Unit Summary In this unit students will revisit the simplification of expressions involving sums, products and powers including the use of index laws as well as working with fractional and negative indices and performing exact calculations with surds. Students will further learn to simplify expressions with surds as well as expand single and double brackets where one, or more, terms are surds and use this skills to rationalise the denominator of an expression which contains a surd. Extend students will also find and use the nth term of a geometric sequence rn where r is a surd as well as solve more complex problems. Big Idea – none | |
Knowledge (Curriculum content) | Simplification of expressions involving sums, products and powers as well as use of the index laws, calculations with indices including those which are negative, fractional and a combination of both. Calculations with exact solutions expressed as surds and simplification such expressions. Expanding single / double brackets where one, or more, terms is a surd and the rationalisation of an expression where the denominator is a single surd or contains a surd. Calculating of the nth term of a geometric series where the common ratio is a surd. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 1 – Surds and indices
12 hours - Autumn 1
A core (H) student should also be able simplify expressions involving sums, products and powers as well as using the index laws. Calculations involving combinations of fractional and negative indices. Expressing exact solutions in surd form and simplification of these expressions. Expanding brackets where one or more term is a surd and rationalisation of an expression where the denominator is a single surd.
A extension student is also expected to be able to solve complex indices problems to find the value of k, use and find the nth term of a geometric sequence (where the common ratio, r, is a surd) and rationalise more complex expressions where the denominator contains surds.
Unit Summary In this unit students will practise working with straight line graphs using the general form y = mx + c to solve a range of problems including identification of the equation of a linear function by inspection of its graph, finding the equation of a linear function given two points on the line, finding the equation of a linear function given the gradient (or parallel line) and a point and using the general form to identify parallel and perpendicular lines. Students will also plot graphs of quadratic functions, simple cubic functions, reciprocal and exponential functions and represent the solution of a single linear inequality in two variables on a graph. Big Idea – none | |
Knowledge (Curriculum content) | Identification of the equation of a linear function from its graph, finding the equation of a linear function in the general form y = mx+c if the gradient and a point are known, two points are known, the gradient of a parallel line and a point are known. Finding the equation of a parallel line and perpendicular line through a point. Plotting quadratic, simple cubic, reciprocal and exponential functions and recognising key features of their graphs. Representing the solution of linear inequalities on a graph. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 2 – Drawing graphs and graphing inequalities
12 hours - Autumn 1
A core (H) student should also be able identify the equation of a linear function by inspecting its graph, find the equation of a linear function if the gradient and a point, two points or the gradient of a parallel line and a point are known and express this equation in the form y = mx+c. They should also be able to find the equation of parallel and perpendicular lines as well as plot quadratic, cubic, reciprocal and exponential functions and simple linear inequalities on a graph.
A extension student is also expected to be able to solve more complex problems finding the equation of linear functions as well as describe the key features of quadratic, cubic, reciprocal and exponential functions and how their graphs vary. They should also be able to represent the solution of linear inequalities in two variables on a graph by finding the region.
Unit Summary In this unit students study quadratic functions including their graphs, solutions and inequalities. Students will learn to manipulate the equations of quadratic functions into a range of different formats (some of these skills of which will support and link into future units of study). Students will also gain an insight into practical scenarios in which quadratic equations can be used to model real life situations and how to interpret (and sometimes disregard) solutions obtained. Big Idea – none | |
Knowledge (Curriculum content) | Expansion of the product of two (or more) binomials, factorisation of a quadratic expression ax2 + bx + c (a ≥1) including using the different of two squares, solving of quadratic equations (a ≥1) through use of the quadratic formula, factorisation and completing the square and discussion of approximate and exact solutions. Ensuring that quadratic equations can be re-arranged in order to be solved, finding approximate solutions using graphical methods, solving quadratic inequalities and one variable and representing solutions on a graph. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 3 – Solving quadratics
12 hours – Autumn 2
A core (H) student should also be able expand the product of two, or more, binomials, factorise quadratic expressions into double brackets (including the difference of two squares), solve quadratic equations (including re-arranging first if needed) through the use of the quadratic formula, factorisation or completing the square and solving equations graphically. In addition students should be able to solve quadratic inequalities.
A extension student is also expected to be able to factorise more complex expressions and recognise more complex expressions which can be written as the difference of two squares and apply this to problem solving questions. They should also be able to represent the solution of a quadratic inequality graphically.
Unit Summary In this unit students will learn to solve functional and theoretical problems relating to the area and circumference of circles and the area, arc length and perimeter of sectors of sectors. Students will be able to find dimensions such as the radius or diameter of a circle, or the radius of a sector or arc when given information about the circumference or area of the circle or the arc length or area of the sector. Students will also apply knowledge of trigonometry to find the area of a segment. A focus will be given on solving practical problems as well as accurate notation and re-arrangement of algebraic equations. | |
Knowledge (Curriculum content) | Finding the area and circumference of circles (and reverse engineering to find the radius or diameter), recap of names of key parts of circles, calculations of the area of a sector of a circle, the length of an arc (and reverse engineering to find the radius), finding the perimeter of a sector, finding the perimeter of a sector when given the area (and vice–versa), finding the area of a segment. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 4 – Arcs and sectors
10 hours – Autumn 2
A core (H) student should be able to solve functional problems by finding the area or perimeter of compound shapes including parts of circles, to be able to find the radius or diameter of a circle when given the circumference or area, calculate the area of sectors and the length of an arc as well as finding the perimeter of a sector when given the area (or vice-versa).
A extension student is also expected to be ablofind the
Knowledge (Curriculum content) | Ordering |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 5 – Circle theorems
10 hours – Autumn 2
A core (H) student should also be able
A extension student is also expected to be able to
Knowledge (Curriculum content) | Ordering |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 6 – Similarity and congruence
10 hours – Spring 1
A core (H) student should also be able
A extension student is also expected to be able to
Knowledge (Curriculum content) | Ordering |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 7 – Complex transformations of shapes
10 hours – Spring 1
A core (H) student should also be able
A extension student is also expected to be able to
Knowledge (Curriculum content) | Ordering |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 8 – Conditional probability
10 hours – Spring 1/2
A core (H) student should also be able
A extension student is also expected to be able to
Knowledge (Curriculum content) | Ordering |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 9 – Volume and algebra
10 hours – Spring 2
A core (H) student should also be able
A extension student is also expected to be able to
Knowledge (Curriculum content) | Ordering |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 10 – Bounds and compound measures
10 hours – Spring 2
A core (H) student should also be able
A extension student is also expected to be able to
Knowledge (Curriculum content) | Ordering |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 11 – Graphs of circles
10 hours – Summer 1
A core (H) student should also be able
A extension student is also expected to be able to
Knowledge (Curriculum content) | Ordering |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 12 – Linear and quadratic simultaneous equations
13 hours – Summer 1
A core (H) student should also be able
A extension student is also expected to be able to
Unit Summary In this unit Big Idea – Counting (start of unit), Dropping a penny off the Empire State Building (end of unit) | |
Knowledge (Curriculum content) | Ordering |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (H) - Unit 13 – Histograms, cumulative frequency and box plots
13 hours – Summer 2
A core (H) student should also be able
A extension student is also expected to be able to