Transcript Gail Gregory Head of English (formerly Head)

GCSE Mathematics B – Modular
Delivery Options
Modular specification allows you to deliver the course in the
way that best suits you and your students with the option of
•
•
•
•
•
•
Teaching Unit 1 or 2 first, though we advise that Unit 3 is taken
towards the end of the course.
Start the course early in Year 9
Make greater use number of assessment windows available for entries
and mock examinations
Mix-and-match tiers, to improve student’s final grade.
Using ResultsPlus Progress – diagnostic tests before you start
teaching a unit
Using ResultsPlus & ResultsPlus booster to improve performance on
resits
Delivery Model 1:Two year course (starting with Unit 1 or 2)
Year 10
Year 10
March
Teach
First unit
Units 1 & 2
exam
Year 10
June
Second unit
exam
(resit
opportunity for
first unit)
Year 11
November
Resit
opportunity
for second
unit
Year 11
March
Unit 3 mock
or live exam
Year 11
June
Unit 3 exam
or resit
opportunity
Delivery Model 2: Start teaching the GCSE course in Year 9
(starting with Unit 1 or 2)
Year 9
Start
teaching
first unit
Year 10
November
First set of
live practice
papers for
Units 1 & 2
Year 10
March
First unit
exam
Year 10
Year 11
Year 11
June
November
March
Second unit
exam
Resit
opportunity
for Units 1 &
2
Unit 3 live or
mock exam
(resit
opportunity for
first unit)
Year 11
June 2012
Unit 3 exam
or resit
opportunity
Delivery Model for linear centres (from June 2012 onwards)
Year 9/10
Year 10
June
Start teaching
the GCSE linear
course
Enter students
on a 1 year
accelerated
course for the
exams
Year 11
November
Mock exam
opportunity
Year 11
March
Mock exam
Opportunity/
Year 11
June
Enter for live
exam
Year 12
November
Resit
opportunity
Enter for live
exam
Mock examinations can be taken in a number of ways:
(a)
In the traditional way by setting the mock papers internally
(b)
Using the Mock Paper Analysis – setting a past paper as a mock, and we will provide the full ResultsPlus
analysis at cohort and individual student level
(c)
Enter students for the live exams. If they do well, they can keep their grades.
Otherwise ResultsPlus analysis can help with remediation ahead of the live exam
Impact on teaching and
learning
We are moving from
AO1
Using and applying
(i)Problem solving
(20% included within subject knowledge)
(ii) Communicating
(iii) Reasoning
AO2
Number and algebra
50 – 55%
AO3
Shape Space and Measures
25 – 30%
AO4
Handling Data
18 – 22%
Impact on teaching and learning
To
AO1 Recall and use their knowledge of the prescribed
content
45 –55%
Number and algebra
Geometry and measures
Statistics and probability
AO2 Select and apply mathematical methods
in a range of contexts
25 –35%
AO3 Interpret and analyse problems
and generate strategies to solve them
15 – 25%
Impact on teaching and
learning
In essence
About 50% Techniques split about
Number and algebra
Geometry and measures
Statistics and probability
50 – 60%
20 – 30%
15 – 25%
About 30% Choose an appropriate method to solve a
problem
About 20% Analyse a problem and find a method of
solution
Impact on teaching and learning
In addition
Functional skills
30 – 40%
20 – 30%
Foundation
Higher
Quality of written communication
About (5% included within the total paper)
Quality of Written
Communication (QWC)
QWC will…
• account for around 5% of the marks in total
generally on questions that are worth 4 marks
or more
• be indicated with asterisk by the question
number on the examination paper, and shown
in mark scheme
Quality of Written
Communication (QWC)
Students will be assessed on their ability to:
i) ensure that text is legible and that spelling,
punctuation and grammar are accurate so that
meaning is clear
Comprehension and meaning is clear by using
correct notation and labelling conventions
e.g. where mathematics shown supports a
decision
ii) select and use a form and style of writing appropriate to
purpose and to complex subject matter
Reasoning, explanation or argument is correct and appropriately
structured to convey mathematical reasoning.
e.g. algebraic/geometric proofs
iii) organise information clearly and coherently, using specialist
vocabulary when appropriate.
The mathematical methods and processes used are coherently and
clearly organised and the appropriate mathematical vocabulary
used.
e.g. charts are drawn
Impact on teaching and learning
This means there will be more questions that
• are set in a context
• will have elements of functional skills
• will have more words
• will be problems to solve
• will need more than one skill area in its solution
• will expect candidates to show their working
Instead of
Find 65% of £120.
(2 marks)
You might get
Jules buys a new jacket in a sale.
Sale
35% off
The original cost of the jacket was £120
In the sale the price is reduced by 35%.
What is the sale price of the jacket?
(3 marks)
Both these questions would be AO1 with the second
having functional skills.
Instead of
Solve
10x + 14 = 22
You might get
The perimeter of this shape is 22 cm.
2x + 7
x
3x
x
Find the area.
All measurements
are in centimetres
The second question is AO2 because there are different methods of solution
and candidates would have to choose which method to use.
This question can be seen on old and new specs
£3.80
£3.50
200g
175g
Large
Regular
A Large tub of popcorn costs £3.80 and holds 200g.
A Regular tub of popcorn costs £3.50 and holds 175g.
Which is the better value for money?
(3 marks)
This would be AO3 as it is a problem to solve and candidates would have
to decide on their strategy.
Best buy questions may become a regular feature on our papers
though with frequent use they will possibly become routine and cease
being a problem to solve.
Questions that are problems to solve
Example Question
Sam and Linda keep hens and sell the eggs that the hens lay.
Eggs for sale
They have 140 hens.
Each hen lays an average of 6 eggs each week.
The hens each eat about 100g of food each day.
The hen food costs £6.75 for a 25kg bag.
What is the least Sam and Linda need to charge for a dozen eggs so
that they cover the cost of the hen food?
(6 marks)
Mark schemes
Outline mark scheme
Per day
M1
140 hens eat 100 × 140 = 14 000 g = 14 kg each day
M1 A1
Cost of 14 kg of hen food = 6.75 ÷ 25 × 14 = £3.78
M1
Number of eggs 140 × 6 ÷ 7 = 120 each day
120 eggs = 10 dozen
M1
Food for 1 dozen eggs costs £3.78 ÷ 10 = 37.8p
C1
Cost for one dozen 38p
Per hen
M1
M1 A1
M1 A1
M1
C1
1 hen eats 100g each day
25 kg ÷ 100 g = 25 000 ÷ 100 = 250 days
6.75 ÷ 250 = 2.7 p each day
It takes 14 days to lay a dozen eggs.
Cost of food = 2.7 × 14 = 37.8p
Cost for one dozen 38p
Per week
M1
M1 A1
M1
M1
C1
140 × 6 = 840 eggs per week or 70 dozen
Weight of food 100 × 140 × 7 = 98 kg
Cost of food = 6.75 ÷ 25 × 98 = £26.46
Cost of food for 1 dozen eggs 26.46 ÷ 70 = 37.8p
Cost for one dozen 38p
Implications for teaching and
learning
• The new programme of study at Key Stage 3
• and the new programme of study at Key Stage 4
• flags up the changes in the assessment objectives
Changes in emphasis
• More emphasis on problem solving
• More emphasis on finding an appropriate method
• More emphasis on showing your working
• More emphasis on proof and explaining your results
• More emphasis on using different skill areas
How can this be achieved in the
classroom?
• Use problem solving strategies and investigations
throughout KS3 and KS4
• Use old GCSE investigations
• Emphasise the importance of showing your working
• Register for the UK Maths challenge at KS3 & 4
• Teach students how to split a question up into its
component parts.
Summer 2009 Paper 1380/1F
18.
Diagram NOT
accurately drawn
A
88O
B
D
96O
C
Success rate ?
93.2% scored 0 marks
1.1% scored 1 mark
5.7% scored 2 marks
This was out of over 130 000
candidates
The question was testing the
understanding of
angles on parallel lines
including elements of
‘using and applying’
mathematics.
The original mark scheme
B2 for Ben and a valid reason, eg ‘it should be
180’ or ‘they are not supplementary (allied,
co-interior) oe
This could be implied by 184 or 84 or 92 seen
[B1 for Ben and 88 + 96 or 180 – 88 or 180 – 96
seen or for just a valid reason (eg. Without Ben
or James)]
High tariff topics at Foundation
High success rates:
Number
Long multiplication (50+%)
Find value of a calculation given another (50-60%)
Exchange rate/money calculations (50+%)
Use of calculator (50+%)
High tariff topics at Foundation
High success rates:
Algebra
Derive an algebraic expression (50-60%)
Basic laws of indices (45-50%)
High tariff topics at Foundation
High success rates:
Shape and Space
Angles on a straight line/triangle, with reasons
(50+%)
Enlargements with given scale factors (70+%)
High tariff topics at
Foundation
High success rates:
Data Handling
Two-way tables (75%)
Questionnaires (50+%)
Scatter graphs (65+%)
High tariff topics at Foundation
Low success rates:
Number
Fractions (<30%)
HCF, LCM and Product of prime factors
(20%)
Ratio (33%)
Significant figures (25%)
High tariff topics at Foundation
Low success rates:
Algebra
Solving equations such as 4x + 1 = 2x + 12
(15-20%)
Substituting negative values (<20%)
Expanding a single bracket (10-25%)
High tariff topics at
Foundation
Low success rates:
Shape and Space
Describing transformations (210%)
2D representations of 3D solids
(25%)
Constructions (10%)
High tariff topics at Foundation
Low success rates:
Data Handling
Probability (20-30%)
Estimating the mean (<5%)
Mid to High tariff topics at
Higher
High success rates:
Number
Standard Form conversions
(65+%)
Use of calculator (80+%)
Compound Interest (65+%)
Mid to High tariff topics at Higher
High success rates:
Algebra
Factorise a 2-term quadratic
expression (50%)
y = mx+ c (50+%)
Indices (rules of) (60-65%)
Mid to High tariff topics at
Higher
High success rates:
Shape and Space
Pythagoras (60%)
Trigonometry of a right angle
triangle (50-55%)
Mid to High tariff topics at
Higher
High success rates:
Data Handling
Cumulative Frequency (60+%)
Probability tree diagrams (50+%)
Box plots (basic information) (60+%)
Mid to High tariff topics at Higher
Low success rates:
Number
Bounds (<20%)
Surds (rationalising, etc.) (<15%)
Mid to High tariff topics at
Higher
Low success rates:
Algebra
Solving inequalities (<30%)
Rearrange complex formulae
(<15%)
Transformation of graphs (10-20%)
Algebraic proofs (5-10%)
Mid to High tariff topics at
Higher
Low success rates:
Shape and Space
Use of Circle theorems (1020%)
Congruency proofs (5-10%)
Trig graphs (10-20%)
Vector algebra (5-15%)
Mid to High tariff topics at
Higher
Low success rates:
Data Handling
Histograms (5-15%)
Conditional Probability (1015%)
Task 3
Write a 3, 4 or 5 mark question, that
could appear on either a Foundation
or Higher tier paper, on each of the
following areas:
• Fractions and Ratio
• Area and/or circumference of a circle
• Probability and/or Averages
Wherever possible, try to address
Sample Question which could be answered in a variety of
ways in KS3.
How about Trial & Improvement or using an Excel
spreadsheet formula?
A room is 2 metres longer than it is wide.
The area of the room is 52 m².
What is the perimeter of the room?
Source:-2010 Edexcel GCSE Maths SAM