Post on 21-Jun-2018
2014 CurriculumPRIMARY
MATHS
Year 6Book 1 of 2
Resources and
teacher ideas for every objective
of the 2014 Curriculum
PM Year 6 Book 1 of 2.indd 1 26/11/2014 15:43:24
Primary Maths Prim-Ed Publishing www.prim-ed.com iii
FOREWORD
CONTENTS
Primary Maths is a photocopiable, six-level, year–specific series designed to address the Primary Framework National Curriculum for Mathematics objectives of:
• number •ratioandproportion • algebra • measurement • geometry • statistics.
Each book in the Primary Maths series includes: • atleastoneactivitypageforeachobjectivewhichcanbephotocopiedordisplayedonaninteractive
whiteboard • comprehensiveteachersnotestoaccompanyeachactivity • additionalteachersnotesonactivitiesandgames • assessmentchecklists • additionalphotocopiableresources • interactivewhiteboardresourcesavailabletodownload.
The Year 6 books in the Primary Maths series are: Primary Maths – Number, Ratio, Proportion and Algebra Primary Maths – Measurement, Geometry and Statistics Primary Maths – The big interactive book of understanding shape/measuring
Teachers notes:
How to use this book ............................................. iv–vSetting up a maths classroom ................................. viActivities and games .................................................. viiAssessment checklists ........................................ viii-xiAdditional resources ........................................ xii–xvii
Pupil activities with accompanying teachers notes:
Number and place value ................................. 2–9Reading, writing, ordering and comparing numbers ................................................ 2–5Rounding .................................................................... 6–7Negative numbers ................................................... 8–9
Addition, subtraction, multiplication and division .................................................. 10–39
Long multiplication ............................................. 10–11Long and short division ..................................... 12–17Mental calculations ........................................... 18–19Factors and multiples ........................................ 20–25Prime numbers ..................................................... 26–27Order of operations ............................................ 28–29Multi-step problems .......................................... 30–37Estimation ............................................................. 38–39
Fractions (including decimals and percentages .................................................. 40–69
Simplifying fractions ......................................... 40–41
Comparing and ordering fractions ................ 42–43
Adding fractions ................................................. 44–45
Subtracting fractions ........................................ 46–47
Multiplying fractions ......................................... 48–49
Dividing fractions ............................................... 50–51
Fraction and decimal equivalents .................. 52–53
Place value in decimals .................................... 54–57
Multiplying decimals ......................................... 58–59
Dividing decimals ............................................... 60–61
Rounding decimals ............................................ 62–65
Equivalent fractions, decimals and percentages ................................................. 66–69
Ratio and proportion ................................... 70–85Quantity problem-solving ................................ 70–71
Percentage problem-solving ........................... 72–79
Scaling and similar shapes .............................. 80–81
Unequal sharing and grouping problems .... 82–85
Algebra ....................................................... 86–105Simple formulae ................................................. 86–89
Number sequences ............................................. 90–99
Missing number problems .......................... 100–101
Equations with two variables .................... 102–105
iv www.prim-ed.com Prim-Ed Publishing Primary Maths
The Primary Maths series provides teachers with a number of varied and challenging activities. At least one activity, often more, is provided for each objective of the Primary National Curriculum for Mathematics.
Suggestions for using the activities in this book:
Objective:• Decide which curriculum objective you wish to address and choose the appropriate activity page(s).
Oral work and mental calculation starter:• Choose which oral and mental activities you will use, from the list provided, to introduce the lesson or sharpen
pupils’ skills.• Someoftheactivitieshaveaccompanyinginteractivewhiteboardactivitiestohelpintroducethelessonandcapture
pupils’ attention.• These activities should occupy the first 5–10 minutes of the lesson.
Main teaching activity:• Decide how much teacher input you will provide for the main activity and whether pupils will be working
individually, in pairs or as a group.• Depending upon the abilities of the pupils in your class, decide whether any additional activities will be needed, from
the list provided, or whether these can be used during subsequent lessons.• This activity should occupy approximately 30 minutes.
Plenary:• Decide what opportunities will be provided during the plenary session. Will pupils be given the opportunity to share
and explain work, compare strategies used or summarise the key facts they have learnt?• Think about how you can use the plenary session to assess pupils’ progress and therefore inform your future
planning.• The plenary should occupy the final 10 minutes of the lesson.
Pupil activity pages:The pupil activities follow a common format:
How to use this book
Title explanation
After initial discussion, some activities can be completed individually, and others in small groups or as a whole class.
The ‘Challenge’ activity can be completed by early finishers or those pupils requiring extension of the task. Pupils may need to complete the activity on the back of the worksheet or investigate an activity further by using concrete materials or creating their own ideas linked to the objective.
The objective provides the teacher with the focus of the activity. It is written in the form of a general objective.
An icon denotes the curriculum strand for each activity.
Number Ratio and Proportion Algebra Measurement Geometry Statistics
TEACHERS NOTES
NNumber
MMeasurement
GGeometry
RPRatio and Proprotion
AAlgebra
SStatistics
Primary Maths Prim-Ed Publishing www.prim-ed.com v
Assessment
AssessmentchecklistshavebeenincludedfortheYear6‘Number’,‘RatioandProportion’and‘Algebra’objectives.Seepages vii–xi. These can be used to assess each pupil’s understanding of the key objectives covered.
• Teaching notes for the strands have been included on page vii. These comprise background information and suggested activities and games.
• Extra teacher resources have been included on pages xii–xvii. These can be enlarged if necessary and used in appropriate activities or as display posters.
• Interactivewhiteboardactivitieshavebeenprovidedtohelpteachtheobjectives.Thesecanbedownloadedfromwww.prim-ed.com.
The objective tells the teacher which strand and objective from the Primary National Curriculum for Mathematics is being covered.
Oral work and mental calculation activities are suggested, for introducing the lesson or sharpening/developing oral and mental skills. The activities should occupy the first 5-10 minutes of the lesson.
Some activities have interactive whiteboard activities available to download. If an interactive activity is provided it is listed here.
The title of the main teaching activity is given. The photocopiable activity is on the page facing the teachers notes. The main activity should occupy approximately 30 minutes.
Answers to all activities are provided.
Suggest ions for addit iona l activities are provided. They can be completed during the lesson, or in subsequent lessons. They can be used to aid differentiation.
Teachers pages
Ateacherspageaccompanieseachpupilworksheet.Itprovidesthefollowinginformation:
How to use this book
Use the key to write the appropriate code next to each task the pupil completes.
A summary of the tasks pupils will complete.
TEACHERS NOTES
vi www.prim-ed.com Prim-Ed Publishing Primary Maths
TEACHERS NOTES
Setting up a mathematics classroom
By having the following materials and visual representations around them, pupils can better engage in mathematical learning.
• Allowroomtomovesopupilscaninvestigatethingsaround the room. Organise desks and floor space appropriately.
• Displaya‘Numbers’chartthatincludesthousands,ten thousands, hundred thousands and millions.
• Displayanumberlineatalevelwherepupilscanuseit.Includenegativenumbersonthenumberline.
• Display numbers, number words and a visualrepresentation of numbers.
• Displayaplacevaluechartwhichincludesfractions(tenths, hundredths and thousandths).
• Displaya100square.
• Ensureyouhaveagoodrangeofmathsgamesanduse them regularly.
• Providecalculators.
• Display‘timestables’charts.
• Haveananalogueanddigitalclockintheclassroom(12-hour and 24-hour).
• Displaypicturesoflabelled2-Dand3-Dshapes.
• Provideathermometer.
• Provide construction materials such as cardboardboxes, cylinders, paper, scissors and so on.
• Ensure you have adequate concrete materials toteach each strand (refer to page vii).
• Allowpupilsopportunitiestoinvestigateoutsidetheclassroom in the school environment.
• Display a chart showing equivalent fractions,decimals and percentages.
• Displayormakevariousgraphssuchaspictograms,bar charts, block graphs, Venn diagrams, Carroll diagrams, line graphs and pie charts.
• Display a class birthday chart which includes themonths of the year.
• Displayanduseacalendar.
• Display a poster showing equivalent metric andimperial measures.
• Have computer software related to mathematicsavailable for use on the classroom computer(s) or in the computer room.
• Displayapostershowingdifferentangles.
• Providearangeofmeasuringequipmentforlength,mass and capacity.
• Displaytheeightcompassdirections:N,S,E,W,NE,NW,SE,SW.
• Ensure you have a good selection of interactivemaths resources for use on a whiteboard (refer to www.prim-ed.com).
Primary Maths Prim-Ed Publishing www.prim-ed.com vii
TEACHERS NOTES
Counting and understanding number/ Knowing and using number facts
– Activities and games• Play‘Bingo’toconsolidatebasicfactsormatchequivalent
fractions, decimals and percentages etc. Vary by calling out the answer in some games and the number sentence or problem in others. Blank bingo cards are on page xvii.
• Divide theclass into teamsandselectonepupil fromeach team to stand at the board ready to write. Call out a number (e.g. 1089) or basic fact (e.g. 25 – 6, 7 x 9, double 12). The first pupil to write the correct answer wins a point for his/her team.
• GivedirectionsforpupilstotakeoutamountsofBase10blocks to add or subtract given decimal numbers with an unlike number of decimal places. Impress on pupils that the blocks have the value they give them – longs can be ones, tens, hundreds, tenths or hundredths. It may help understanding to use a counter as a decimal point. Recording of results is not important, development of understanding of concepts is the focus.
• Usecalculatorstogeneratelargenumbers;forexample,show a number on the calculator that is between 847 639and857639;768274and768374;900000and900003;420762and420027;549387and594387;600000and500000;999999and888888;7269486and 7 296 488.
• Boardthesenumberpatterns,thenhavepupilscontinuethe patterns.
7, 13, 19, , , , , , , , , ,
106, 212, 318, , , , , , , , , 2, 5, 11, 23, , , , , , , , ,
Pupils make patterns of their own to share with classmates.
• Estimationisanessentialskillandshouldbeusedpriorto any calculation.
– Have pupils estimate how many people can stand in their classroom—treat this as a record attempt. Pupils describe how this may be checked without filling the room.
– Estimate, then calculate, how many months, days and hours they have been alive.
– Estimate, then calculate, how many letters are used in a whole newspaper, library book and or/class reading book. Describe how they worked out the answer.
Materials required
• placevalueblocks• interconnectingcubes• placevaluemats(seepagesxiiandxiii)• calculators• fractioncharts(seepagexvi)• abacus• tablescharts(seepagexv)• 100schart(seepagexiv)• numberlines• bingocards(seepagexvii)
viii www.prim-ed.com Prim-Ed Publishing Primary Maths
AAssessment
Pupils’ names Read
and
writ
e nu
mbe
rs u
p to
10
000
000.
Ord
er a
nd c
ompa
re n
umbe
rs u
p to
10
000
000
.
Dete
rmin
e th
e va
lue
of e
ach
digi
t in
num
bers
up
to
10 0
00 0
00.
Roun
d w
hole
num
bers
.
Use
nega
tive
num
bers
in c
onte
xt.
Calc
ulat
e in
terv
als
acro
ss z
ero.
Solv
e nu
mbe
r pr
oble
ms
invo
lvin
g or
derin
g an
d co
mpa
ring
num
bers
.
Solv
e nu
mbe
r pr
oble
ms
invo
lvin
g ro
undi
ng
who
le n
umbe
rs.
Solv
e nu
mbe
r pr
oble
ms
invo
lvin
g ne
gativ
e nu
mbe
rs.
KeyD = DemonstratedNFO = Needs further
opportunity
YEAR 6 NUMBER AND PLACE VALUE – ASSESSMENT CHECKLIST
Primary Maths Prim-Ed Publishing www.prim-ed.com ix
AAssessment
Pupils’ names Usin
g lo
ng m
ultip
licat
ion
for
4-di
git
x 2-
digi
t nu
mbe
rs.
Use
long
div
isio
n fo
r 4-
digi
t ÷
2-di
git
num
bers
.
Inte
rpre
t di
visi
on r
emai
nder
s as
num
bers
and
fr
actio
ns.
Roun
d di
visi
on r
emai
nder
s.
Use
shor
t di
visi
on f
or 4
-dig
it ÷
2-di
git
num
bers
.
Perf
orm
men
tal c
alcu
latio
ns w
ith m
ixed
op
erat
ions
.
Iden
tify
com
mon
fac
tors
.
Iden
tify
com
mon
mul
tiple
s.
Iden
tify
prim
e nu
mbe
rs.
Use
know
ledg
e of
ord
er o
f op
erat
ions
to
carr
y ou
t ca
lcul
atio
ns.
Solv
e ad
ditio
n m
ulti-
step
pro
blem
s.
Solv
e su
btra
ctio
n m
ulti-
step
pro
blem
s.
Solv
e pr
oble
ms
invo
lvin
g +,
–, x
and
÷.
Use
estim
atio
n to
che
ck a
nsw
ers
to
calc
ulat
ions
.
KeyD = DemonstratedNFO = Needs further
opportunity
YEAR 6 ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION – ASSESSMENT CHECKLIST
x www.prim-ed.com Prim-Ed Publishing Primary Maths
AAssessment
Pupils’ names Use
com
mon
fac
tors
to
sim
plify
fra
ctio
ns.
Use
com
mon
mul
tiple
s to
exp
ress
fr
actio
ns.
Com
pare
and
ord
er f
ract
ions
.
Add
frac
tions
with
diff
eren
t de
nom
inat
ions
and
mix
ed n
umbe
rs.
Subt
ract
fra
ctio
ns w
ith d
iffer
ent
deno
min
atio
ns a
nd m
ixed
num
bers
.
Mul
tiply
sim
ple
pairs
of
prop
er f
ract
ions
.
Divi
de p
rope
r fr
actio
ns b
y w
hole
nu
mbe
rs.
Asso
ciat
e a
frac
tion
with
div
isio
n.
Calc
ulat
e de
cim
al f
ract
ion
equi
vale
nts
for
a si
mpl
e fr
actio
n.
Iden
tify
the
valu
e of
eac
h di
git
in
num
bers
giv
en t
o th
ree
deci
mal
pla
ces.
Mul
tiply
and
div
ide
num
bers
by
10, 1
00
and
1000
.
Mul
tiply
dec
imal
s to
tw
o pl
aces
by
who
le
num
bers
.
Use
writ
ten
divi
sion
met
hods
for
de
cim
als
up t
o tw
o pl
aces
.
Roun
d an
swer
s to
a r
equi
red
degr
ee o
f di
fficu
lty.
Know
equ
ival
ence
s be
twee
n fr
actio
ns,
deci
mal
s an
d pe
rcen
tage
s.
KeyD = DemonstratedNFO = Needs further opportunity
YEAR 6 FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) – ASSESSMENT CHECKLIST
Primary Maths Prim-Ed Publishing www.prim-ed.com xi
AAssessment
Pupils’ names Solv
e m
issi
ng v
alue
s pr
oble
ms
usin
g m
ultip
licat
ion
and
divi
sion
fac
ts.
Solv
e pe
rcen
tage
pro
blem
s an
d us
e pe
rcen
tage
s fo
r co
mpa
rison
.
Solv
e pr
oble
ms
invo
lvin
g si
mila
r sh
apes
and
sc
ale.
Solv
e pr
oble
ms
invo
lvin
g un
equa
l sha
ring
and
grou
ping
.
Use
sim
ple
form
ulae
.
Gene
rate
and
des
crib
e lin
ear
num
ber
sequ
ence
s.
Expr
ess
mis
sing
num
ber
prob
lem
s al
gebr
aica
lly.
Find
pai
rs o
f nu
mbe
rs t
hat
satis
fy a
n eq
uatio
n w
ith t
wo
unkn
owns
.
Enum
erat
e po
ssib
ilitie
s of
com
bina
tions
of
two
varia
bles
.
KeyD = DemonstratedNFO = Needs further
opportunity
YEAR 6 RATIO, PROPORTION AND ALGEBRA – ASSESSMENT CHECKLIST
xii www.prim-ed.com Prim-Ed Publishing Primary Maths
Place value mat
Tens millions Millions Hundred
thousandsTen
thousands Thousands Hundreds Tens Ones
TEACHER RESOURCES
Primary Maths Prim-Ed Publishing www.prim-ed.com xiii
TEACHER RESOURCES
Place value mat
Ten thousands
(10 000)
Thousands
(1000)
Hundreds
(100)
Tens
(10)
Ones
(1)•
Tenths
(1/10)
Hundredths
(1/100)
Thousandths
(1/1000)
Ten thousands
(10 000)
Thousands
(1000)
Hundreds
(100)
Tens
(10)
Ones
(1)•
Tenths
(1/10)
Hundredths
(1/100)
Thousandths
(1/1000)
xiv www.prim-ed.com Prim-Ed Publishing Primary Maths
100 chart
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
0–99 chart
TEACHER RESOURCES
Primary Maths Prim-Ed Publishing www.prim-ed.com xv
TEACHER RESOURCES
Basic multiplication facts
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
Basic multiplication facts
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
xvi www.prim-ed.com Prim-Ed Publishing Primary Maths
TEACHER RESOURCES
Equivalent fractions, decimals and percentages
Fraction Decimal Percentage
1 100%
0.5 50%
0.33 33 13 %
0.66 66 23 %
0.25 25%
0.75 75%
0.2 20%
0.4 40%
0.6 60%
Fraction Decimal Percentage
0.8 80%
0.125 12 12 %
0.375 37 12 %
0.1 10%
0.3 30%
0.7 70%
0.9 90%
0.01 1%
0.99 99%
Fraction chart
whole 11
half
third
quarter
sixth
eighth
twelfth
13
13
12
14
14
14
16
16
16
16
16
18
18
18
18
18
18
18
112
112
112
112
112
112
112
112
112
112
112
11
12132314
43
51
52
53
54
18
83
101
103
107
109
1001
10099
86 www.prim-ed.com Prim-Ed Publishing Primary mathematics
TEACHER INFORMATIONA
Algebra
Oral work and mental calculation
• Asaclass,workouttheruleforandcompletelargefunction machines.
• Introducetheuseofsymbolsanddiscusstheirmeaning;forexample,Theareaofarectangleislxb (length x breadth), the perimeter of a triangle is 3l (length x 3).
• Verballyworkoutproblemssuchasthenumberofmonths in a year using the symbols m (months) and y (years).
• Workoutandrecordaformulatoshowthecostof3sweets (s) at 5p each.
Interactive whiteboard activity
Interactive whiteboard activity available to support this copymaster. Visit www.prim-ed.com.
Main teaching activity
Find the formula (page 87)
Additional activities suitable for developing the objective
• Workoutperimetersusingformulas;forexample,
The perimeter of a square is 4l. Each side of the square is 5 cm, so what is the perimeter?
The perimeter of a rectangle is 2 x (l + b). What is the perimeter if l = 6 cm and b = 4 cm?
Answers
1. (a) (b)
(c) (d)
2. (a) 150n (b)y÷5 (c) 3x + 4 (d) y - 12 = 20 (y = 32) (e) £x + £15 = £45 (x = £30)
3. (a) 5n x 1.75p (b) 4n + 7 (c) l x b
Challenge: Teacher check
Rule: 3n Rule: n ÷ 2
5 15 2 1
6 18 4 2
7 21 6 3
8 24 8 4
9 27 10 5
Rule: n ÷ 9 Rule: n x 10, +2
81 9 1 12
72 8 2 22
63 7 3 32
54 6 4 42
45 5 5 52
ALGEBRA
Objective
• Usesimpleformulae.
Objective
Primary Maths Prim-Ed Publishing www.prim-ed.com 87
5n = £1.75 4n + 7 = 155n x 35p
FIND THE FORMULA
Expressesrelationshipsasaformula,usinglettersasasymbol.
Write some problems of your own and see if a friend can work out the algebraic sentence to solve it.
1. Work out the rule which will help you complete each table.
(a) (b) (c) (d)
2. Read the scenario and the problem. Write an algebraic sentence to represent the problem. If there is enough information, solve the problem.
(a)
(b)
(c)
(d)
(e)
3. Match the problem to the formula.
(a) 5 chocolate bars cost (b) 4 times a number (c) Area of a rectangle. £1.75. plus 7 equals 15.
Rule:
5 15
18
7 21
24
9
Rule:
2 1
2
6 3
4
10
Rule:
81 9
8
63
6
45 5
Rule:
1 12
22
3
4 42
5
Scenario Problem Algebraic sentence
Trucks have n wheels. How many wheels would 150 trucks have?
Mike has y sweets.He shares the sweets among 5 friends. How many sweets does each friend get?
Mary has x pencils.Her friend has three times that amount plus 4 more. How many pencils has her friend?
Jane had y CDs.She gave 12 of them to Chris. She then had 20. How many CDs had she at first?
Alex has £x He won £15 in a competition. He now has £45. How much money had he at first?
CHALLENGE
88 www.prim-ed.com Prim-Ed Publishing Primary mathematics
TEACHER INFORMATIONA
Algebra
Oral work and mental calculation
• Verballymakeupwordproblemstogivennumbersentences involving formulae and equations. Work out the answers.
• Explaindifferentcalculationsthatcanbeusedtosolve the same problem. Discuss which calculation methods are preferred and why.
• Answergivenwordproblems,usingformulaeandequations to represent the information.
Interactive whiteboard activity
Interactive whiteboard activity available to support this copymaster. Visit www.prim-ed.com.
Main teaching activity
Formulae and equations (page 89)
Additional activities suitable for developing the objective
• Writewordproblemstogivennumbersentencesinvolving formulae and equations. Work out the answers.
• Writetwodifferentmethodsthatcouldbeusedtosolve the same word problem correctly. Work out the answers.
• Answergivenwordproblems,usingformulaeandequations to represent the information.
Answers
1. (a) 5 (b) 9 (c) 7 (d) 4 (e) 15 (f) 7 (g) 6 (h) 20
2. (a) (b) (c) (d)
(e)
3. (a)2n (b)n+2 (c)n–4 (d)2n÷4(e) n (f) 3n (g) 1/2n(orn÷2)
(h) Answers will vary, but one simple answer would be: n + n + 3n + 1/2n, (or 51/2n)
Challenge: Teacher check
5 8 813 16
29
9 8 617 14
31
7 8 415 12
27
3 7 910 16
26
8 6 414 10
24
ALGEBRA
Objective
• Usesimpleformulae.
Objective
Primary Maths Prim-Ed Publishing www.prim-ed.com 89
5 8
29
7 4
27
3 9
26
8 4
24
9 6
31
5 n 8
n + 5 n + 8
29
5 8 8
13 16
29
FORMULAE AND EQUATIONS
Representsinformationorunknownnumbersusingformulaeorequations.
Check your answers to Question 3 by substituting numbers for each letter ‘n’. Tick ( ) them if they are correct and cross ( ) them if they are incorrect. Redo the incorrect answers in a different coloured pen/pencil.
1 . Solve these equations.
(a) n + 7 = 12 (b) 3n = 27 (c) 2n + 4 = 18 (d) 5n = 20
n = n = n = n =
(e) n – 8 = 7 (f) 2n – 2 =12 (g) 7n = 42 (h) n – 4 = 16
n = n = n = n =
2. In these diagrams, the number in each box is made by adding the two numbers above it. Complete the missing numbers. Question (a) is done as an example. Follow the arrows.
(a) (n + 5) + (n + 8) = 29 5 + 8 = 13 29 – 13 = 16 2n = 16, :.n = 8
(b) (c) (d) (e)
3. Write simple algebraic formulae for these word problems. (a) Kelly has n apples. Priya has twice as many apples as Kelly.
How many apples does Priya have?
(b) Kelly is given 2 more apples. How many apples does she have altogether?
(c) Kelly gives away 4 apples. How many apples does she have left?
(d) Priya shares her apples equally between herself and 3 other friends. How many apples do they get each?
(e) John bakes n biscuits. He bakes the same amount of jam tarts as biscuits. How many jam tarts does John bake?
(f) John bakes 3 times as many muffins as biscuits. How many muffins does John bake?
(g) John bakes only half as many cup cakes as biscuits. How many cup cakes does John bake?
(h) How many items does John bake altogether? Try and write your answer as simply as possible.
apples
apples
apples
apples
jam tarts
muffins
cup cakes
CHALLENGE