Unit 12 Geometry and Measure

Intent

The intention of this unit is to secure and build upon knowledge from Key Stage 2 and to introduce new concepts that lay the foundations of key concepts that will underpin units in Year 8 and Year 9 such as

  • Algebraic manipulation using inverse operations

We want all student to become keen problem solvers and agile mathematical reasoners. This unit in particular develops these skills with

  • Multiple step angle reasoning problems

  • Formal deductive reasoning with angles.

Implementation

For each strand in the unit students begin with lessons refreshing primary knowledge before new concepts are introduced. At the end of each strand there are revision and mastery lessons to consolidate and ensure all students have picked up on new ideas.

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 before the test.

During this unit there will be two longer written homework tasks which include a skills check as well as problem solving questions. Students will have an opportunity to follow-up and improve their work.

Impact

The impact of this unit of work will be measured through a 45 minute written assessment. The assessment will feature questions similar to the skills check and homework tasks. 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 test.

Topics covered in this unit:

Star / Star*

23s Area and perimeter of shapes made from 1 cm²

27s Calculate the area and perimeter of a rectangle

10s Deciding which measuring instrument to use

22s Reading scales on measuring instruments and deciding appropriate metric units for a measurement

11s Reading the time from a clock or drawing where clock hands would be

12s Knowledge of time units, including how many seconds in minute, minutes in a hour, hours in a day, days in week, weeks in a year

21s Calculating lengths of time and converting between hours, minutes and seconds

13s Know there are 360⁰ in a full turn (180⁰ = half turn; 90⁰ = quarter turn) and recognising types of angle: acute, obtuse, reflex or right

26s Use the sum of angles at a point or on a line or vertically opposite to calculate angles

28s Measure and draw angles accurately (including obtuse and reflex angles)

15s Measuring lines accurately and understand and use the terms horizontal, vertical and diagonal

38s Using map scales and making a scale drawing

18s Use a compass to draw a circle of a given radius or diameter

28s Measure and draw angles accurately (including obtuse and reflex angles)

16s Recognise and label parallel and perpendicular lines

17s Know mathematical names for 2D shapes including special quadrilaterals and triangles

30s Know the properties of sides and angles of special quadrilaterals and the names of parts of circles

14s Plotting and reading coordinates in the first quadrant

25s Plotting and reading coordinates in all 4 quadrants

19s Reflect simple shapes in a mirror line or translate a shape on a grid

29s State the order of rotational symmetry of a 2D shape and show what a shape would look like rotated by 90⁰ or 180⁰

24s Show how a shape tessellates

Core

33s Calculate the perimeter of compound shapes

39s Calculate the area of a compound shape

35s Calculate the area of a parallelogram or a triangle

42s Calculate the area of a trapezium or a compound shape involving trapeziums

50s Calculating the area or circumference of a circle giving answers approximately or in terms of π

55s Calculating the area or perimeter of a semi-circle or quadrant or work with circular measure in context

36s Calculate the volume of shapes made from 1 cm cubes and cuboids

49s Calculate the volume of a prism or the surface area of a cuboid

57s Calculate the volume of a cylinder giving answers approximately or in terms of π

34s Converting between metric units (and to imperial given the conversion factor)

37s Reading timetables and using them to plan journeys

44s Solve speed-distance-time problems (including converting minutes to hours when necessary)

67s Solve density-mass-volume or pressure-force-area problems

32s Know and use the sum of angles in a triangle or quadrilateral to work out angles

41s Calculate angles using angle facts (including isosceles triangles) and provide full geometric arguments

53s Calculate angles using parallel lines (including reversing bearings) and provide full geometric arguments

45s Reading and using bearings

38s Using map scales and making a scale drawing

40s Know the properties of diagonals of special quadrilaterals

31s Naming 3D solids, matching nets to 3D solids and counting faces, edges and vertices including recognising which edges will meet

47s Drawing plans and elevations of 3D shapes

43s Construct triangles and nets using ruler, protractor and compass

58s Know the ruler and compass constructions for perpendicular lines and bisectors

59s Use a perpendicular to find the shortest distance from a point to a line

56s Use ruler and compass to construct loci according to a list of instructions

51s Use Pythagoras' theorem to find hypotenuse or short side or check if a triangle is right-angled

66s Solve problems requiring either multiple steps of Pythagoras or amending a diagram to locate a right-angled triangle

46s Work out the midpoint between two coordinates

20s Draw all the lines of symmetry on 2D shapes

48s Translate a shape by a vector on a coordinate grid and describe a translation

52s Reflect a shape on a coordinate grid and describe a reflection stating the equation of the mirror

54s Rotate a shape from a given centre on a coordinate grid and fully describe a rotation