The KING’S Medium Term Plan – Mathematics
Year 9 senior programme – Learning cycle one
Module
Overarching
Subject
Challenging
question
Lines of
Enquiry
Number and Algebra – real life applications
‘How useful is algebra in my life?’
Week 1: How can we use estimation to carry out mathematical problems reliably?
Week 2: What is the difference between decimal places and significant figures?
Week 3: How do we identify the different varieties of algebra and which rules to use? Why do we need algebra?
Week 4: In what areas of life is substitution a useful skill?
Week 5: Can the inverse method be used to solve all algebraic problems? What does inverse proportion mean?
Week 6-7: Assessment followed by gap teaching – from assessment analysis.
Progress
Objectives
An overview of the LC’s key learning intentions:
 Recall how to simplify expressions with all 4 operations
 Identify which form of simplification that has to take place
 Understand how to substitute into a range of expressions and formula
 Analyse how to rearrange formulae
 Evaluate how to expand brackets and factorise
 Create expressions, equations and formulae to solve problems
 Solve real life problems and GCSE tasks through the application of number and algebra together
By the end of LC1 in Mathematics SWBAT achieve these AQA objectives:
Basic Number (AQA objectives N1, N2, N3, N4, N14, N15 and N16) Weeks 1-2
In this number revision unit pupils will master the following;

Recognise and use relationships between operations including inverse operations (e.g. cancellation to simplify calculations
and expressions), order a variety of numbers

Check calculations using approximation and estimation, including answers obtained using technology

Estimate solutions

Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples,
highest common factor, lowest common multiple, prime factorisation, including using product notation, and the unique
factorisation theorem

Round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or
significant figures)

Use inequality notation to specify simple error intervals due to truncation or rounding (Higher content)

Apply and interpret limits of accuracy
Basic Algebra (AQA objectives A1, A3 and A4 supported by N4) Weeks 3-4
In week 3 pupils will master these skills;

Understand and use the concepts and vocabulary of expressions, equations, formulae, identities (higher content),
inequalities, terms and factors

Use and interpret algebraic notation, including all 4 operations, simplifying methods and indices (it is expected that
answers are given in their simplest form without an explicit instruction given in the question)

Use coefficients written as fractions rather than decimals

Use conventional notation for priority of operations, including brackets, powers, roots and reciprocals

Simplify and manipulate algebraic expressions by:
o
collecting like terms
o
multiplying a single term over a bracket
o
taking out common factors
o
Substitute values into expressions and formulae
o
Be able to create formulae/expression/equation from written problems to find a solution (mainly higher)
Equations (AQA objectives A2 and A17) Week 5
In this unit pupils will develop further mastery in applying knowledge of algebra to writing and solving equations. They will;

Develop more complex work on how to substitute numerical values into formulae and expressions, including scientific
formulae

Solve linear equations with one unknown algebraically (1 step and 2 step using inverses) including those with the unknown
on both sides of the equation (higher)

Pupils will understand how to write an equation form a worded problem in order to find a solution (higher)
NOTE: In week 3 there will be a mid LC assessment to check current progress.
Assessment at the end of week 6 will be against the above AQA objectives following on from 2 lessons of REACH
and revision.
Gap teaching from analysis of assessments will take place in week 7.
IMPORTANT INFORMATION AND WEEKLY NEEDS
Personalised
Learning and
Reach work
and Mastery
The AQA objectives above cover a wide range of mathematical skills and applications at varying levels of
difficulty. Each practitioner has access to sets of exam based questions and activities that are aimed at these
different levels of application and will ensure that all pupils are provided with work that will both challenge and
support them at their targeted Grade Point as well as pushing them towards the next. All pupils will meet the
progress objectives outlined above at a pace that suits them and will be delivered in a way that is personalised to
how they learn. The use of iPads will be planned for carefully so that they can maximise learning.
Maths in real
life
Each week, there will be discussion and slides planned in so that pupils can value the relevance of what they are
learning, which areas of life or careers that skill may be useful to and lessons will, as much as possible, contain
resources where maths has to be applied to real world problems in order to find solutions.
Cognitive
Acceleration
CA will be taught in a variety of forms throughout the Learning Cycle, particularly in the Do Now or Plenary phase
of the lessons where more open ended questions/tasks will be provided to provoke deeper thought processes.
However, in weeks 2 and 4 full CA lessons will be delivered with resources from ‘Let’s Think!’
Planning for
Feedback
Pupils will receive written feedback each week in the form of teacher marking, peer/self-assessment and small
quizzes to check key knowledge. Mark schemes will be provided where appropriate for pupil self-assessment and
development. REACH lessons each week will allow time for acting on feedback and making improvements to their
work in order to develop further and fill in GAPs.
Within each week time is allocated for REACH work. During this time, once pupils have responded in green pen to
their feedback, they will be provided with a range of problems solving and real life application questions to
deepen their understanding of that topic. These are taken from the AQA GCSE specification.
Mastery and
problem
solving
MEDIUM TERM PLAN
Week 1
Line of Enquiry: How can we use estimation to carry out mathematical problems reliably?
4 hours of
lessons plus 1
hour of
homework
each week
Here is how each week is broken down;
Additional
intervention
and reach is
provided
during
lessons and
where
 Hypotheses for the week’s lessons;
These will act as the title for the lessons, in which the work done will be reflected upon to either prove or disprove each
hypothesis. It may be that 1 hypothesis can last more than 1 lesson yet others are achieved quickly. This depends upon
how far the pupils move on from the knowledge section and get through the different success criteria within the main body
of the lesson. All hypotheses should be answered to some degree over the course of the week.
 Learning Intentions:
These are the key objectives laid out by the exam board (as seen above).
 Weekly success criteria for completion across 4 lessons (or across 3 for weeks with REACH lessons or
tests);
possible
outside of
lessons
This is where after teaching the knowledge necessary the pupils will work at their grade point on exam questions in order
to achieve the learning intention.
Hypothesis 1 – Place value is important for ordering numbers
Learning intention:
 Apply place value to write integers, decimal and negative numbers in numerical order
Knowledge:
GP 2 = Pupils will be taught how to read and write larger numbers
GP 3 = Pupils will be taught how to use place value to order decimals and negative numbers
GP 4 = Pupils will be taught how to order numbers including those with powers
GP5+ = Pupils will be taught how to order a mixture of numbers and FDP including powers
Success criteria:
GP 2-3 = Understand the place value of digits in small and large whole and decimal numbers by using the place value
headings and explaining the value of each digit. Write and read large numbers, spelling correctly. Say which number is
largest in sets of numbers and explain why – particularly with decimal numbers.
GP 3 = As above but include more complex decimals and negative numbers.
GP 4 = Apply knowledge of number size to order numbers and complete questions on powers of numbers and put a variety
of numbers with indices in the correct order.
GP 5+ = As above plus solve questions converting between FDP to write numbers and proportions in order.
Hypothesis 2 – Rules are not helpful when using negative numbers and all 4 operations
Learning intention:

Recognise and use relationships between operations for negative numbers
Knowledge:
ALL GP = Pupils will be taught handy division facts, how to utilise the multiplication tables and shown how using the
inverse of a number operation can be useful.
GP 2-3 = Delivery to recall how we add, subtract, multiply and divide with one negative number (using a number line)
GP 3 = Pupils will be shown tips and rules for adding/subtracting and multiplying/dividing with more than 1 negative
number
GP 4 = Pupils will be taught and apply the rules in order to carry out more complex calculations where they will apply
BIDMAS.
GP 5+ = Pupils will be shown how to solve problems with positive and negative numbers using inverse operations (real life
puzzles)
Success criteria:
GP 2 =Quick questions where pupils will develop understanding of how to do simple calculations using timestables and
division facts and number lines. They will solve questions with positive numbers before then applying their understanding
to questions with 1 to 2 negative numbers.
GP 3 = As above but pupils will solve problems calculating the answers to sums with all 4 operations and a mixture of
negative and positive numbers.
GP 4 = As GP 3 but pupils will be required to apply their knowledge in order to solve longer calculations without a
calculator using BIDMAS. These questions will include indices and roots.
GP 5+ = As GP 4 but pupils will also work with fractions/decimals and cube roots. These pupils will be given real life
calculations and will evaluate how to solve them.
Hypothesis 3 – Factors are a useful tool for division
Learning intention:
 Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors,
common multiples, highest common factor, lowest common multiple
Knowledge:
All GP – Pupils will be reminded of factors, multiples and primes
GP 2-3 = Pupils will be taught how to identify prime numbers and solve simple divisions without remainders
GP 3-4 = Pupils will be taught mastery in multiplication and division methods and shown how to use factors as divisors
GP 5+ = Pupils will be taught how to solve more complex calculations with and without a calculator and they will be
reminded of LCM and HCF (and how these can be used to help find solutions)
Success criteria:
ALL GP = Quick task for all pupils to identify and find factors, multiples and primes and define them with examples of their
own.
GP 2-3 = Understand and apply division facts from previous lesson in order to list prime numbers up to 100. Pupils will
then use a written method of short division to solve problems (without remainders or large numbers). Pupils will use the
grid multiplication method for solving 1 by 2 digit and 2 by 2 digit multiplications.
GP 3-4 = As above plus analyse how to use long division and multiplication of numbers 2 digits and higher and including
decimals and remainders.
GP 5+ = As GP 4 plus questions where they apply their knowledge of written arithmetic alongside their understanding of
factors and multiples in order to solve a variety of problems. Pupils will need to calculate HCF and LCM in order to help
them with division problems.
Hypothesis 4 – Estimation is useful when finding mathematical solutions (a good precursor to developing mastery of
rounding)
Learning intention:
 Check calculations using approximation and estimation, including answers obtained using technology
Knowledge:
All GP – Pupils will be reminded of how we can estimate solutions to simple problems (ignoring the normal rules of
rounding but instead applying rules of estimation for ease of calculation). All pupils will use estimation to check answers
and compare for accuracy.
GP 2-3 = Pupils will be taught how to estimate for simple questions involving all 4 operations for integers.
GP 4 = Pupils will be taught how to use estimation for all 4 operations including decimals and negative numbers.
GP 5+ = Pupils will be taught how to carry out complex calculations applying BIDMAS through estimation. Pupils will
calculate the percentage error against the actual accurate solution.
Success criteria:
GP 2-3 = Pupils will complete questions where they will estimate the answers to basic questions on a quick quiz. Pupils will
say which one they think is the closes answer and debate it by carrying out their own version of the ‘estimated’ sum. Pupils
need to show that they can re-write a calculation to make the numbers easier to work with mentally and find a close and
suitable solution. Pupils need to apply this so that they then understand how to check answers by applying skills in
estimation.
GP 4 = As above but pupils will work through harder questions including decimals, negatives and indices.
GP 5+ = As GP 4 plus tasks challenging the pupils carry out longer, more complex solutions then finding the exact answer
(with and without calculator questions) and comparing it to the estimate to find the percentage error.
Home learning: Given lesson 4 of each week and due in by lesson 4 of the following week.
Week 2
4 1hr lessons
plus 1hr
homework
For the first home learning tasks, pupils will do an online assignment using the ‘Stuck for schools’ website. Questions will
be based around all work done this week and will last for 1 hour. Videos and hints are available to support development.
Pupils will get instant feedback on their progress and have the opportunity to improve scores. This work can be set up to
suit their target GP but also challenge them to go beyond.
Line of Enquiry: What is the difference between decimal places and significant figures?
Lesson 1 (first half) of the week: Cognitive Acceleration Task
This ‘Count the Crayons’ activity gets pupils to think about why and how we use estimation
and helps them to develop this skill by thinking and discussing their ideas. (Resources are
in the drive)
Take a look at these pictures:
Estimate how many pencils/pens you can see in each one.
What was your method?
How else could you do it?
Is there one way that is particularly useful? Why?
For pupils who solve this quickly this web link on NRICH has games that will deepen their thought process of
working with numbers and all 4 operations and will ensure pupils start to think strategically.
http://nrich.maths.org/6606
Lesson 1 (second half): REACH – improving my numeracy knowledge (to be done after completion of CA task or
at any appropriate time within the first 2 lessons).
Pupils will use this lesson to engage with and respond to work marked and done the previous week. They will read through
teacher comments and respond by following a given set of criteria. This will allow them to make improvements on their
work, carry out corrections, seek help and make further progress before moving to the next unit of work. To extend their
knowledge of the content from week 1 pupils will be given examination type problems from the new GCSE specification at
and above their targeted grade point to stretch their comprehension. ‘Stuck for schools’ will also be used as REACH
activities and can be personalised in the level of difficulty.
Hypothesis 1 – It does not matter if there are many decimal places when rounding to 2d.p
Learning intention:

Round numbers and measures to an appropriate degree of accuracy using decimal places
Knowledge:
All GP – Pupils will reminded of how to apply the rules of rounding numbers.
GP 2-3 = Pupils will be taught how to round numbers (long and short) to the nearest whole, 10, 100 and 1000 and will
practice reading and writing very large numbers.
GP 3-4 = Pupils will be taught how to round small and large numbers to a number of decimal places.
GP 5+ = Pupils will taught how to apply rounding to large, complex calculations using a calculator.
Success criteria:
GP 2-3 = Understand how to round numbers using number lines with segment marking to support. Pupils will complete a
table of rounding questions where they will be given a range of different whole and negative numbers to round in different
ways. Pupils should be able to explain why they have rounded them that way and read out loud the larger numbers being
used as well as provide the place value of the digits.
GP 3-4 = As above plus pupils should be able to round short and long positive and negative decimal numbers to 1 and 2
decimal places.
GP 5+ = Pupils will use a calculator efficiently to solve large numerical problems that have decimal and whole solutions.
Pupils should be able to choose the most suitable way to round the number whilst thinking about accuracy and keeping
true to the value.
Hypothesis 2 – Rounding to significant figures is only done for integers
Learning intention:

Round numbers and measures to an appropriate degree of accuracy using significant figures
Knowledge:
All GP – Pupils will be taught how to apply rounding rules to the use of significant figures.
GP 2-3 = Pupils will be taught how to round small and large whole numbers to 1 and 2 significant figures.
GP 4 = Pupils will be taught how to round decimal numbers to any number of significant figures and how to identify the
number of significant figures within a given number.
GP 5+ = Pupils will taught how to apply rounding with S.F to large, complex calculations using a calculator.
Success criteria:
GP 2-3 = Understand the meaning of significant figures and define with examples. Pupils will be able to round numbers
from 2 digit to 4 digit positive whole numbers to 1 or 2 significant figures. Pupils can use calculators to solve a range of
sums then round answers to 1 and 2 significant figures.
GP 4 = As above plus pupils will be able to round decimal numbers to 1 or 2 significant figures and be able to explain what
happens when numbers have zero’s at the start or in the middle of a number.
GP 5+ = As GP 4 plus pupils will need to solve more complex calculations then round solutions to either a number or D.P.
or S.F. or both and compare for accuracy.
Hypothesis 3 – When finding limits we MUST follow the ‘5 or above’ rule
Learning intention:
 Apply and interpret limits of accuracy (higher)
For pupils following the Foundation route only or at lower GP, they will use this lesson to continue mastering
rounding with DP or SF and real life applications/calculations where rounding is needed.
Knowledge:
GP 4-5 = Pupils will be taught how to find the upper and lower bounds of numbers that have been rounded to a given
number of D.P (GP4) and S.F (GP 5).
GP 6 = Pupils will calculate the percentage error of the limits against the rounded value and actual value.
Success criteria:
GP 4-5 = Understand that when given a value that has been rounded, that it was previously a different value. Pupils will
firstly identify as many values as they can that the rounded number may have come from. Then pupils will discuss what the
maximum and minimum values could have been (limits/boundaries). Pupils will complete questions writing the upper and
lower limits/bounds of rounded numbers (whole numbers and simple decimals).
GP 6 = pupils will need to practice finding one number as a percentage of another and percentage change then apply this
to find the percentage error of the upper and lower bound.
Home learning: Given lesson 4 of each week and due in by lesson 4 of the following week.
Pupils will be given a task making a presentation on the real life uses of rounding. It must include examples of it being used
with demonstrations of how it has been rounded. Pupils will present in class.
Week 3
Line of Enquiry: How do we identify the different varieties of algebra and which rules to use?
4 1hr lessons
plus 1hr
homework
Lesson 1 of the week: REACH lesson – improving my accuracy and rounding knowledge
Pupils will use this lesson to engage with and respond to work marked and done the previous week. They will read through
teacher comments and respond by following a given set of criteria. This will allow them to make improvements on their
work, carry out corrections, seek help and make further progress before moving to the next unit of work. To extend their
knowledge of the content from week 1 pupils will be given examination type problems from the new GCSE specification at
and above their targeted grade point to stretch their comprehension. ‘Stuck for schools’ will also be used as REACH
activities and can be personalised in the level of difficulty. Prior learning will be ascertained in this lesson on basic rules of
algebra via a quick knowledge check quiz in order to asses current understanding and aid further planning and types of
resources (some pupils may understand algebra and be at a place where they can extend or apply current depth of
understanding).
Hypothesis 1 – Equations and formulae are both the same thing
Learning intention:

Understand and use the concepts and vocabulary of expressions, equations, formulae, identities (higher
content), inequalities, terms and factors
Knowledge:
All GP – All pupils will need to be taught about the key terms with examples and definitions; expressions, terms, equations,
formulae, inequalities, factors.
GP 2-3 = Pupils will be taught how to identify the key differences between an expression, equation and inequality.
GP 4-5 = Pupils will be taught how to identify expressions, terms, equations, formulae, inequalities and factors within
different algebraic situations.
GP 6 = Identities will be explained to these pupils plus all of the above.
Success criteria:
ALL GP = pupils will match up and complete definitions with the key terms and provide written examples.
GP 2-3 = Understand how to identify an expression, equation and inequality by sorting a variety of them into a table and
peer marking. Pupils will label expressions with terms. Pupils need to learn how to use inequality symbols to demonstrate
which number is larger and they can place these on an inequality line. Pupils can write sentences to match the inequality.
GP 4-5 = As above plus define and demonstrate with example understanding of the difference between an equation and a
formulae and the language associated with these within problems. Pupils can complete work sorting these into the correct
category and move on to working with inequalities and number lines.
GP 6 = As above plus identities.
Hypothesis 2 – The 4 operations of number behave in the same way when working with algebra
Learning intention:

Use and interpret algebraic notation, including all 4 operations, simplifying methods and indices; collect
like terms, simplify expressions following the rules of indices
Knowledge:
GP 2-3 = Pupils will be taught how to simplify expressions by collecting like terms. They will be reminded of how we use
notation for multiplying and dividing terms (and how to simplify simple cases).
GP 4-5 = Pupils will be taught how to simplify more complex sets of expressions involving indices.
GP 6 = Pupils will be taught how to simplify more complex sets of expressions involving indices and including fractional coefficients.
Success criteria:
GP 2-3 = Understand how to add and subtract terms by matching the letters. Pupils will be able to demonstrate that they
can collect like terms in order to simplify a long expression. These should include both positive and negative co-efficients.
Pupils will write expressions simply that involve division or multiplications. Pupils should write in their books the key rules
for simplifying with their own examples. GP 3 pupils may move on to collecting like terms with multiple letter terms such as
3ab + 6ab – 4a.
GP 4-5 = Pupils will complete work such as that for GP 3 pupils but will collect like terms involving indices such as
4p2 + 6p2 + 10p. Pupils should simplify simpler versions of terms with indices for multiplication and division.
GP 6 = Pupils should be able to demonstrate that they can simplify all of the above and apply their understanding to
evaluate how to simplify more complex expressions with fractions and decimals and a variety of indices such as
½ d + d2 + 6d2 – 3d + 1.5d2. Pupils at GP 6 will complete sets of questions applying the rules of indices for both
multiplication and division and apply the rules of BIDMAS to simplify larger, longer expressions with a range of operations.
Hypothesis 3 – Algebra is simply letters and does not create full sentences
Learning intention:

Be able to create and use written expressions/equations from written problems (to solve problems )
For pupils following the Foundation route at GP 2-3 only, they will use this lesson to continue mastering working
with the rules of algebra to deepen their understanding of how to simplify expressions. Pupils working well at GP
may follow the GP 3-4 path as REACH.
Knowledge:
GP 3-4 = Pupils will be taught how to write simple expressions from worded situations/problems.
GP 5 = Pupils will be taught how to write expressions and simple equations for worded situations/problems.
GP 6 = Pupils will be taught how to write larger more complex expressions in order to solve real life problems.
Success criteria:
ALL GP = For the first task to help gain an understanding of how an expression works, all pupils will be shown some
expressions and be asked to write them into words.
GP 3-4 = Pupils will be able to write expressions for simple situations and explain in full sentences such as, ‘The number of
clips in a tub plus 10 more’ = n+10 etc.
GP 5 = pupils should be able to write expressions as with GP 4 plus create an equation/formulae to solve a worded
problem such as ‘The cost C of hiring a car is £50 per 100 miles M plus a deposit of £80’ (C = 50m + 80). Pupils should
say which one the equation is and which one is the formula. An example of an equation would be ‘Sarah’s sister is X years
old. If Sarah is 9 years older than her sister and our total ages are 39, how old are they both?’ (X + X + 9 = 39, this
simplifies to 2X + 9 = 39, this could then be solved to find X and how old Sarah is).
GP 6 = As for GP 5 but for more complex situations that require different or more variables and powers.
LEARNING CYCLE ONE MIDTERM TO ALSO BE DONE THIS LESSON
Home learning: Given lesson 4 of each week and due in by lesson 4 of the following week.
This week pupils will complete a GCSE booklet with questions to deepen their mastery of the rules of algebra at their GP,
with real life applications to test understanding.
Week 4
Line of Enquiry: In what areas of life is substitution a useful skill?
4 1hr lessons
plus 1hr
homework
Lesson 1 of the week: REACH lesson – improving my midterm score
Pupils will use this lesson to learn from the mistakes made in their LC1 midterm.
Prior learning will be ascertained in this lesson on BIDMAS and extend into revising basic substitution in preparation for
the week’s activities.
Hypothesis 1 – The 4 operations of number behave in the same way when working with algebra
Learning intention:

Simplify and manipulate algebraic expressions; substitute values into expressions
Knowledge:
ALL GP = Pupils will be taught how to apply the rules of algebra in order to solve substitution problems.
GP 2 = Pupils will be taught how to substitute positive integers into expressions to solve problems.
GP 3-4 = Pupils will be taught how to substitute positive and negative integers into expressions to solve problems.
GP 5-6 = Pupils will be taught how to substitute positive and negative integers into expressions to solve problems including
the use of decimals, powers and fractions.
Success criteria:
GP 2 = Pupils will apply their knowledge of the rules of algebra and simplifying to substituting values into simple
expressions with positive numbers and all 4 operations.
GP 3-4 = As for GP 2 but pupils will also need to complete substitution questions with negative numbers and multiple
steps. GP 4 pupils should solve problems including powers and will need to apply the rules of BIDMAS.
GP 5-6 = Questions on substitution to be completed with positive, negative, fractional values, indices, brackets and
multiple steps. Pupils will develop by creating their own expressions for their peers to answer through substitution.
GP 6 REACH = pupils will be taught how to solve a simple trial and error problem using substitution to find the best
possible solution.
Hypothesis 2 – The 4 operations of number behave in the same way when working with algebra
Learning intention:

Simplify and manipulate algebraic expressions; substitute values into formulae
Knowledge:
This lesson will follow the same format as the previous lesson, but will involve the use of formulae.
GP 2 = Pupils will use simpler formulae when substituting values.
GP 3-4 = Pupils will substitute into formulae using all 4 operations.
GP 5-6 = Pupils will substitute values into more complex formulae testing their application of number and the rules of
algebra including brackets. Pupils will be taught how to rearrange formulae in order to find solutions for the other variables.
These pupils following the higher content will also create formulae from worded problems to deepen mastery (more for GP
6).
Success criteria:
All GP = As for previous lesson but with formulae rather than expressions.
Hypothesis 3 – I can crack any code! (Cognitive Acceleration lesson)
In this lesson pupils will complete a CA lesson on substitution linked to an activity provided by a resource bank
on ‘LET’s THINK’. An additional resource can be found on NRICH at this link; http://nrich.maths.org/2197
Home learning: Given lesson 4 of each week and due in by lesson 4 of the following week.
This week pupils will complete a fun practical code cracking activity and create their own algebraic codes.
Week 5
Line of Enquiry: Can the inverse method be used to solve all algebraic problems?
4 1hr lessons
plus 1hr
homework
Lesson 1 of the week: REACH lesson – improving my algebraic manipulation
Pupils will use this lesson to engage with and respond to work marked and done the previous week. They will read through
teacher comments and respond by following a given set of criteria. This will allow them to make improvements on their
work, carry out corrections, seek help and make further progress before moving to the next unit of work. To extend their
knowledge of the content from week 1 pupils will be given examination type problems from the new GCSE specification at
and above their targeted grade point to stretch their comprehension. ‘Stuck for schools’ will also be used as REACH
activities and can be personalised in the level of difficulty. Prior learning will be ascertained and developed in this lesson
on using the grid method and identifying factors.
Hypothesis 1 – Expand means to multiply by integers
Learning intention:
 Use and interpret algebraic notation, including all 4 operations; expand over a set of brackets (for higher,
expand sets of double brackets), factorise expressions by finding common factor terms
Knowledge:
GP 2-3 = Pupils will be taught how to expand a single set of brackets with positive factors
GP 4-5 = Pupils will be taught how to expand single sets of brackets with a variety of factors including indices and negative
factors. Some pupils at GP 5 may be able to factorise a simple expressions into a single bracket.
GP 6 = Pupils will be taught how to expand both single and double sets of brackets including indices and negatives. The
meaning of ‘quadratic’ should be explained. Pupils will develop by factorising sets of single brackets.
REACH: some pupils at high GP6 may be able to apply factorising to simple cases of quadratic expressions (quadratic
factorisation).
Success criteria:
GP 2-3 = Pupils will complete simple questions on multiplying terms together to gain further mastery of the rules of algebra.
They will need to demonstrate that they can find common factors within sets of algebraic terms (should they be able to
move onto simple forms of factorisation). Then pupils who are able and those at GP 3 will solve problems expanding single
brackets such as 4(x + 2). They can use normal multiplication or the grid method if they need support.
GP 4-5 = Pupils at this GP will solve questions multiplying (expanding) brackets with numerical and algebraic factors and
will need to evaluate how to apply previous work done on the rules of indices and multiplying with negatives. Questions
should look like 5m(m2 – 2mp). GP5 pupils can begin to reverse the process in order to factorise expressions by identifying
the HCF in the terms.
GP 6 = Pupils should be able to demonstrate competence in all of the above but apply it to expanding double brackets
such as (x + 7)(x – 8) and will solve problems at varying levels of difficulty to suit their understanding. REACH tasks will
involve factorising a quadratic for those who excel, but this topic will come along later in the year.
Hypothesis 2 – Using inverses is the best method to solve 1 and 2 step equations
Learning intention:

Solve linear equations with one unknown algebraically (1 step and 2 step using inverses)
Knowledge:
GP 2 = Pupils will be taught how to use inverses to solve numerical problems and simple 1 step equations.
GP 3 = Pupils will be taught how to use inverses to solve 1 and 2 step equations with simple solutions and positive
numbers.
ALL GP = All pupils will be reminded of how inverses work.
GP 4 = Pupils will be taught how to solve more difficult 1 and 2 step equations including decimal/fraction solutions.
GP 5 = Pupils will be taught how to solve 1 and 2 step equations including a set of single brackets.
GP 6 = Pupils will be taught how to apply BIDMAS to solve more complex 2 step equations with fractional co-efficients,
powers and roots.
Success criteria:
GP 2 = Pupils will begin to solve 1 step equations using inverse operations such as 5 + x = 11, then apply their knowledge
of substitution in order to ‘check’ their solutions. These equations will consist of smaller, positive numbers and should allow
pupils to demonstrate that they understand the rules of algebra and how inverses work (by solving equations of all types –
the 4 operations such as 3f = 12, x ÷ 2 = 10 etc.).
GP 3 = Pupils will solve a variety of 1 step equations like those for GP 2 and will apply this understanding to solve 2 step
equations using inverses, such as 4x + 6 = 18. A variety of equations that require these repetitive steps will be given so
that full mastery can be achieved.
GP 4 = As above but these pupils will need to demonstrate that they can solve 1 and 2 step equations with more difficult
steps and non-whole number solutions for X.
GP 5 = Pupils will need to recall how to expand a single set of brackets in order to solve equations such as 3(x + 7) = 21
etc.
GP 6 = Pupils should master all of the above and then complete problems solving equations using inverses again with
more difficult co-efficients such as ½ X – 7.5 = 20.5 etc. These pupils will be able to solve for solutions of X in equations
with indices such as 3X2 + 13 = 25 etc.
Hypothesis 3 – Balancing scales can help when solving equations with unknowns on both sides
Learning intention:


Solve linear equations with an unknown on both sides (higher)
Write simple equations/formulae to solve problems (higher)
Knowledge:
GP 2 - 3 pupils will continue mastering 1 and 2 step equations moving up through varying levels of difficulty
before attempting simple single step versions of equations with unknowns on both sides.
GP 3-4 = Pupils will be taught how to use the balancing method (elimination) to find the solution of double sided equations.
These will be of a simpler format with integer answers and small steps.
GP 5-6 = Pupils will be taught how to use both the balancing and inverse methods to solve equations with an unknown on
both sides. These questions will be more difficult with decimal/fractional solutions and have multiple steps including
brackets.
GP 6 REACH = Pupils will be taught the skills to break down a worded problem then create an equation in order to make
sense of it mathematically and find a solution.
Success criteria:
GP 2-3 = Pupils will continue to practice and master a range of 1 and 2 step equations, gradually getting through harder
problems until they develop full independence.
At GP 3 once mastery is achieved, these pupils may work on some problems solving an equation with an unknown on both
sides such as 2X + 6 = X + 14 (either using the balancing or inverse method depending upon the pupil and their
confidence). There will be no subtraction questions and solutions will be simple whole numbers. Co-efficients will not go
higher than 2.
GP 4 = As GP 3 but pupils will develop further by solving equations such as 3X - 4 = X + 4 etc. These have subtraction and
larger co-efficients.
GP 5-6 = Pupils will complete a range of double sided equations with addition and subtraction, larger co-efficients and
decimal solutions for X.
GP 6 REACH = Pupils will develop their understanding of how equations work and why they are so useful for solving
problems by creating equations for worded written problems.
Home learning: Given lesson 4 of each week and due in by lesson 4 of the following week.
Week 6
4 1hr lessons
including end
of term exam.
This week pupils will have a graded revision booklet on LC1 content which will be worked through and marked with peers
at the start of week 6.
This week all lessons will be based on GCSE questions from past papers and new specification examples to develop the
application of algebra and number. Pupils will take part in problems solving tasks and simple proof work. This will help
them to put all of these skills to practice and will help them with exam strategy. It will also be a focus where they can use
their learning to answer the challenge question.
Hypothesis – (algebra problem solving) To utilise algebra is to abbreviate long sentences
Learning intention: Use smaller numbers and algebraic expressions to solve problems such as:
Answer the overarching challenge question: ‘How useful will algebra be to me?’
Lessons 3 and 4 will be used for exams
Gap Analysis Reinforcement
Gap
As seen in the lesson activities each week, gap teaching will not just be at the end of the semester after exam analysis has
Reinforcement taken place. Gap teaching is an integral part to each unit of work and will consist of summary sheets, mini-tests and tasks
in week 7
where gaps can be filled and REACH activities can be delivered.
Extended Learning
Extended learning will in a variety of forms. During home learning pupils may be asked to use the following sites where they complete quick quizzes, CIMT
tasks, GCSE style questions and more open ended problem solving tasks.
1) Levelled quizzes http://www.educationquizzes.com/ks3/maths/
2) Lots of maths online help and activities – as well as mini tests http://www.bbc.co.uk/schools/websites/11_16/site/maths.shtml
3) http://uk.ixl.com/math/year-7 This link is useful for additional revision and practice on all areas of maths. For LC1 pupils should click on the
Geometry areas for practice questions.
4) www.onlinemathlearning.com
5) https://corbettmaths.com/more/gcse_practice_papers/
6) www.studymaths.co.uk