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Intent
Intent
The intention of this unit is build on and increase the level of rigour in students' mathematical understanding from Key Stage 3, whilst introducing new Key Stage 4 concepts.
Students develop a flexible understanding of percentage multipliers to solve a range of abstract and financial problems
Students extend their understanding of transformations to include negative scale factors, invariant points and transformations of graphs.
Students extend their algebraic manipulation to algebraic fractions and their equation solving to simultaneous equations.
Students extend their trigonometric reasoning and problem solving to non-right-angled triangles.
Students extend their ratio and proportional reasoning to formulae for direct and inverse proportion
Students extend their angle reasoning to proving congruency and appreciate the links with trigonometry.
Students extend their reasoning with rounding to upper and lower bound calculations
Implementation
Implementation
To develop students as independent learners this unit of work covers three terms with a period of revision before a substantial assessment in term 3. This require students to take ownership of their mathematical understanding and engage in a process of identifying gaps and improving ahead of the tests.
From the 3rd week of the unit students will complete a weekly knowledge check so they can measure how their knowledge and expertise is building. The content of the knowledge checks updates as more concepts are covered, to provide a rolling check of what students can recall.
During this unit there will also be several longer written homework tasks which include a knowledge check as well as problem solving questions. Students will have an opportunity to follow-up and improve their work on these homework tasks.
Impact
Impact
The impact of this unit of work will be measured through a Three 45 minute written assessments in term 3
The assessment will cover every aspect of the unit of work and using the knowledge organiser together with this website is a great way to prepare for the tests.
A shorter mid-term assessment in term 1 provides students with a indication of their progress with the unit. Students can use their feedback from the min-term to prepare for the assessments at the end of the unit.
Topics covered in this unit:
Star / Star*
Star / Star*
26n Finding any percentage of an amount by combining simple percentages
38n Converting between decimals and percentages (and to fractions)
25a Simplify expressions by applying standard algebraic notation
27a Substitute positive whole numbers into simple expressions or formulae and evaluate
23n Use a written method of multiplication with 2/3 digit whole numbers
11n Recognising which operation is required for a word problem
Core
Core
51n Increase or decrease an amount by a percentage and calculate simple interest
65n Calculate compound interest using repeated percentage change
66n Writing a change as a percentage
70n Calculate compound interest using a percentage multiplier
71n Reverse percentage change using a multiplier (or otherwise)
52n Putting fractions, decimals and percentages in order
56n Converting fractions to terminating decimals or percentages by short division
20s Draw all the lines of symmetry on 2D shapes
54s Rotate a shape from a given centre on a coordinate grid and fully describe a rotation
48s Translate a shape by a vector on a coordinate grid and describe a translation
29a Simplify expressions by collecting terms
33a Simplify expressions by multiplying terms
32a Solve equations formally by using 1/2 inverse operations
48a Solve equations with x on both sides and solving inequalities by algebraic manipulation
60a Solve difficult linear equations with brackets and fractions
55a Changing the subject of a formula by using 1/2 inverse operations
64a Solving linear simultaneous equations by elimination
65a Derive and solve simultaneous equations from word problems
51s Use Pythagoras' theorem to find hypotenuse or short side or check if a triangle is right-angled
62s Use SOH CAH TOA trigonometry to calculate sides of right-angled triangles
63s Use SOH CAH TOA trigonometry to calculate angles in right-angled triangles
71s Solve problems requiring multiple steps of SOH CAH TOA trigonometry and/or Pythagoras
73s Know the exact values for 0⁰, 30⁰, 45⁰, 60⁰, 90⁰ for sin, cos and tan
44a Using the nth term rule of a sequence to find a given term
46a Finding the nth term of an arithmetic sequence
27n Simplifying ratios and identifying fractions from ratios
40n Share a quantity in a two part or three part ratio
41n Solve ratio problems without the original amount
59n Solving problems using a combination of percentages, fractions and ratio
73n Solve hard ratio problems involving combining two or more ratios
46n Use an exchange rate to convert between currency
50a Use graphs of direct or inverse proportion or solve inverse proportion problems
72a Use and interpret an equation or graph for direct or inverse proportion
59a Write or plot a linear function for a given ratio
26s Use the sum of angles at a point or on a line or vertically opposite to calculate angles
32s Know and use the sum of angles in a triangle or quadrilateral to work out angles
70s Know the proofs of angles sums in triangles or quadrilaterals
74s Recognising congruent triangles using SSS, SAS, ASA or RHS
40d Distinguish between types of data: discrete, continuous and categorical
65d Define random sample and explain a method of selecting a random sample
56d Draw up and use a two-way table from a list of information
55d Draw up a frequency tree from a list of information and use it to solve problems
61n Dividing by decimals using an equivalent calculation and short division
62n Use inequalities to specify error due to truncation or rounding
37n Multiplying and dividing integers
44n Using a calculator correctly with powers, roots and division
Plus / Plus+
Plus / Plus+
79s Enlarge a shape by a negative scale factor from a given centre
81s Describe change or invariance under a combination of transformations
81a Simplifying algebraic fractions by factorising then cancelling
83a Simplifying algebraic fractions by adding or subtracting
93a Solve algebraic fraction equations which lead to quadratic equations
86a Rearrange a formula where the subject appears more than once
94a Solve non-linear simultaneous equations
71a Form the equation of a line through two points or through one point with a given gradient
82a Recognise perpendicular gradients and form the equation of a line perpendicular to a given line
90a Sketch transformations of graphs (translations, reflections) including images of intercepts
91a Interpret transformations of polynomial or trig graphs
91s Using SOH CAH TOA trigonometry in 3D Shapes
82s Know Sine rule and use it to calculate missing sides in non-right-angled triangles
83s Know Cosine rule and use it to calculate missing sides in a non-right-angled triangle
85s Know Sine rule and use it to calculate missing angles in non-right-angled triangles
94s Deal with the ambiguous case in Sine rule
86s Know Cosine rule and use it to calculate missing angles in a non-right-angled triangle
84s Using the area of a triangle formula ½abSin C including finding the area of a segment
93s Solve multi-step Sine / Cosine rule questions involving area or perimeter
78a Finding the nth term of a quadratic sequence
88n Recognising a geometric sequence where the common ratio is a surd
72a Use and interpret an equation or graph for direct or inverse proportion
76n Stating the upper and lower bounds of a rounded number or measurement
80n Calculating an upper or lower bound for xy or x/y
85n Using upper and lower bounds to round to a suitable degree of accuracy
89n Calculating an upper or lower bound in the context of a shape or measure problem
Mid-term Test - Revision Checklists
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