CFE 4th Level Course Breakdown Key

CFE 4th
Level Course Breakdown
Pupil Self Assessment Key
S – Secure I have covered this experience/outcome and with confidence I can achieve it MTH – Math E/O
C – Consolidating I have covered this experience/outcome but I need a bit more revision to confidently achieve it MNU – Numeracy E/O
D – Developing I have covered this experience/outcome and I am currently unable to achieve it
BLOCK 1 Outcome/Experience Success Criteria Examples Pupil Self
Assessment
Topic 1
Number & Number processes
Bodmas
More complex examples
including Integers
I have investigated how introducing
brackets to an expression can change the
emphasis and can demonstrate my
understanding by using the correct order of
operations when carrying out calculations.
MNU 4-03b
I can use BODMAS when answering
calculations
I can answer calculations with
brackets
5 + 32 x 4
(6 + 3)2 ÷ (23 + 1)
S C D
Topic 2.1
Expressions & Equations
Multiplying algebraic terms.
Expanding brackets.
Solving problems.
Having explored the distributive law in
practical contexts, I can simplify, multiply
and evaluate simple algebraic terms
involving a bracket.
MTH 4-14a
I can use index rules to simplify
expressions
I can multiply out and expand
expressions that include brackets
I can evaluate expressions by
substituting given values into them
5t3 x 3t = 15t4
c(3 – 4c) = 3c – 4c2
Perimeter of a rectangle is 2(a + b)
If a = 23m & b = 45m calculate the
perimeter
Topic 2.2
Finding Factors.
Factorisation.
I can find the factors of algebraic terms, use
my understanding to identify common
factors and apply this to factorise
expressions. MTH 4-14b
I can find the HCF of algebraic
expressions
I understand that the HCF will
fully factorise an expression
The HCF of 4gh and 6h is 2h
Find the HCF and factorise:
5b2
– 25b
= 5b(b - 5)
Topic 3
Solving Equations.
Creating an equation or
formula to solve a problem.
Inequations.
Solving inequations.
Creating an inequation to
solve a problem.
Having discussed the benefits of using the
mathematics to model real-life situations, I
can construct and solve inequalities and an
extended range of equations.
MTH 4-15a
I can confidently form an equation
to model and solve a variety of real
life problems
I can solve a variety of inequations
I can confidently model and solve
a variety of real-life problems using
inequations
Mark spent £86. He bought jeans, a t-shirt
& jacket. The jacket cost £10 more than
the jeans & the t-shirt was £8 less than the
jeans. How much did each item cost?
5x+4 < 3x+12 , 4(2x+1) > 7(2x-3)
Harry has £350 to spend. It cost £100 to
Rent a hall and £9 per person for food.
Write down & solve an inequation for the
max number of people ha can invite.

CFE 4th
Assessment
Topic 4.1
Powers & Roots
Powers.
Roots.
Using a calculator.
I have developed my understanding of the
relationship between powers and roots and
can carry out calculations mentally or using
technology to evaluate whole number
powers and roots, of any appropriate
number.
MTH 4-06a
I can calculate the power of whole
numbers, fractions & decimals using
mental or written strategies
I can use the relationships between
powers & roots to find the root of a
number without a calculator using
trial & error if necessary
23 = 2 x 2 x 2 = 8
(
𝟑
𝟒
)2 =
𝟑 𝒙 𝟑
𝟒 𝒙 𝟒
=
𝟗
𝟏𝟔
0.42 = 0.4 x 0.4 = 0.16
√49 = 7, ∛64 = 4, √400 = 20
S C D
Topic 4.2
Powers & Roots
Scientific notation.
Very large numbers.
Very small numbers.
Using a calculator to solve
problems.
I have developed my understanding of the
relationship between powers and roots and
can carry out calculations mentally or using
technology to evaluate whole number
powers and roots, of any appropriate
number.
MTH 4-06b
I can write in full very large & very
small numbers when given in scientific
notation
I can change very big and very small
numbers into scientific notation
I can carry out calculations involving
my calculator
2.3 x 104 = 23000
4.56 x 10-3 = 0.00456
36900 = 3.69 x 104
0.00365 = 3.65 x 10-3
3.4 x 105 – 2.654 x 103

CFE 4th
Assessment
Topic 5.1
Properties of 2-D shapes & 3-D
objects
The circle and its parts.
Circumference of a circle.
Historical approximations.
Historical values for C/d.
Perimeter of compound
shapes.
Area of a circle and
compound shapes.
Topic 5.2
Properties of 2-D shapes & 3-D
objects
Arcs and sectors.
Having investigated the relationships
between the radius, diameter,
circumference and area of a circle, I can
apply my knowledge to solve related
problems.
MTH 4-16b
I can use a formula to calculate the
Circumference/area of a circle
I can calculate the perimeter and area
of compound shapes involving circles
I can find the length of an arc and
area of a sector of a circle
S C D

CFE 4th
BLOCK 1 Outcome/Experience Success Criteria Examples
Topic 6
Properties of 2D shapes and 3D
objects
Right-angled triangles:
Pythagoras.
I have explored the relationships that exist
between the sides, or sides and angles, in
right-angled triangles and can select and
use an appropriate strategy to solve related
problems, interpreting my answer for the
context.
MTH 4-16a
I can use Pythagoras’ theorem to
solve problems involving right-angled
triangles
I can use the converse of Pythagoras
I find the distance between two
points on a Cartesian diagram
Does the walkway reach to deck level if the deck
of the ferry sits 1.75m above the dock?
S C D

CFE 4th
Assessment
Topic 7
Angle, Symmetry &
Transformation
Tangents to a circle.
Angles in a semi-circle.
Using Pythagoras’ theorem in
circles.
Tangent kites
Having investigated the relationship
between a radius and a tangent and
explored the size of the angle in a semi-
circle, I can use the facts I have established
to solve related problems.
MTH 4-17a
I can use my knowledge of tangents
to solve problems
I can use my knowledge of angles in a
Semi-circle to solve problems
I can calculate the size or length of
an unknown angle or side in a triangle
I can use my knowledge of tangents
to find angles and sides in a tangent
kite
S C D

CFE 4th
Assessment
Topic 8.1
Data & Analysis
Dot plots.
Stem-and-leaf diagrams.
Scatter graphs.
Analysing a range of
information.
I can evaluate and interpret raw and
graphical data using a variety of methods,
comment on relationships I observe within
the data and communicate my findings to
others.
MNU 4-20a
By analysing dot plots and stem & leaf
diagrams I can describe the
distribution of data sets
I can use scatter diagrams and lines
of best fit to describe relationships/
correlation or not between data sets
I can draw sensible conclusions from
data given in different formats
Relating to a graph/table:
What happened to Brazil’s economy
during 1998- 2004
S C D
Topic 8.2
Data & Analysis
Dot plots.
Stem-and-leaf diagrams.
Scatter graphs.
Choosing the best table,
chart, diagram or graph.
I can select appropriately from a wide range
of tables, charts, diagrams and graphs when
displaying discrete, continuous or grouped
data, clearly communicating the significant
features of the data.
MNU 4-21a
I can draw dot plots/stem & leaf/
scatter graphs and understand the
different features of each data display

CFE 4th
Assessment
Topic 1
Fractions, Decimal fractions &
Percentages
Recurring decimals.
Equivalence.
Calculating common
percentages mentally.
Choosing the most suitable
method.
Calculating percentages using
a calculator.
Calculating a percentage
increase or decrease in one
step.
Expressing an increase or
decrease as a percentage.
I can choose the most appropriate form of
fractions, decimal fractions and percentages
to use when making calculations mentally,
in written form or using technology, then
use my solutions to make comparisons,
decisions and choices.
MNU 4-07a
I can represent recurring decimals
I can compare percentages/fractions/
decimal fractions by converting them
to equivalent forms
I can choose whether to use
equivalent fractions or combination of
1 & 10% when calculating percentages
without a calculator
I can calculate percentages with a
calculator using a suitable method
I can calculate percentage
increase/decrease in one step
I can express one quantity and a
percentage of another and can use this
idea to express an increase/decrease
as a percentage
𝟓
𝟗
= 5 ÷ 9 = 0.55555555 = 0.𝟓̇
2
5
= 2 ÷ 5 = 0.4 = 40%
14% of £90 = 14 ÷ 100 x 90 = £12.60
105% of 38 = 1.05 x 38 = 39.9
86% of 103 = 0.86 x 103 = 88.58
Chris scored 34 out of 38 in a test
𝟑𝟒
𝟑𝟖
= 34 ÷ 38 = 0.8947… = 89%
S C D

CFE 4th
Assessment
Topic 2.1
Money
Managing credit and debt.
Credit cards.
Calculating gross and net pay.
Calculating income tax.
Personal finance products.
Percentages and compound
interest.
Borrowing money.
Saving money.
Insurance.
I can discuss and illustrate the facts I need
to consider when determining what I can
afford, in order to manage credit and debt
and lead a responsible lifestyle.
MNU 4-09a
I can read and interpret bank
statements and make calculations
I can consider the different financial
aspects of a person’s situation and
make recommendations
I can reflect on my spending & work
out budgets for living within my means
I can calculate the cost associated
with using a credit card
S C D
Topic 2.2
Money
Credit cards.
interest.
Borrowing money.
Saving money.
Insurance.
I can source information on earnings and
deductions and use it when making
calculations to determine net income.
MNU 4-09b
I can calculate gross pay and total
deductions to find the net pay on a
range of payslips
I can calculate income tax using tax
bands and personal allowance
Net Pay = Gross Pay - Deductions

CFE 4th
Assessment
Topic 2.3
Money
Credit cards.
interest.
Borrowing money.
Saving money.
Insurance.
I can research, compare and contrast a
range of personal finance products and,
after making calculations, explain my
preferred choices.
MNU 4-09c
I can explain why I chose a particular
financial product
I can calculate the amount of money
lost or gained given a percentage and
a duration
I have compared savings and loan
products by calculating the amount of
interest charged or received.
You invested £3000 which lost 4% each
year for 3 years. How much is it worth?
Which 10 yr mortgage option is best:
£539.60 per month plus £700 fee
£187.50 p.m. (no fee) – interest only
S C D
Topic 3
Time
Speed, distance and time.
Calculating distance using
common fractions of an hour.
Using decimal fractions for
time.
More complex problems.
Mixed problems extension.
I can use the link between time, speed and
distance to carry out related calculations.
MNU 4-10b
I can solve problems involving speed,
distance & time
I can change time from minutes to
fractions of an hour and use this to
find the distance of a journey
I know the decimal forms of simple
fractions of an hour
I can change between time in different
units to solve real-life problems
I can compare speed in different
units by converting to the same units
Donna rides her motorbike at an
average speed of 54mph for 50mins.
how many miles does she travel?
Change 0.28hrs to hours & mins
Order the speed from slow to fast
40cm/min 100km/h 5m/s

CFE 4th
Assessment
Topic 4
Patterns & Relationships
Linear sequences.
Solving problems.
Non-linear sequences.
Having explored how real-life situations can
be modelled by number patterns, I can
establish a number sequence to represent a
physical or pictorial pattern, determine a
general formula to describe the sequence,
then use it to make evaluations and solve
related problems. MTH 4-13a
I can find the nth term formula of a
linear sequence
I can find the nth term formula of a
non-linear sequence
I can recognise linear patterns in the
form y= mx
I can recognise linear patterns in the
form y= mx + c
S C D
Topic 5.1
Measurement
Surface area of cubes.
Surface area of cuboids.
Exploring cubes.
Nets of 3D objects.
Efficient use of materials.
Making nets efficiently.
Nets of real objects.
Through investigating real-life problems
involving the surface area of simple 3D
shapes, I can explore ways to make the
most efficient use of materials and carry out
the necessary calculations to solve related
problems.
MTH 4-11b
I can calculate surface area of cubes
and cuboids
I can calculate the surface area of a
3D object from its net
I can recall how to calculate the
volume of cubes
and cuboids (revision)

CFE 4th
Assessment
Topic 5.2
Measurement
Volume and surface area of
prisms.
Volume of a cylinder.
Surface area of a cylinder.
Fruit juice cartons
investigation.
I have explored with others the practicalities
of the use of 3D objects in everyday life and
can solve problems involving the volume of
a prism, using a formula to make related
calculations when required.
MTH 4-11c
I can calculate the surface area &
volume of prisms
I can calculate the surface area &
volume of a cylinder.
S C D
Topic 6.1
Estimating & Rounding
Rounding and accuracy.
Upper and lower bounds.
Effects of rounding.
Tolerance.
Having investigated the practical impact of
inaccuracy and error, I can use my
knowledge of tolerance when choosing the
required degree of accuracy to make real-
life calculations.
MNU 4-01a
I have learned that different degrees
of accuracy are acceptable in different
situations
I can both interpret and write
measurements given in tolerance
notation

Topic 6.2
Measurement
Degrees of accuracy.
Errors in calculations.
Calculations using tolerance.
I can apply my knowledge and
understanding of measure to everyday
problems and tasks and appreciate the
practical importance of accuracy when
making calculations.
MNU 4-11a
I can use appropriate degree of
accuracy when working with measures
I can use tolerance notation to
express the accuracy in calculations
involving measurements of real objects

CFE 4th
Assessment
Topic 7
Properties of 2D shapes and 3D
objects
Trigonometry.
I have explored the relationships that exist
between the sides, or sides and angles, in
right-angled triangles and can select and
use an appropriate strategy to solve related
problems, interpreting my answer for the
context.
MTH 4-16a
I can use Trigonometry to find the
size of lengths and angles in a right
an led triangle
S C D

CFE 4th Level Course Breakdown Key

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CFE 4th Level Course Breakdown Key