10 c-lower stream 2014
TRANSCRIPT
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Strand : Number Substrand : NS4.4
Topic : ProbabilitySolves probability problems involving simple events
Language :
Knowledge and Skills Working Mathematically Learning Experiences egister
Students learn about
listing all possible outcomes o! a simple e"ent
using the term #sample space$ to denote all possible
outcomes eg !or tossing a !air die% the sample spaceis &% '% (% )% *% +
assigning probabilities to simple e"ents by
reasoning about e,ually likely outcomes eg theprobability o! a * resulting !rom the throw o! a !air
die is+
&
expressing the probability o! a particular outcome
as a !raction between - and &
assigning a probability o! .ero to e"ents that are
impossible and a probability o! one to e"ents that
are certain recognising that the sum o! the probabilities o! all
possible outcomes o! a simple e"ent is &
identi!ying the complement o! an e"ent
eg #The complement o! drawing a red card !rom adeck o! cards is drawing a black card/$
!inding the probability o! a complementary e"ent
Students learn to
sol"e simple probability problems arising in games
(Applying Strategies)
use language associated with chance e"ents
appropriately (Communicating)
e"aluate media statements in"ol"ing probability
(Applying Strategies, Communicating)
interpret and use probabilities expressed as
percentages or decimals(Applying Strategies,Communicating)
explain the meaning o! a probability o! -% '&
and
& in a gi"en situation (Communicating,Reasoning)
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Strand : Number Substrand : NS5.1.3
Topic : 1robability
Determines relative frequencies and teoretical probabilities
Language :
Knowledge and Skills Working Mathematically Learning Experiences egister
Students learn about
repeating an experiment a number o! times to
determine the relati"e !re,uency o! an e"ent
estimating the probability o! an e"ent !rom
experimental data using relati"e !re,uencies expressing the probability o! an e"entAgi"en a
!inite number o! e,ually likely outcomes as
23AP 4
n
outco!a"ourableo!number
where nis the total number o! outcomes in thesample space
using the !ormula to calculate probabilities !or
simple e"ents
simulating probability experiments using random
number generators
Students learn to
recognise and explain di!!erences between
relati"e !re,uency and theoretical probability ina simple experiment (Communicating,
Reasoning) apply relati"e !re,uency to predict !uture
experimental outcomes (Applying Strategies)
design a de"ice to produce a speci!ied relati"e
!re,uency eg a !our5coloured circular spinner(Applying Strategies)
recognise that probability estimates become
more stable as the number o! trials increases(Reasoning)
recognise randomness in chance situations
(Communicating)
apply the !ormula !or calculating probabilitiesto problems related to card% dice and othergames (Applying Strategies)
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Strand : Number Substrand : NS5.1.1
Topic : !ational Numbers
"pplies inde# la$s to simplify and evaluate aritmetic
e#pressions and uses scientific notation to $rite large and small
numbers
Language :
Knowledge and Skills Working Mathematically Learning Experiences egister
Students learn about
describing numbers written in index !orm using
terms such as base% power% index% exponent
e"aluating numbers expressed as powers o!
positi"e whole numbers
establishing the meaning o! the .ero index and
negati"e indices eg by patterns
'(
& -(
&( '(
6 ( &(
&6
&
writing reciprocals o! powers using negati"e
indices
eg0&
&
(
&(
)
)==
translating numbers to index !orm 3integralindices2 and "ice "ersa
de"eloping index laws arithmetically by
expressing each term in expanded !ormeg
+)')'((2((((32((3(( === +
('*'*
((((
((((((( ==
=
( ) ( ) ( ) ( ) ( ) ')' (((((((((( ==
using index laws to simplify expressions
Students learn to
sol"e numerical problems in"ol"ing indices
(Applying Strategies)
explain the incorrect use o! index laws
eg why +)' 6(( (Communicating,
Reasoning)
"eri!y the index laws by using a calculator
eg to compare the "alues o! ( ) '* %'
'&
*
and
* (Reasoning)
communicate and interpret technical
in!ormation using scienti!ic notation(Communicating)
explain the di!!erence between numerical
expressions such as )&-'
and )' %particularly with re!erence to calculatordisplays (Communicating, Reasoning)
sol"e problems in"ol"ing scienti!ic notation
(Applying Strategies)
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Knowledge and Skills Working Mathematically Learning Experiences egister
using index laws to de!ine !ractional indices !or
s,uare and cube roots
eg ( ) 66'
= and 66'
'&
=
% hence
'
&
66 =
writing s,uare roots and cube roots in index
!orm
eg '00 ((&
=
recognising the need !or a notation to express
"ery large or "ery small numbers
expressing numbers in scienti!ic notation
entering and reading scienti!ic notation on a
calculator
using index laws to make order o! magnitude
checks !or numbers in scienti!ic notationeg
( ) ( ) &-+) '/&&-&'&-'/)&-&'/( con"erting numbers expressed in scienti!ic
notation to decimal !orm
ordering numbers expressed in scienti!ic
notation
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8/13/2019 10 C-Lower Stream 2014
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Strand : Number Substrand : NS5.1.%
Topic : &onsumer "ritmetic
Solves consumer aritmetic problems involving earning andspending money
Language :
Knowledge and Skills Working Mathematically Learning Experiences egister
Students learn about
calculating earnings !or "arious time periods
!rom di!!erent sources% including:5wage5salary5commission
5piecework5o"ertime5bonuses5holiday loadings5interest on in"estments
calculating income earned in casual and part5
time obs% considering agreed rates and specialrates !or Sundays and public holidays
calculating weekly% !ortnightly% monthly and
yearly incomes
calculating net earnings considering deductions
such as taxation and superannuation calculating simple interest using the !ormula
PRTI = where&--
rR=
whereIis the interest%Pthe principal% theannual interest rate and Tthe number o! years
Students learn to
read and interpret pay slips !rom part5time obs
when ,uestioning the details o! their ownemployment (Questioning, Communicating)
prepare a budget !or a gi"en income%
considering such expenses as rent% !ood%
transport etc(Applying Strategies2
interpret the di!!erent ways o! indicating wages
or salary in newspaper #positions "acant$ad"ertisements eg 8'-K (Communicating)
compare employment conditions !or di!!erent
careers where in!ormation is gathered !rom a"ariety o! mediums including the 9nterneteg employment rates% payment (ApplyingStrategies)
compare simple interest with compound interest
in practical situations eg loans (ApplyingStrategies)
interpret spreadsheets or tables when
comparing simple interest and compoundinterest on an in"estment o"er "arious timeperiods(Applying Strategies, Communicating)
realise the total cost andor hidden costs
in"ol"ed in some types o! purchasearrangements(Applying Strategies)
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&'
Knowledge and Skills Working Mathematically Learning Experiences egister
applying the simple interest !ormula to problems
related to in"esting money at simple interestrates
calculating compound interest !or two or three
years by repeated multiplication using acalculator eg a rate o! *; per annum leads torepeated multiplication by &/-*
calculating compound interest on in"estments
using a table
calculating and comparing the cost o!
purchasing goods using:5cash5credit card5lay5by5de!erred payment5buying on terms5loans
calculating a #best buy$
make in!ormed decisions related to purchases
eg determining the best mobile phone plan !ora gi"en situation (Applying Strategies)
interpret the
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Strand : Patterns and "lgebra Substrand : P"S5.1.1
Topic : "lgebraic 'ecniques
"pplies te inde# la$s to simplify algebraic e#pressions
Language :
Knowledge and Skills Working Mathematically Learning Experiences egister
Students learn about
using the index laws pre"iously established !or
numbers to de"elop the index laws in algebraic!orm
eg *('(' '''' == + nmnm aaa +=
('*'*'''' ==
nmnmaaa
=
( ) +(' '' = mnnm aa =23
establishing that &- =a using the index laws
eg -(((( aaaa ==
and &(( =aa
&- =a
simpli!ying algebraic expressions that include
index notationeg
(*'(
)'+
*('
-
+'2(3'
)(&'
+('
0(*
mmmm
aaa
xxx
x
+=+
=
=
=+
Students learn to
"eri!y the index laws using a calculator
eg use a calculator to compare the "alues o!') 2(3 and 0( (Reasoning)
explain why &- =x (Applying Strategies,Reasoning, Communicating)
link use o! indices in =umber with use o!
indices in >lgebra (Reflecting)
explain why a particular algebraic sentence is
incorrect
eg explain why +'( aaa = is incorrect
(Communicating, Reasoning)
examine and discuss the di!!erence between
expressions such as
aa *( '
and aa *( '
+
by substituting "alues !or a(Reasoning, Applying Strategies,
Communicating)
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&)
Strand : Data Substrand : DS5.1.1
Topic : Data !epresentation and "nalysis
(roups data to aid analysis and constructs frequency and
cumulative frequency tables and graps
Language :
Knowledge and Skills Working Mathematically Learning Experiences egister
Students learn about
constructing a cumulati"e !re,uency table !or
ungrouped data
constructing a cumulati"e !re,uency histogram
and polygon 3ogi"e2 using a cumulati"e !re,uency polygon to !ind the
median
grouping data into class inter"als
constructing a !re,uency table !or grouped data
constructing a histogram !or grouped data
!inding the mean using the class centre
!inding the modal class
Students learn to
construct !re,uency tables and graphs !rom data
obtained !rom di!!erent sources 3eg the 9nternet2and discuss ethical issues that may arise !rom
the data (Applying Strategies, Communicating,Reflecting)
read and interpret in!ormation !rom a
cumulati"e !re,uency table or graph(Communicating)
compare the e!!ects o! di!!erent ways o!
grouping the same data (Reasoning)
use spreadsheets% databases% statistics packages%
or other technology% to analyse collected data%present graphical displays% and discuss ethicalissues that may arise !rom the data
(Applying Strategies, Communicating,Reflecting)
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Strand : )easurement Substrand : )S5.1.1
Topic : Perimeter and "rea
*ses formulae to calculate te area of quadrilaterals and finds
areas and perimeters of simple composite figures
Language :
Knowledge and Skills Working Mathematically Learning Experiences egister
Students learn about
de"eloping and using !ormulae to !ind the area o!
,uadrilaterals:5 !or a kite or rhombus%Area xy
'
&= where
x andy are the lengths o! the diagonals?
5 !or a trape.ium%Area 23'&
bah += where
h is the perpendicular height and a and b thelengths o! the parallel sides
calculating the area o! simple composite !igures
consisting o! two shapes including ,uadrants andsemicircles
calculating the perimeter o! simple composite!igures consisting o! two shapes including,uadrants and semicircles
Students learn to
identi!y the perpendicular height o! a trape.ium
in di!!erent orientations (Communicating) select and use the appropriate !ormula to
calculate the area o! a ,uadrilateral (ApplyingStrategies)
dissect composite shapes into simpler shapes
(Applying Strategies)
sol"e practical problems in"ol"ing area o!
,uadrilaterals and simple composite !igures(Applying Strategies)
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Strand : Patterns and "lgebra Substrand : P"S5.1.%
Topic : &oordinate (eometryDetermines te midpoint+ lengt and gradient of an interval
,oining t$o points on te number plane and graps linear and
simple non-linear relationsips from equations
Language :
Knowledge and Skills Working Mathematically Learning Experiences egister
Students learn about
i!point, "ength an! #ra!ient determining the midpoint o! an inter"al !rom a
diagram
graphing two points to !orm an inter"al on the
number plane and !orming a right5angled triangleby drawing a "ertical side !rom the higher pointand a hori.ontal side !rom the lower point
using the right5angled triangle drawn between
two points on the number plane and 1ythagoras$theorem to determine the length o! the inter"aloining the two points
using the right5angled triangle drawn between
two points on the number plane and therelationship
run
risegradient =
to !ind the gradient o! the inter"al oining twopoints
determining whether a line has a positi"e or
negati"e slope by !ollowing the line !rom le!t toright @ i! the line goes up it has a positi"e slopeand i! it goes down it has a negati"e slope
Students learn to
describe the meaning o! the midpoint o! an
inter"al and how it can be !ound(Communicating)
describe how the length o! an inter"al oining
two points can be calculated using 1ythagoras$theorem (Communicating, Reasoning)
explain the meaning o! gradient and how it can
be !ound !or a line oining two points(Communicating, Applying Strategies)
distinguish between positi"e and negati"e
gradients !rom a graph (Communicating)
relate the concept o! gradient to the tangent
ratio in trigonometry !or lines with positi"egradients (Reflecting)
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Knowledge and Skills Working Mathematically Learning Experiences egister
!inding the gradient o! a straight line !rom the
graph by drawing a right5angled triangle a!teroining two points on the line
#raphs of Relationships constructing tables o! "alues and using
coordinates to graph "ertical and hori.ontal linessuch as
(%'
&%(
==
==
yy
xx
identi!ying thex5 andy5intercepts o! graphs identi!ying thex 5axis as the liney4 $
identi!ying they5axis as the line x 4 $
graphing a "ariety o! linear relationships on the
number plane by constructing a table o! "aluesand plotting coordinates using an appropriatescale eg graph the !ollowing:
xy
yx
yx
xy
xy
(
'
'*
'
&
(
=
=
=+
+=
=
graphing simple non5linear relationships
eg
xy
xy
xy
'
''
'
=
=
=
determining whether a point lies on a line by
substituting into the e,uation o! the line
describe hori.ontal and "ertical lines in general
terms (Communicating)
explain why thex5axis has e,uationy 4$
(Reasoning, Communicating)
explain why they5axis has e,uationx4 $
(Reasoning, Communicating)
determine the di!!erence between e,uations o!
lines that ha"e a negati"e gradient and thosethat ha"e a positi"e gradient (Reasoning)
use a graphics calculator and spreadsheet
so!tware to graph% compare and describe arange o! linear and simple non5linearrelationships(Applying Strategies, Communicating)
apply ethical considerations when using
hardware and so!tware (Reflecting)
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8/13/2019 10 C-Lower Stream 2014
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Strand : )easurement Substrand : )S5.1.%
Topic : 'rigonometry
"pplies trigonometry to solve problems diagrams given/
including tose involving angles of elevation and depression
Language :
Knowledge and Skills Working Mathematically Learning Experiences egister
Students learn about
Trigonometric Ratios of Acute Angles
identi!ying the hypotenuse% adacent and opposite
sides with respect to a gi"en angle in a right5angled triangle in any orientation
labelling the side lengths o! a right5angled
triangle in relation to a gi"en angle eg the side cisopposite angle C
recognising that the ratio o! matching sides in
similar right5angled triangles is constant !or e,ualangles
de!ining the sine% cosine and tangent ratios !or
angles in right5angled triangles
using trigonometric notation eg sinA using a calculator to !ind approximations o! the
trigonometric ratios o! a gi"en angle measured indegrees
using a calculator to !ind an angle correct to the
nearest degree% gi"en one o! the trigonometricratios o! the angle
Students learn to
label sides o! right5angled triangles in di!!erent
orientations in relation to a gi"en angle(Applying Strategies, Communicating)
explain why the ratio o! matching sides in
similar right5angle triangles is constant !or e,ualangles (Communicating, Reasoning)
sol"e problems in practical situations in"ol"ing
right5angled triangles eg !inding the pitch o! aroo!(Applying Strategies)
interpret diagrams in ,uestions in"ol"ing angles
o! ele"ation and depression(Communicating)
relate the tangent ratio to gradient o! a line
(Reflecting)
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&6
Knowledge and Skills Working Mathematically Learning Experiences egister
Trigonometry of Right-Angled Triangles
selecting and using appropriate trigonometric
ratios in right5angled triangles to !ind unknownsides% including the hypotenuse
selecting and using appropriate trigonometric
ratios in right5angled triangles to !ind unknownangles correct to the nearest degree
identi!ying angles o! ele"ation and depression
sol"ing problems in"ol"ing angles o! ele"ation
and depression when gi"en a diagram
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