Hathershaw College

Maths

Maths

 

Curriculum Intent

 

  • Educate students on the origins of mathematics and to view it as a work in progress, the future discoveries of which will invariably shape how we view the world
  • Giving purpose to the theory of mathematics through application to some of history’s most intriguing problems
  • To promote high cultural capital by encouraging students to pursue careers in maths and other STEM subjects, which would enable them to make a positive contribution to society
  • To provide students who are lower attaining on entry with high levels of financial literacy that they can adapt into everyday life, such as managing monthly budgets by taking into account rent, mortgage, gas, electric and food bills.
  • To develop an inquisitive mindset through a desire to understand the deep roots of mathematics, thus encouraging students to foster a lifelong love for the subject
  • To inspire students to pursue further education in maths, hence lifting students out of an area of poverty and into an environment where they build a high quality of life for themselves and their family.
  • Provide students from deprived families with appropriate mathematical equipment so that lack of family income does not become a barrier to learning
  • To empower students to solve problems in more than one way by their ability to interleave topics and to treat the question “why?” as the most powerful tool to conceptually understanding a given branch of mathematics. This will challenge students continuously to become more confident, resilient and reflective learners
  • Promoting communication skills by integrating opportunities in lesson to reason and debate – a skill many students lack in an area where oracy on entry is below national average
  • Instil an ethos where students are encouraged to work independently and collaboratively to break down complex mathematical problems into small steps

 

Curriculum Overview

HT1 HT2 HT3 HT4 HT5 HT6
Y7

Algebraic Thinking

Students will form relationships between number and pictorial patterns.

Generalising numbers using letters comes next, followed by solving equations
Rich task: Fibonacci

 

Place Value

Exploring integers up to one billion, decimals to hundredths and standard index form.
Understanding of the links between fractions, decimals and percentages.

 

Applying Number

This unit builds on the formal methods of numeracy from KS2.
Extending their knowledge from HT1, students will transition to solving further equations.

 

Number/Fractions

Multiple representations and contexts will be used to give meaning to negative integers.
Fraction addition and subtraction will be explored. Rich Task: Unit Fractions

 

Lines/Angles

Students will use equipment to measure increasingly complex diagrams, before delving into letter notation.
Finally, basic geometric language and reasoning will be explored.

Number Reasoning

Students will adapt number facts to algebraic contexts.

FDP equivalence will be explored in probability, followed by work on primes.
Rich Task: Prime number commonality

 
Y8

Proportion

This unit focuses on using various models to represent and manipulate ratio. Students will advance to scaling before finishing with further fraction work.
Rich Task: Proportion

 

Representations

Students will study the Cartesian plane and its properties.
Applications to correlation will follow before ending with a brief introduction to tabular probability.

 

Further Algebra
Simplifying algebraic expressions and solving equations will build on prior knowledge from Y7. Sequences and index expressions will follow. Rich Task: Solving Equations

Developing Number
Percentage change and percentages in reverse will begin the unit, followed by working in standard index form and powers of 10. Rich Task: Percentage equivalences

Developing Geometry
This unit will challenge students to understand angles formed using parallel lines. Area of trapezia and circles will follow, with students finishing on lines of symmetry. Rich Task: Parallel Lines Inquiry

 

Data Reasoning
Comparing and designing, and critiquing data charts comprises most of this unit, followed by a more in depth analysis of averages in relation to statistics.
Y9

Graphs/Equations

/Conjectures
Students will learn about the equation of a line and how it links to graphs. Following this, further exploration of solving and manipulating algebraic equations will stretch students, with the block finishing with finding the product of two binomials

Shape/Constructions
Continuing work from Year 8, students will find the area and volume of 3-D figures before learning about equal distances and loci of shapes. The block will finish with constructions of basic triangles

 

Number/Percentage

/Money
A recap of basic number problems will start the term, followed by various methods of calculating percentages of numbers and percentage change. Maths applied to money will follow

Deduction/Transf./

Pythagoras
Angle problems revision from Year 8 will help retrieve key skills to access the challenging problem solving angle questions later. Transformations will follow before further work on right angled triangles

Similarity/Ratio/

Probability
Students will learn to enlarge shapes by various scale factors before moving linking the ratio they learnt to more abstract ratio problems. To finish the unit students will delve into probability and the various calculations of events

 

Algebraic Represent.
This unit will be comprised of graphical representations of inequalities and various polynomials. Simultaneous equations will also be explored graphically

 

 

HT1 HT2 HT3 HT4 HT5 HT6

Y10

F

Congruence/

Similarity/

Trigonometry
Students will explore areas and volumes of similar shapes and work fluently with trigonometry, revisiting KS3 knowledge of Pythagoras. Higher tier students will cover the sine and cosine rule.

 

Inequalities/Simultaneous Equations

Solve and interpret solutions to equations and inequalities, solve simultaneous equations both algebraically and graphically.
Higher tier students will solve quadratic inequalities and simultaneous equations.

 

Angles/Circles/Vectors

Students will build on their KS3 knowledge of angles to draw and interpret scale drawings. They will then find lengths of arcs and areas of sectors. Higher tier students will begin learning the first four circle theorems. Students will begin to look at vector journeys.

Ratio/Fractions/

Percentages/Probability
Solve problems with ratios, percentages and fractions, including currency conversions. Higher tier students will look at ratio in area and volume problems, as well as iterative processes. All students will expand on KS3 probability by calculating probabilities from Venn and tree diagrams.

Data/Non Calc Methods
Understanding populations and samples, constructing diagrams to represent and interpret data. Higher tier students will construct and interpret histograms and cumulative frequency diagrams. Students will explore fraction arithmetic and bounds.  

Number/Indices/

Manipulating Expressions
Exploring indices, roots and numbers in standard form. Describing and continuing sequences – higher tier students exploring sequences involving surds, algebraic fractions and proof.

Y11

F

Probability/

Reasoning
Students will expand on their KS3 knowledge of probability before finishing the term with multiplicative reasoning topics such as compound interest

Constructions/

Algebra
Construct 2D shapes, draw loci and know and use bearings.  Expand, factorise and solve quadratic equations. Find turning points & roots.

Area/Volume/SF
Area, perimeter and volume of shapes that involve circles.   multiplying and dividing fractions, before learning advanced index laws

Standard form/vectors
Students will learn standard form before learning similar shapes and vector notation of moving objects

Further Algebra
Plotting non-linear graphs starts the unit before moving onto rearranging difficult formulae and simultaneous equations

 

GCSE Examinations

 

Y11

H

 

Further Trigonometry
Trig functions/graphs and learning sine rule, cosine rule and formula for finding area of any triangle

Data/Algebra

Questionnaires, sampling and representing data using cumulative frequency/histograms.

Algebra/Circles
Students will expand and plot further algebra expressions and equations before moving onto circle geometry

Vectors/Functions
Students will stretch their knowledge of complex algebra and surds before delving into vector notation and proof

Graphs/Proportion
Starting with analysing the area under a curve, students will explore acceleration

GCSE Examinations

 

To download this table, please click below.

Curriculum Overview 2022-2023

 

Medium Term Plans

 

 

 

 

 

 

 

 

 

  

Maths

 

Spiritual development in Mathematics

The study of mathematics enables students to make sense of the world around them and we strive to enable each of our students to explore the connections between their numeracy skills and every-day life. Developing deep thinking and an ability to question the way in which the world works promotes the spiritual growth of students. Students are encouraged to see the sequences, patterns, symmetry and scale both in the man-made and the natural world and to use maths as a tool to explore it more fully.

Moral development in Mathematics

The moral development of students is an important thread running through the mathematics syllabus. Students are provided with opportunities to use their maths skills in real life contexts, applying and exploring the skills required in solving various problems. For example, students are encouraged to analyse data and consider the implications of misleading or biased statistical calculations. All students are made aware of the fact that the choices they make lead to various consequences. They must then make a choice that relates to the result they are looking for. The logical aspect of this relates strongly to the right/wrong responses in maths.

Social development in Mathematics

Problem solving skills and teamwork are fundamental to mathematics through creative thinking, discussion, explaining and presenting ideas. Students are always encouraged to explain concepts to each other and support each other in their learning. In this manner, students realise their own strengths and feel a sense of achievement which often boosts confidence. Over time they become more independent and resilient learners.

Cultural development in Mathematics

Mathematics is a universal language with a myriad of cultural inputs throughout the ages. Various approaches to mathematics from around the world are used and this provides an opportunity to discuss their origins. This includes different multiplication methods from Egypt, Russia and China, Pythagoras’ Theorem from Greece, algebra from the Middle East and debates as to where Trigonometry was first used. We try to develop an awareness of both the history of maths alongside the realisation that many topics we still learn today have travelled across the world and are used internationally.

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