Geometry Lessons

Lesson titleDescription (objectives)Lesson WorksheetCalculator requiredProblem Solving QuestionsProblem Solving Worksheet
Use isometric grids & understand and draw nets and elevationsBe able to drawing and identify nets, followed by being able to draw 3D shapes on isometric paper. The being able to draw different elevations of shapes.
Understand and use translations, using vectors and describing translations Be able to translate shapes from given words, then by using vector notation, ending in being able to describe translations using vector notation.
Prove and use each of the circle theoremsProof of all the circle theorems
Recognise linear and rotational symmetryTo be able identify shapes' lines of symmetry and their order of rotational symmetry
Calculate the length of an arc and area of a sectors and segmentsTo be able to calculate arc lengths of a circle, area of sectors and leading onto area of segments.
Understand and use Pythagoras' theorem and Trigonometry in 3D problems To be able to calculate missing lengths using pythagoras' in 3D, followed by calculating missing angles / sides using trigonometry in 3D….extending to using Sine/Cosine Rules in 3D scenarios.
Find the volume and surface area of conesTo be able to calculate the surface area of a cone, leading onto using pythagoras, and then to be able to calculate the volume of a cone - extending to missing sides given the volume.
Find the surface area of shapes of cubes and cuboids by using the formulae for rectanglesTo be able to calculate the surface area of a cube, leading onto surface area of a cuboid / rectangular prism
Find the volume and surface area of pyramidsTo be able to calculate the surface area of a pyramid, leading onto using pythagoras, and then to be able to calculate the volume of a pyramid - extending to missing sides given the volume.
Find the volumes of frustumsTo be able to calculate the volume of frustrums
Enlarge a shape by a negative scale factor and describing enlargementsTo be able to enlarge shapes given a negative scale factor leading onto being able to describe enlargements.
Enlargements To be able to enlarge shapes given a scale factor and centre of enlargement, leading onto finding the centre of enlargement from already enlarged shapes
Find the volumes of Prisms and CylindersTo be able to find the volume of prisms and cylinders, leading onto missing sides given the volume, extending to shapes with missing sections (working out two volumes to subtract one from another)
Find the surface Area of Prisms and CylindersTo be able to find the surface area of prisms and cylinders, leading onto missing sides given the surface area
Understand and describe reflections To be able to reflect shapes using a mirror lines, leading onto being able to reflect lines in a linear equation and finishing with describing a transformation ( reflection ) given a first shape and it's reflection.
RotationsTo be able to rotate shapes given instruction, leading onto being able to identify and describe how shapes have been rotated
Undestand how to solve problems using vectorsTo be able to solve problems with vectors by adding subtracting and multiplying - and also being able to find midpoints using vectors
Find the surface area and volume of spheres and hemispheres To be able to surface area and volume of spheres and hemispheres extending to missing lengths given surface area/volume.
Calculate the area of a triangle using the formulae, A = ½abSinC To be able to the area of a triangle using the formulae.Area = ½abSinC, leading onto using cosine rule prior to find missing values
Use the formula to calculate the volume of a cuboidTo be able to use number of cubes to calculate the volume of a cuboid, leading onto using a formula to calculate the volume of a cuboid
Calculate the sum of interior angles in a polygon and external angles add up to 360 degrees, and how shapes tessellateTo calculate sum of internal angles of regular shapes, leading onto shapes with more sides, followed by size of interior and exterior angles - finishing with why and when shapes tessellate (tessellations).
Knowledge of circles - know the parts, and how to calculate circumference and area:To know the parts of a circle, followed by circumferene of circle and the area of a circle questions, extending to portions of circles
Understand vector notation, and be able to add, subtract and mulitply vectorsTo understand vectors, vector notation, and to be able to add, subtract and multiply vectors by constants
Circle Theorems - Part 1Understand and apply 3 circle theorems - Angles at the centre, Cyclic Quadrilaterals and Angles in a Semi-circle, with questions.
Circle Theorems - Part 2 Understand and apply 3 circle theorems - Angles subtended by the same arc, Tangents and Altenate segment theorem, with questions.
Use the cosine rule to solve 2D problems Use the Cosine Rule to calculate missing sides followed by using Cosine Rule to calculate missing angles
Use the sine rule to solve 2D problems Use the Sine Rule to calculate missing sides followed by using Sine Rule to calculate missing angles
Be able to deduce the number of sides of a regular polygon, given one of its angles To be able to work out and use interior / exterior angles of polygons. Followed by being able to find the number of sides of a polygon given it's internal/external angle
To be able to calculate / know exact trig ratiosTo be able to calculate the exact values of trigonometric ratios
Understand trigonometric relationships in right angled triangles and use it to find missing sides in 2D problemsTo understand trigonometric relationships in right angled triangles and use them to calcaulte missing sides in 2D problems
Find angle of elevation and angle of depressionTo be able to calculate the angle of depression or elevation in real life scenarios
Use trigonometry to find the angle between 2 lines To use knowledge of trigonometric relationships to calculate missing angles in triangles.
Perimeter of ShapesTo be able to find perimeter by counting, calculating distance with numbers, and moving onto perimeter of compound shapes
Algebra in ShapesTo be able to use algebra (creating expressions and solving equations) to solve problems involving angles, area and perimeter
Volume and Surface Area of Compound ShapesTo be able to find the volume and surface area of 3d compound shapes, from cuboids up to cones and frustrum combinations
Angles in Triangles and QuadrilateralsTo be able to find angles in triangles and quadrilaterals
Area of ParallelogramsTo be able to use formula to find area of parallelograms and hence missing sides given it's area
Area of TrapeziumsTo be able to use formula to find area of trapeziums and hence missing sides given it's area
Area under a curve and Gradient of a curve- To be able to calculate the gradient of a curve at a point
- To be able to calculate the average gradient of a curve
- To be able to calculate an estimate of the area under a curve
Area of RectanglesTo be able to work out area of a rectangle by counting squares, followed by multiplying dimensions, leading onto compound shapes
Area of Compound ShapesTo be able to find the area of compound shapes made up of rectangles, triangles, parallelograms, trapeziums and circles
PythagorasTo use pythagoras to find hypoteneuse, leading onto any side, extending to using pythag to prove a triangle is right angled
Area of TrianglesTo be able to work out area of a triangle using formula, leading to finding missing dimensions given it's area
Missing AnglesTo be able to find missing angles in a right angle, on a straight line or around a point
Parallel and Perpendicular LinesTo identify if lines are parallel or perpendicular
Types of AnglesTo be able to identify different types of angles from drawings, and from given angles in degrees
Types of TrianglesTo be able to classify different types of triangles based on information given
Compound Measures- To be able to calculate speed, density and pressureTo be able to solve harder compound
measures problems which include converting
units
Angles on Parallel Lines- To be able to find missing angles on parallel lines
- To be able to give reasons for your answers
Converting Units
- To be able to convert between lengths
- To be able to convert between masses
- To be able to convert between volumes
Converting Square and Cube Units- To be able to convert units of area
- To be able to convert units of volume
Speed - Distance Time Graphs- To be able to interpret distance time graphs
- To be able to represent a journey on a distance time graph
- To be able to calculate the speed from a distance time graph

Conversion Graphs

-To be able to use conversion graphs to change units\\\
Constructions- To be able to draw a perpendicuar bisector of a line using a compass and a ruler
- To be able to draw a perpendicuar line through a point on a line
- To be able to bisect an angle using a compass and a ruler
- To be able to construct a 60° angle using a compass and a ruler
Loci- To be able to draw locus around a point or line
- To be able to shade regions between loci
- To be able to find the locus which is equidistant from two points
Bearings- To be able To understand and use bearings To specify the direction of an object
Types of Quadrilaterals- To be able To identify different types of quadrilaterals
Similarity- To be able to find the missing side lengths and angles of similar shapes
- To be able to calculate areas and volumes of similar shapes
Congruence- To be able to identify congruent shapes
- To be able to identify congruent triangles from their sides and angles
Graph Transformations- To be able to apply transfomations to a function f(x)
- To be able to describe the transformation which has taken place
Scale Drawings- To be able to convert between scaled and real life distances
- To be able to use scales to find real distances on a map
Types of graphs- To be able to identify different types of graphs
- To be able to identify different types of graphs from their equations
- To be able to recognise proportion graphs
Trigonometric graphs- To be able To draw and recognise the graphs of sin, cos and tan
Using a ruler

-To measure items/lines accurately using a ruler
-To be able to draw lines of certain lengths using a ruler

Using a protractor

-To measure angles accurately using a protractor
-To be able to draw angles using a protractor

Constructing triangles with protractors and a pair of compasses

-To be able to construct a triangle with a protractor and ruler
-To be able to construct a triangle with a pair of compasses and a ruler