Download Unit 1 Number I core

Unit 1: Number I Core ( 20 lessons)
Syllabus
Main Learning Objectives
Reference
Suggested Teaching Activities
Resources/Extra
material
References from Pimentel
and Wall Core IGCSE
Mathematics Second
Editions unless stated
otherwise
9.1
9.2
9.3
NEW Notation and meaning for is an
element of  , is not an element of, is a
subset of  , is a proper subset of  ,
universal set U, empty set  or { },
complement of A, A’, number of
elements in A, n(A)
Sets in descriptive form {x } or as a
list.
NEW Venn diagrams with at most
three sets.
9.4
New Find intersection and union of
sets by using Venn Diagrams.
1.1
RECAP (A) Know the vocabulary and
notation for different sets of numbers:
natural numbers N (N = 0,1,2,3…),
primes, squares, integers Z, rational
numbers Q, irrational numbers, real
numbers R
RECAP Irrational Numbers
Be able to determine if a number is
irrational or not
1.1
Use Venn Diagrams to illustrate
the relationship between the
different sets of numbers (this
will be a NEW approach)
Calculator/
Non calc.
activity
Old
IGCSE
ref.
Worksheet
Not on
old
IGCSE
Worksheet
Not on
old
IGCSE
Not on
old
IGCSE
Worksheet
Mention these sets when
introducing Venn diagrams –see
above
Non Calc
Ex. 1.9 (p. 8)
GDC
1.1
RECAP Prime Numbers. Be able to
determine if a number is prime.
1.3
RECAP (A) Know how to determine
Prime Factors, the Highest Common
Factor, Multiples, Lowest Common
Multiple
RECAP (A)Be able to add, subtract,
multiply, divide and apply the use of
brackets appropriately with whole
numbers, manually. Understand the
meaning of the word product.
Investigating- working
systematically, listing outcomes
Investigating – working
systematically
Investigating – working
systematically, elimination
RECAP (A) Be able to find equivalent
fractions and be able to convert
fractions from improper to mixed
number form.
1.2
Paper 3
Paper 3
Paper 3
1.2
1.2
RECAP (A) Be able to convert
fractions from improper to mixed
number form.
Sieve of Eratosthenes, prime
factor trees, use of 1 – 100
number grids. When finding
factors of a number try to find the
factor pair.
The Four Fours Problem. Use
four 4s and any combination of
operations to create all the
numbers between 1 and 20
Triples.
Biggest number
Prime Numbers
A visual presentation of
equivalence is helpful. Students
will need to be shown how to use
the GDC to input and manipulate
fractions ie 2 ½ is input as 2 +
1÷2
Ex. 1.5 (p. 6)
Ex. 1.6 (p. 6)
Ex. 1.7 (p. 7)
Ex. 1.8 (p. 7)
Ex. 7.1 (p. 44)
Non Calc
Non Calc
Worksheet – copy
on maths server
Worksheet
Worksheet– copy
on maths server
Ex. 7.2 (p. 46)
Ex. 4.3
(p.26)
Non Calc
Non Calc
1.2
1.2
1.2
1.2
1.2
1.2
RECAP(A)Be able to add and subtract
fractions with the same and different
denominators and when written as
improper fractions and/or mixed
numbers
RECAP(A) Be able to multiply and
divide fractions when written as
improper fractions and/or mixed
numbers.
Be able to find the reciprocal of a
fraction (or a whole number!)
NEW(A) Be able to divide by a
fraction and then another fraction.
Divide a whole number by a fraction.
Multiply a whole number by a fraction
RECAP (A) Convert from fractions to
decimals and vice-versa
RECAP(A)Be able to add and subtract
with integers, manually.
A visual presentation of adding
with different denominators, for
example, is helpful.
Ex. 7.3 (p. 47)
Non Calc
A visual presentation of the
equivalence of dividing by a
fraction and multiplying by its
denominator is helpful.
Ex. 7.4 (p.48)
Non Calc
These manipulations of fractions
are essential foundation for later
work on algebraic fractions.
Fraction Action
worksheet
Non Calc
Ex. 7.5 (p.48)
Ex. 7.6 (p.49)
Ex. 1.1 (p. 1)
Ex. 1.2 (p. 2)
Non
Calc/Calc
Non Calc
Ex. 1.3 (p. 3)
Dividing is not
covered in these
exercises see
Worksheet
Negative
Numbers 1
Non Calc
Familiarise students on how to do
this on the GDC
This is a key topic and impacts
later on algebra if it is not
mastered at this stage!! Introduce
the topic by playing “walk the
plank” see DM for details.
RECAP(A)Be multiply and divide and Students will need to be shown
apply the use of brackets appropriately how to use the GDC to input and
with integers, manually. Apply
manipulate integers ie using (-)
directed number in practical situations button not minus button.
1.2
RECAP(A) Apply directed number in
practical situations
1.2
RECAP (A) Be able to add, subtract,
multiply, divide and apply the use of
brackets appropriately with decimals,
manually.
1.2
RECAP (A) Apply decimals in
practical situations
Investigating – being systematic,
drawing a picture
Investigating – using a table, looking
for patterns, making predictions,
testing them, making generalisations
RECAP Convert from percentages to
decimals to fraction and vice-versa
Paper 3
Paper 3
1.8
Diagonals
Worksheet
Negative
Numbers 2
Decimals
Worksheet 1
(there are some
speed tests at the
end of this
worksheet which
might be fun!)
Decimals
Worksheet 2
Worksheet
Digit Sum
Worksheet
Ex. 4.4 (p.27)
Ex. 4.5 (p.27)
1.8
RECAP Calculate a fraction of a
quantity
Use this as an introduction to
finding a % of a quantity.
Ex. 4.2 (p. 25)
1.8
RECAP Calculate a % of a quantity
Practice calculating 5%, 10%,
20%, 50% etc mentally.
Ex. 11.2 (p. 71)
1.8
RECAP Express one quantity as a
percentage of another
Use statistics that are taken from the
class eg what % of the class live in
Sha Tin? Use two-way tables to
gather the data eg gender v how you
get to school
Ex. 11.3 (p.72)
Non Calc
Non Calc
Non Calc
Non Calc
for simple
cases
Non Calc
for simple
cases
Non Calc
for simple
cases
Non Calc
for simple
cases
1.8
RECAP Calculate % increase or
decrease
1.5
RECAP(A) Ratio – write equivalent
ratios.
RECAP(A) Ratio - divide a quantity
in a given ratio
1.5
1.5
NEW Use the unitary method for direct
proportion and understand common measures
of rate
NEW Recognise what the graph of direct
proportion looks like. Know that the rate is the
gradient of the straight line graph
1.5
NEW Use the unitary method for inverse
proportion
NEW Recognise what the graph of inverse
proportion looks like.
Paper 3
Investigating – collecting data,
constructing, proving
RECAP(A) Rounding to a degree of
accuracy or number of decimal places
RECAP(A) Rounding to a number of
significant figures.
1.11
1.11
1.11
RECAP(A) Rounding to enable
estimation
Ensure when calculating %
increase and decrease that
students use x 1.05 to increase by
5% etc
ICT–mymaths–Number –
Percent – compound interest
Ex. 11.4 (p.74)
Non Calc
for simple
cases
Ex. 10.3 (p. 64)
Non Calc
Ex. 10.4 (p.65)
Non Calc
Ensure that students graph situations of
direct proportion. Eg Total wage v hours
worked. Use the GDC to plot these
points. Note that the gradient for direct
proportion represents the rate.
ICT – mymaths – Number – Ratio
and Proportion - Higher
Ensure that students graph situations of
inverse proportion eg Time v Speed to
cover a constant distance. Use the GDC
to plot these points. ICT – mymaths –
Number – Ratio and Proportion Higher
Ex. 10.1 (p.62)
Ex. 10.2(p.64)
Non Calc
for simple
cases
What is the Golden Ratio?
Worksheet
Note that for IGCSE and IB
where not stated, students must
round all answers correct to 3 sf
GDC
Ex. 10.5(p.67)
Non Calc
for simple
cases
GDC
Ex. 8.1 (p. 51)
Ex. 8.2 (p. 52)
Ex.8.3 (p. 52)
Non Calc
Ex. 8.4 (p. 53)
Non Calc
Non Calc