calculate 196 ÷ 6 and discuss different strategies:
Repeated subtraction method A more compact method:
6 196 6 × 6 196
–60 –180
136 16
–12
–60 6 ×
6 × 4 6 ×
76
–60
16 6 ×
–12
6 ×
4
Answer: 32 remainder 4 Answer: 32 remainder 4
Learners should be encouraged to move towards a more compact method. Ask them
out 259 ÷ 4 using the more compact method.
144 Unit 2A 15 Multiplication and division (2)
LB: p64
t cards (CD-ROM) with 0 and 1 removed.)
Look out for!
Learners who fail to deal correctly with zeros. It
can best be avoided by estimating the answer
before calculating.
Look out for!
Learners that do not feel comfortable with the compact
method yet. Let them practise with the repeated
subtraction method.
to work
Summary
Learners become increasingly prof i cient with calculation, estimating first, then
appropriate, efficient calculation for division.
Notes on the Learner’s Book
Division (2) (p64): learners practise with a variety of questions; some with exac
others with a remainder. Questions 7 and 8 use the vocabulary: share, group and
More activities
No remainder challenge
(pairs)
You will need a set of 0–9 digit cards (CD-ROM) with 0 and 1 removed.
Players take turns to pick three cards at random. Arrange them to make this calcu
÷
Score three points if there is no remainder, score two points if the remainder is a
first player to reach ten points wins the game.
Games Book (ISBN 9781107667815)
Division line (p36) is a game for two players. It focuses on division where the an
choosing an Check up!
ct answers and “Divide 405 by 5.”
divide. “What is the most efficient way to divide 256 by 8?”
ulation and work out the answer.
an even number and score one point if the remainder is an odd number. The
nswer is not exact and must, in this case, be treated as a decimal.
Core activity 15.3: Division 145
(2)
Table pa
2× table units digit
9 0
1
8
2
73
64
5
4× table 0 units digit 5× table
91
82
7 3
4
6
5
Instructions on page 138
atterns units digit
3× table 1
0 2
9
8
7 3
6 4
5
e 0
9 1
8
2
7
units digit
6
3
4
5
Original Material © Cambridge University Press, 2014
Find the error –
multiplication
1. 6435 × 6
× 6000 400 30 5
6 36000 2400 180 30
= 38210
2. 1984
7×
13388
6 52
3. 324 × 23
× 300 20 4
20 6000 400 80
12
3 90 60
6480 + 162 = 6642
4. 22
12 ×
44
22
66
Instructions on page 140 Original Material © Cambridge University Press, 2014
MUSEUM P
Average attendance
670 people a day
Average attendance CITY MUSEU
67 people a day (closed on Mond
Visitors this week
Average
70 peo
Instructions on page 144
POSTER
Average attendance
574 people a day
UM
day)
k: 4020
Average attendance
700 people a day
e attendance
ople a day
Original Material © Cambridge University Press, 2014
2A 16 Special numbers
Quick reference
Core activity 16.1: Special numbers (Learner’s Book p)
Learners have an opportunity to revise and consolidate work on different types o
prime. Reference is also made to other types of number, for example, square num
Prior learning Objectives* – please note that listed objectives
taken as a whole
This chapter builds on work
done earlier in this stage. All 2A: Numbers and the number sy
the objectives have previously 6Nn15 – Recognise and extend number seq
been covered. 6Nn17 – Recognise odd and even numbers
6Nn18 Make general statements about su
6Nn19 – Recognise prime numbers up to 20
2A: Problem solving (Using unde
6Ps3 – Use logical reasoning to explore an
6Ps9 – Make, test and re ne hypotheses, e
*for NRICH activities mapped to the Cambridge Primary o
Vocabulary
No new vocabulary.
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Sp ecial nu mb ers
Let’s investigate
Plac e th e n um bers 1 , 2, 3, 4 , 5, 6 , 7, 8 an d 9 in
th e s q uares s o th e su m of the three n um bers in
eeaacc hh rrooww aannd c olum n is a p rime n um ber .
of number including odd, even, multiple and Ma e a lis t of
mbers first met in stage 5. th e kpr ime nu mber s
to 2 0.
1 I dentify the following numbers. (b) The number is less tha n 8 0. It is
(a) The number is even. It is a multiple of 5.
a multiple of 4.
It is a factor of 2 4. The sum of the d ig its is 9 .
It is between 10 an d 2 0.
(c) The number is prime. It is o dd. It is
less tha n 5 0. (d) The number ha s 9 factors.
It has two d ig its which are It is between 1 0 an d 99.
sa m e .
The s um of the digits is 9 . b oth the
It is even.
It is a s quare number.
2 Ex plain w hether these s tatements are true or false. Ex plain y our answer.
(a) Every multiple of 5 en ds in 5.
(b) If y ou dou ble an od d number the answer is alway s even.
(c) When y ou halve an even number the answer is alway s od d.
(d) All pr ime numbers are odd .
(e) A multip le of 4 can never end in 3.
(f) All numbers that end in 4 are multip les of 4.
(g) When y ou halve a number ending in 8 the answer will alway s end in 4.
65
s might only be partially covered within any given chapter but are covered fully across the book when
ystem
quences.
s and multiples of 5, 10, 25, 50 and 100 up to 1000.
ums, differences and multiples of odd ad even numbers.
0 and nd all prime numbers less than 100.
erstanding and strategies in solving problems)
nd solve number problems and puzzles.
explain ad justify methods, reasoning, strategies, results or conclusions orally.
objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 2A 149
Core activity 16.1: Special numbers
Resources: (0–9 digit cards photocopy master (CD-ROM), or 0–9 spinners (CD-R
Display five number sequences and ask learners to work with a partner to:
identify the sequences by giving the first term in the sequence together with the r
generate subsequent terms
give the next two terms.
1, 4, 9, 16, 25 . . .
(First term 1. Rule: next square number. Next terms 36, 49.)
75, 100, 125, 150, 175 . . .
(First term 75. Rule: next multiple of 25. Next terms 200, 225.)
1000, 900, 800, 700, 600 . . .
(First term 1000. Rule: multiples of 100 in descending order. Next terms 500
2, 3, 5, 7, 11 . . .
(First term 2. Rule: next prime number. Next terms 13, 17.)
650, 600, 550, 500, 450 . . .
(First term 650. Rule: multiples of 50 in descending order. Next terms 400, 3
Review the work done.
Play the game, ‘Play your cards right’, with the learners, using it as an opportunity to
definitions of words: odd, even, prime, square, multiple, factor and deal with any
misconceptions. The game is played as follows:
Teacher has a set of digit cards 0 to 9 or a spinner showing the digits. Randomly
display five different digits, for example 3, 6, 8, 5 and 1. Set tasks and get learner
answers so that the teacher can check results. Example tasks:
make a 3-digit number that is the highest possible multiple of two (Answer: 856)
make a number between 10 and 20 that is prime (Answer: 13)
make the largest 4-digit number that is odd. (Answer: 8653)
“Discuss this statement with a partner:”
Amir says, ‘I added three odd numbers and my answer was 20
150 Unit 2A 16 Special numbers
LB: p65
ROM). (Optional: Number detective photocopy master (CD-ROM).)
rule to
0, 400.)
350.) Look out for!
o revise the Learners who confuse the meanings of multiple
ly generate and and factor. Remind them that factors are smaller
rs display their than or equal to the number and that multiples are
the times table of the number.
Learners who believe that 1 is a prime number.
Remind them that prime numbers have exactly two
different factors, themselves and one. 1 does not
have two different factors.
Learners who believe that all prime numbers
are even. Ask them if, say, 3 is a prime number.
(Answer: yes.) Is 3 even? (Answer: no.)
0.’
Allow thinking time, then ask:
“Is Amir correct?” (Answer: no.)
“Explain how you know?” (Answer: odd + odd = even, then even + odd = od
Ask for learners responses, write them down and re-draft until you have a model
Summary
Learners understand the different types of number including odd/even, multip
They identify, describe and continue sequences.
They explain reasoning using appropriate mathematical vocabulary.
Notes on the Learner’s Book
Special numbers (p65): in question 1, learners are given a set of clues to identify
vocabulary used in the unit.
Question 2 gives learners an opportunity to justify statements. Teachers may wis
statement with a partner before revising their ideas to give a precise written expl
More activities
Multiple grid (pairs, groups or the whole class)
You will need 0–9 digit cards or 0–9 spinner (CD-ROM).
Each player draws a grid.
factor
factor total
Spin the spinner four times. After each spin players must place the number in on
boxes. When all four boxes have been filled it produces four 2-digit numbers (tw
two reading down). Learners find the largest factor of each 2-digit number that i
than 10. The factors are added to give the score. The highest score wins the roun
‘Show me’ activities of this type provide a quick and
easy mode of assessment.
dd and 20 is even.)
l answer.
ple/factor, square and prime. Check up!
y a number. The question revises the “F ind the factors of 12. Find
sh to suggest that learners discuss each
lanation. two multiples of 12. Give
me a definition of the words
multiple and factor.”
“What is the smallest prime
number? How do you know?”
Example: 45 scores 9 (45 is a multiple of 9)
459 32 scores 8 (32 is a multiple of 8)
328 43 scores 1 (43 is a prime number)
1 4 22 52 scores 4 (52 is a multiple of 4)
Total score, 22.
ne of the un-shaded
wo reading across and
is less
nd.
Core activity 16.1: Special numbers 151
Number detective (groups of four)
You will need the Number detective activity sheets (CD-ROM).
Groups work together to solve number puzzles (full instructions can be found with th
Games Book (ISBN 9781107667815)
Place the numbers in the square (p36) is a game for teams of two to four players. It r
double/halve and, < and >.
152 Unit 2A 16 Special numbers
he activity sheet on the CD-ROM).
revises number properties such as multiple, factor, square, prime, odd/ even,
2B 17 Mass and capacity
Quick reference
Core activity 17.1: Measuring mass and capacity (1) (Learner’s Book p
Learners select and use standard metric units of measure for mass and capa
between kg and g, and l and ml, using decimals to two and three places. They
equipment for measuring mass and capacity. They estimate, measure, and calcu
to the nearest millimetre.
Core activity 17.2: Measuring mass and capacity (2)
Learners interpret readings on a variety of equipment for measuring mass and ca
They estimate, measure, and calculate the difference between lengths to the near
Prior learning Objectives* – please
fully acr
• Read, choose, use and record standard units to
2B: Measure (L
estimate and measure length, mass and 6Ml1 – Select and use
6Ml2 – Convert betwee
capacity to a suitable degree of accuracy.
• Convert larger to smaller metric (units, decimals to three places,
6Ml3 – Interpret reading
to one place) e.g. 2.6 kg to 2600 g. 6Ml4 Draw and meas
• Order measurements in mixed units.
• Round measurements to the nearest whole 2B: Problem so
unit. 6Pt2 – Understand eve
• Interpret a reading that lies between two un-
numbered divisions on a scale. and use these to
• Compare readings on different scales. 6Pt5 – Estimate and ap
2B: Problem so
6Ps4 – Use ordered list
*for NRICH activities mapped t
Vocabulary
capacity • liquid volume • litre • millilitre • mass • gram • kilogram
Cambridge Primary Mathematics 6 © Cambridge University Press 2014
Me asu re
p66) Mass and capacity Vocab ulary
acity. They convert measurements
y interpret readings on a variety of Let’s investigate capacity : the amoun t
ulate the difference between lengths O ne litre of p etr ol weig hs a ppr o xima tely 7 00 g. acontainerca n ho ld.
liq uid v olume: the
apacity. T he m as s of my car was 1 2 2 8 kg w he n I started my s pac e ta ken u p by a
rest millimetre. jour ney . At the e n d of th e jo ur ney it wa s 1 2 1 4. 7 kg.
liq uid .
If I did n o t c ha n ge the m as s o f the car in a ny way ,
exc ep t us in g the pe tro l, h o w ma ny litres of petr ol ha d e:a un itof ca pa city
I use d ? litr
or liq u id vo lume.
millilitre: a un it
of capacity or liq uid
volume, one
tho usan dth of a litre.
mass: q uantity of matter in
an o bject.
gram: a un it of mass.
kilogram: a unit of mass,
one th ou sand grams.
Loo k at the scales on the meas urin g eq uipment on the page op posite. Match each
ingredient to the equ ipment sh owing the same amoun t. Write the number of the
ingredient an d the letter of the equ ipmen t.
123
1.3 kg 850 ml 950 g
66
note that listed objectives might only be partially covered within any given chapter but are covered
ross the book when taken as a whole
Length, mass and capacity)
standard units of measure. Read and write to two and three decimal places.
en 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.
gs on different scales, on a range of measuring instruments.
sure lines to the nearest centimetre and millimetre.
olving (Using techniques and skills in solving mathematical problems)
eryday systems of measurement in length, weight, capacity, temperature and time
o perform simple calculations.
pproximate when calculating, e.g. use rounding, and check working.
olving (Using understanding and strategies in solving problems)
ts or tables to help solve problems systematically.
o the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths
Unit 2B 153
Core activity 17.1: Measuring mass and capacity (1)
Resources: Measuring mass poster photocopy master (p158). Measuring capacity
sheet photocopy master (p160). Selection of equipment for measuring mass and ca
Display the Measuring mass poster and Measuring capacity poster and ask learners to sh
experiences they have had of measuring mass and capacity, including their learning in
Encourage the learners to refer to the posters to support their learning throughout the sess
learners that during this session they will be converting between units of measure, increa
accuracy in reading different scales of measurement and solving problems involving mea
Give pairs of learners the Reading scales resource sheet. Ask them to discuss, and the
some ideas with the class about, what each of the items of measuring equipment on th
might be used to measure.
Demonstrate how the measurement shown on the first measuring jug can be read by c
between the labelled measurements in different amounts to find the interval for the u
measurements. Try counting in 1’s, 5’s and 25’s, before finding that the jug is marked
intervals. Comment that it would be quicker to identify the marked label interval then
number of unlabelled marks to find the unlabelled intervals. Demonstrate this
by showing that the labelled interval is 100 ml, there are 5 unlabelled intervals betwe
labelled marks, so the unlabelled intervals must by 100 ÷ 5 = 20 ml.
Learners should complete (a) to (c) on the Reading scales resource sheet, comparing m
solutions with a partner.
Give groups of learners a selection of real measuring equipment. Ask them to discuss th
and unlabelled intervals on each item of equipment. Ask learners to challenge each othe
different points on the measurement scale.
Ask learners to reflect on which scales were most difficult to read, the strategies they
reading a scale, and what advice they had given and received when working with the
learners during the activities. Tell them to write a set of instructions for successfully
scales. Learners should comment on other learners’ instructions to help them make th
and complete.
154 Unit 2B 17 Mass and capacity
LB: p66
y poster photocopy master (p159). Reading scales resource
apacity (e.g. measuring jug, weighing scales).
hare some Vocabulary
Stage 5.
sion. Tell capacity: the amount a container can hold.
asing their liquid volume: the space taken up by a liquid.
asuring. litre: a unit of capacity or liquid volume.
millilitre: a unit of capacity or liquid volume, one
en share thousandth of a litre.
he sheet mass: quantity of matter in an object.
gram: a unit of mass.
counting up kilogram: a unit of mass, one thousand grams.
unlabelled
d at 20 ml Opportunities for display!
n divide by the Display two or three copies of the mass and capacity
posters for learners to refer to during the chapter.
een the
methods and Look out for!
he labelled Learners whose division skills may slow them down
er to identify when trying to work out the values of the unlabelled
intervals. Allow them to use the trial and
y used for improvement method of counting in 1’s, then 2’s etc
other until they become more comfortable with measure
reading and surer with their division skills.
hem clearer
Summary
Learners will select and use standard metric units of measure for mass and ca
They will convert measurements between kg and g, and l and ml, using decim
They will interpret readings on a variety of equipment for measuring mass an
Notes on the Learner’s Book
Mass and capacity (p66): learners convert measurements to different units and id
that measurement. They change the amounts needed for a recipe and convert the
More activities
Different scales (whole class)
Practise counting in 2’s, 5’s, 10’s, 20’s, 25’s, and 100’s. Ask learners to identify s
Fill the bath (groups)
Challenge learners to work out how many 5 ml teaspoons of water would be nee
they were able to pour in one teaspoon per second.
Games Book (ISBN 9781107667815)
The ‘four in a row’ scale game (p69) is a game for two players. Players generate
player who makes four marks in a row is the winner.
apacity. Check up!
mals to two and three places.
nd capacity. Give learners a small amount of dry
material and a small amount of water.
dentify scales that show Ask them to choose equipment to
e amounts to different units. measure the amounts and write each
amount in two ways, using different units.
scales available in the classroom that use some of these intervals.
eded to fill a bathtub with a capacity of 150 litres, and how long would it take it
numbers with two decimal places and mark them on a kilogram scale. The
Core activity 17.1: Measuring mass and capacity (1) 155
Core activity 17.2: Measuring mass and capacity (2)
Resources: Modelling dough instructions photocopy master (p161). Weighing s
sheet photocopy master (p163). Selection of equipment for measuring mass and ca
flour. Water. Empty yoghurt pots (larger than 240 ml). Cream of Tartar. Rulers.
Show learners the Modelling dough instructions sheet. Ask learners to convert the
measurement in kilograms and litres to grams and millilitres. Give learners the Weigh
scales resource sheet. Explain that each section of the sheet shows the scales that a gro
children are using to weigh the flour for a portion of modelling dough. Ask learners to
complete (a) to (c) on the sheet.
Repeat the activity with the Measuring jug resource sheet.
Ask groups of learners to select and use equipment to measure out the correct amount o
water for the recipe (but not to mix them yet).
Tell learners that in recipes from the USA both liquid and dry ingredients are often m
using a standard measuring cup. This standard cup measures 0.24 litres of liquid, or
0.15 kg of flour (depending on the type of flour).
Give each group an empty yoghurt pot and ask them to mark it with the US cup measure
The groups should choose and explain their method for creating the measuring cup as a
as possible. Ask the groups to use the measuring cup they have made to measure as cl
as possible the amounts of flour and water needed for the modelling dough recipe. They
compare these measurements to the measurements made with the metric equipment ea
Learners should make a portion of the modelling dough using the instructions 1 to 5. Th
divide the dough equally, using the scales to measure, between the members of their gr
Challenge the learners to roll a sausage shape without measuring, estimating as close a
to 20 cm in length. The learners should then measure the length of their ‘sausage’ and t
group the difference between their measurement and 20 cm in millimetres. The learner w
smallest difference wins the challenge.
156 Unit 2B 17 Mass and capacity
scales resource sheet photocopy master (p162). Measuring jug resource
apacity (e.g. measuring jug, weighing scales) (p163). Mixing bowl. Plain
hing Opportunities for display!
oup of
o Display two or three sets of Modelling dough
instructions sheet alongside the mass and capacity
posters for learners to refer to during the chapter.
of flour and Opportunities for display!
Display photographs of the dough ‘sausages’
measured
approximately next to rulers with the measurement given in
mm and cm.
ement.
accurately
losely
y should
arlier.
hey should
roup.
as possible
tell the
with the
Ask learners to make their ‘sausage’ back into a ball of dough. They should take pa
and make a model out of it. Explain that this model will be baked and can be kept la
model is made learners should weigh their model and record the mass.
After the session the models should be baked by an adult following the instructio
sheet.
Once the models are baked and cooled they can be given back to the learners to
learners to discuss why their models are lighter after baking. As necessary, expla
have been dried in the oven so some of the water from the recipe has been remov
model in the baking process. Ask learners to nd a way to nd out how much wa
removed from their model and discuss as a class.
Learners may also like to paint their models.
Summary
Learners interpret readings on a variety of equipment for measuring mass and
They estimate, measure, and calculate the difference between lengths to the ne
art of their dough Look out for!
ater. Once the Learners who are unsure how to determine the
amount of water lost from the model during baking.
ons on the Direct them to compare the mass of the model
before and after baking, weighing out the same
reweigh. Ask amount of water and then measuring the water in
ain that the models ml.
ved from the
ater has been Opportunities for display!
Display the learners’ models. Ask learners to write
information about the weight of the model before and
after baking, and the amount of water removed by
baking.
d capacity.
earest millimetre.
Core activity 17.2: Measuring mass and capacity (2) 157
Measuring m
Some of the units mass is measured in are kilograms and g
Kilograms can be abbreviated to kg, e.g. 20 kilograms = 2
Grams can be abbreviated to g, e.g. 400 grams = 400 g
There are 1000 grams in 1 kilogram.
So, 8 kg = 8000 g and 2400 g = 2 kg 400 g
Use decimals to show part of a whole unit kilogram.
Examples:
1.6 kg = 1600 g 7420 g = 7.4
Measuring Mass
Balance scales Weigh
0
9 kg 1 kg
8 kg 2kg
7 kg 3kg
6 kg 4 kg
5 kg
Instructions on page 154
mass poster
grams.
20 kg
42 kg 0.295 kg = 295 g
hing scales
Spring balance
kg
0
1
2
3
4
5
Original Material © Cambridge University Press, 2014
Measuring ca
Some of the units capacity is measured in are litres and
Litres can be abbreviated to l, e.g. 20 litres = 20 l
Millilitres can be abbreviated to ml, e.g. 400 millilitres
There are 1000 millilitres in 1 litre.
So, 2400 ml = 2 l 400 ml and 8 l = 8000 ml
Use decimals to show part of a whole unit litre.
Examples:
1.6 l = 1600 ml 7420 ml
Measuring Capacity
Measuring jug Teasp
ml
1000
900
800
700
600
500
400
300
200
100
Instructions on page 154
apacity poster
d millilitres.
s = 400 ml
l = 7.42 l 0.259 l = 259 ml
poon Tablespoon
15 ml
Original Material © Cambridge University Press, 2014
Reading scales resource sheet
0
70 kg 10 kg
ml 60 kg 20 kg
500
50 kg 30 kg
400
40 kg
300
200
100
ml 0 kg
250 9.5 0.5
200 8.5 1.5
150 7.5 2.5
100
6.5 3.5
50 5.5 4.5
0
0g Ltr
800 200
2
600 400 1.9
1.8
For each scale identify: 1.7
1.6
1.5
1.4
1.3
1.12
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
(a) the interval between two labelled marks on the scale
(b) the interval between two unlabelled marks on the scale
(c) the mass or capacity shown on the scale, and the unit of measure used.
Instructions on page 154 Original Material © Cambridge University Press, 2014
Modelling dough
instructions
Ingredients
0.5 kg plain flour
0.25 kg salt
5 teaspoons cream of tartar
0.75 l water
Method
1. Pre-heat the oven to 160 ˚C.
2. Line two or three baking trays with baking parchment.
3. Mix the flour, salt and cream of tartar together.
4. Add the water, a little at a time, mixing with a spoon until the mixture
forms into a ball.
5. Knead the dough on a lightly floured surface until smooth.
6. Make models with the dough.
7. Place models onto the baking trays. Bake until slightly golden (models
will take between 15 minutes to 1 hour to bake depending on their size).
8. Allow models to cool.
9. Once cool, models can be painted and decorated.
Instructions on page 156 Original Material © Cambridge University Press, 2014
Weighing scales resource sheet
gm
0
50
100
150
200
250
300
350
400
450
500
0g
900 100
800 200
700 300
600 400
500
0 kg 9.5 0 kg 0.5
0.9 0.1
9 1
0.8 0.2 8.5 1.5
0.7 0.3 8 2
0.6 0.4
0.5 7.5 2.5
73
6.5 3.5
64
5.5 5 4.5
0 kg
1.2
1 0.2
0.8 0.4
0.6
For each group record:
(a) how much flour has been weighed in kilograms
(b) how much flour has been weighed in grams
(c) how much more flour is needed to make 0.5 kg
Instructions on page 156 Original Material © Cambridge University Press, 2014
Measuring jug resource sheet
ml ml
1000 500
900 450
800 400
700 350
600 300
500 250
400 200
300 150
200 100
100 50
Ltr Ltr
1 1.5
0.9
0.8 1
0.7
0.6 0.5
0.5
0.4
0.3
0.2
0.1
Ltr 2 Ltr 1.2
1.8 1.1
1.6
1.4 1
1.2 0.9
1 0.8
0.8 0.7
0.6
0.6 0.5
0.4
0.2 0.4
0.3
0.2
0.1
For each group record:
(a) how much water has been measured in litres
(b) how much water has been measured in millilitres
(c) how much more water is needed to make 0.75 l
Instructions on page 156 Original Material © Cambridge University Press, 2014