## Shape

Units, Measurements and Drawing Area and Volume Pythagoras and Trigonometry Congruence and Similarity Transformations Shape and Angle Properties (2D) Shape and Angle Properties (3D) Constructions Vectors ## Calculation and MeasuresPythagoras and Trigonometry
Pythagoras' Theorem
Use Pythagoras’ Theorem to solve problems involving right-angled triangles (KS3)Apply Pythagoras’ Theorem to find lengths in right-angled triangles and in two-dimensional figures (KS4) Coming soon. Trigonometry in Right-Angled Triangles
Use trigonometric ratios in similar triangles to solve problems involving right-angled triangles (KS3)Apply trigonometric ratios to find angles and lengths in right-angled triangles and in two-dimensional figures (KS4) Exact Trigonometric Values
Know the exact values of sin θ, cos θ and tan θ for θ = 0, 30, 45, 60, 90 degrees (KS4)Pythagoras and Trigonometry in 3D (H)
Apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles (and, where possible, general triangles) in three dimensional figures (KS4 Higher only) Sine and Cosine Rules (H)
Know and apply the sine rule and cosine rule to find unknown lengths and angles (KS4 Higher only)Coming soon. Area of a Triangle using 1/2 ab sin C (H)
Know and apply area = 1/2 ab sin C to calculate the area, sides or angles of any triangle (KS4 Higher only)Coming soon. ## Properties and ConstructionsCongruence and Similarity
Congruence and Similarity
Know and use the criteria for congruence of triangles (KS3)Identify and construct congruent triangles (KS3) Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides and use known results to obtain simple proofs (KS3) Apply the concepts of congruence and similarity, including relationships between lengths, in similar figures (KS4) Coming soon. Similar Areas and Volumes (H)
Apply the concepts of congruence and similarity, including the relationships between areas and volumes in similar figures (KS4 Higher only)The Unbelievable Bulk (alutwyche via TES)A great investigation about "The Unbelievable Bulk" and "Doctor Tanner" - students find how cross the Bulk is based on his size by calculating the scale factor of enlargement. This also has a nice extension about surface area and volume. NRICH**Growing rectangles**: Investigating how enlargement affected area and volume by looking at different sizes of rectangles. Great for extension or whole-class investigation**Who Is The Fairest Of Them All:**Brilliant for a bit of enlargement practise, with scope to develop further.
Transformations
Translations, Rotations and Reflections
Identify properties of, and describe the results of translations, rotations and reflections applied to given figures (KS3)Describe translations as 2D vectors (KS4) Transformation package (TristanJones via TES)Lovely bank of worksheets - pupils complete transformations on a selection of shapes to spell out a word in the centre of the page. Always popular whenever I use these. Transformation puzzle (ECBayliss via TES)Similar puzzle with a combination of rotations, reflections and translations. Transformation interactives (EChalk via Eduqas)**Reflections**: Superb interactive for demonstrating reflections, with moveable shapes and mirror lines.**Rotations**: Similar interactive for demonstrating rotations.
Transformation interactives (TeacherLED) **Translation**: Simple interactive for demonstrating translations in words or as vectors.**Virtual tracing paper**: Great for demonstrating how to use tracing paper to complete reflections and rotations.
Enlargement by Positive Scale Factor
Construct similar shapes by enlargement, with and without coordinate grids (KS3)Interpret and use fractional scale factors for enlargements (KS4) Spell a Word (whidds via TES)These really are great - students carry out the required transformations which creates a picture of a related word (in this case, SIZE). Whenever I've used these, students have found them very engaging. The worksheet on enlargement does include two negative scale factors, but students can "guess" these at the end, leading to a good discussion about how negative scale factors work.Coming soon. topic or as quick revision. Inside Maths (via STEM Centre)Video with many practical applications of enlargement, as well as flagging up and looking at misconceptions with a few common exam questions. Middle of Centres (Transum)A nice little starter looking at finding the centre of enlargement. Note that you need to scroll down to the "advanced" problem. Photographic Enlargements (STEM centre)Useful for a bit of quick-fire questioning as a starter or plenary. Your computer will tell you when you download the application that it might be a virus - don't worry, it's not (it's flagged because it's an infrequently downloaded .exe file). There are also some explanatory notes available here. Requires registration with the National STEM centre, which is free and full of great resources.Enlargement by Negative Scale Factor (H)
Interpret and use negative scale factors for enlargements (KS4 Higher only)Fractional and negative SF - spell a word (alicecreswick via TES)Five question grids with problems on fractional and negative enlargements, which spell out the letters MATHS. 8-bit Mario negative enlargements (solvemymaths)Great practice using negative scale factors to produce an 8-bit picture of Mario. Negative scale factor enlargement worksheets (eChalk)Free printable worksheets - saves a considerable amount of time drawing graphs and grids. Enlargement with Negative Scale Factors (alutwyche via TES)Quick, simple printable worksheet. Enlargement worksheet - negative scale factors (HolyheadSchool via TES)Standard worksheet with lots of negative scale factor practice. Diagrams will need copying into books. Maths takeaway booklet - Enlargements by negative scale factor (KESH)Exam questions for Edexcel 1MAO specification; valid for all 2015 GCSE specs. Revision booklet (CorbettMaths)QR linked to video revision; old spec but still valid. Enlargement scale factor root 2 (Don Steward)While not a negative enlargement problem, I've included this here as it's a really nice, challenging problem with lots of scope for links to other topics. Enlargements teaching tool (EChalk via Eduqas)This interactive has options to select negative scale factors, and show/hide centre of enlargement, scale factor and coordinate axes; the best I've found for demonstrations. Invariance (H)
Describe the changes and invariance achieved by combinations of rotations, reflections and translations (KS4 Higher only)Invariance activity sheet (Peter Mattock via TES)A RAG worksheet around identifying invariant points on different transformations, incorporating a CLOZE activity (fill in the blanks), a matching activity, and a Venn Diagram activity Shape and Angle Properties (2D)
Angles Around a Point, on a Line and in a Triangle
Apply the properties of angles at a point, angles at a point on a straight line and vertically opposite angles (KS3) Derive and use the sum of angles in a triangle (KS3) Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles (KS3) Coming soon. Angles in Parallel Lines
Understand and use the relationship between parallel lines and alternate and corresponding angles (KS3)Coming soon. Properties of Triangles
Use the standard conventions for labelling the sides and angles of triangle ABC (KS3) Derive and illustrate properties of triangles (for example, equal lengths and angles) using appropriate language and technologies (KS3) Identifying types of triangle (greatschools.org)Straightforward simple practice worksheet identifying equilateral, isosceles, scalene and right-angled triangles. Properties of Quadrilaterals
Derive and illustrate properties of quadrilaterals and other plane figures (for example, equal lengths and angles) using appropriate language and technologies (KS3)Properties and Angles in Polygons
Describe, sketch and draw using conventional terms and notations: regular polygons, and other polygons that are reflectively and rotationally symmetric (KS3) Deduce the angle sum in any polygon, and to derive properties of regular polygons (KS3) Circle Properties
Derive and illustrate properties of circles using appropriate language and technologies (KS3) Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment (KS4) Coming soon. Circle Theorems
Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results (KS4 Higher only)Coming soon. Shape and Angle Properties (3D)
Faces, Vertices and Edges
Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D (KS3)3 dimensional shapes (greatschools.org)Pupils identify vertices on common 3D shapes. They could also identify faces and edges, and cut out/stick the sheet into their exercise books with the properties listed. Plans and Elevations
Construct and interpret plans and elevations of 3D shapes (KS4)Isometric drawing tool (Illuminations)An absolutely fantastic interactive isometric drawing tool; create shaded isometric drawings or 3D cube models, rotate and automatically generate plans and elevations. Constructions
Constructions
Derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle)Recognise and use the perpendicular distance from a point to a line as the shortest distance to the line (KS3) Coming soon. Shape: Vectors
Vectors
Vector calculationsApply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors (KS4) Vector proofs (H)Use vectors to construct geometric arguments and proofs (KS4 Higher only) Probability
Probability Basics
The probability scale Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale (KS3) Understand that the probabilities of all possible outcomes sum to 1 (KS3) Mutually exclusive events Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one Simple sets and Venn diagrams Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams (KS3) Theoretical and Experimental
Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities (KS3) Use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size (KS4) Independent and Conditional
Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions (KS4) Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams (KS4 Higher only) Statistics
Presenting Data
Simple charts and graphsConstruct and interpret frequency tables, bar charts and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data (KS3) Pie chartsConstruct and interpret pie charts for categorical data (KS3) Time-series graphsInterpret and construct tables and line graphs for time series data (KS4) Scatter graphsDescribe relationships between two variables and illustrate using scatter graphs (KS3) Recognise correlation and know that it does not indicate causation (KS4) Draw estimated lines of best fit, make predictions Interpolate and extrapolate apparent trends whilst knowing the dangers of so doing Cumulative frequency and box plots (H)Construct and interpret cumulative frequency graphs, and know their appropriate use (KS4 Higher only) Use box plots to interpret, analyse and compare the distributions of data sets (KS4 Higher only) Histograms (H)Construct and interpret histograms with equal and unequal class intervals and know their appropriate use (KS4 Higher only) Processing Data
Ungrouped data - averages and spreadDescribe, interpret and compare single-variable distributions through measures of central tendency (mean, mode, median) and spread (range, consideration of outliers) (KS3) Grouped data - averages and spreadDescribe, interpret and compare single-variable grouped distributions through measures of central tendency (mean, mode, median) and spread (range, consideration of outliers) (KS3) Interpret, analyse and compare distributions through appropriate measures of central tendency (including modal class) (KS4) Quartiles and inter-quartile range (KS4 Higher only)Interpret, analyse and compare distributions using quartiles and inter-quartile range (KS4)Data collection and sampling
Sampling (KS4) Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling (KS4) Apply statistics to describe a population (KS4) |
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