040220 rray maths ks3 y9 ssm1 by 3UYFPmEM


									      YEAR 9: AUTUMN TERM
Shape, space and measures 1 (9 hours)
Geometrical reasoning: lines, angles and shapes (178–189, 194–197)
Construction and loci (220–227)
Solving problems (14–17)

Teaching objectives for the main activities
From the Y9 teaching programme
   A. Distinguish between conventions, definitions and derived properties.
       Explain how to find, calculate and use:
   B. - the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons,
   C. - the interior and exterior angles of regular polygons.
   D. Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other
      polygons, justifying inferences and explaining reasoning with diagrams and text.
   E. Know the definition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed
      by equal divisions of a circle.
   F. Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS); use ICT to
      explore constructions of triangles and other 2-D shapes.
   G. Find the locus of a point that moves according to a simple rule, both by reasoning and by using ICT.
   H. Explore connections in mathematics across a range of contexts: shape and space.
Unit:                           SSM1                          Year Group:      9

Number of 1 Hour Lessons:       9                             Class/Set:       Core

Flexibly use the 1 or 2 lesson structure
Oral and Mental                     Main Teaching (2 lessons)                               Notes            Plenary
Objective r                         Objective A                                             Key Vocabulary    Model solutions and notation
Using pictures from worksheet See page 179 of framework to distinguish between              Definition        Assess understanding of
9SSM1a or others, ask one           convention, definition and derived properties.          Derived             conventions.
student to describe the shape       Also give a practical demonstration as in framework     Property          Check key vocabulary.
using mathematical words etc.       but establish it is not a proof. (This will be          Demonstration     Pose challenging problem for
Rest of class try and draw the      developed in the mini-pack)                             Proof               students to discuss e.g.
pattern/shape described.                                                                    Transversal
                                    Objective D
                                    Revisit and strengthen Y8 work using parallel lines
                                    and transversals, angles around a point, angles in a                            a
Objective A                         triangle, vertically opposite angles (perhaps revisit                                            c
Use some of the diagrams from bearings).
9SSMa to discuss conventions. Encourage students to write brief notes to justify                                    a+b=c
Label vertices with letters.        solutions. (Model this).                                                        always
Ask question about sides and        Assess where weaknesses lie and address them.
angles using letter conventions Include diagonals and intersecting lines in polygons.                           Is a square a rectangle?
to describe them.                                                                                               Is and isosceles triangle an
                                                                                                                 equilateral triangle? (and vice
Oral and Mental                    Main Teaching (1 or 2 lessons)                        Notes            Plenary
Objective O and aa and n           Objective F                                           Key Vocabulary    Take feedback from last exercise.
Does 360o divide exactly by 2?     Revisit Y8 constructions (Page 221)                   Bisector          Discuss outcomes
Extend to ÷ 3, 4, 5, 6, 7, 8, 9,                                                         Perpendicular     Form generalisations
10 etc.                            Construct a triangle given R.H.S.                     Intersection      Discuss approaches
                                   Establish that with given properties only one         Locus.            Establish SSS, R.H.S. rules for
Discuss methods of division        triangle can be constructed. (constructing and        Loci                constructing triangles.
e.g. 360 ÷ 12                      cutting out or making with pipe cleaners and straws   Hypotenuse        Perhaps use AAA in two triangles,
extend to factor pairs of 360.     could be undertaken).                                                     calculate a missing side using
Where does 360o come into our      Re-establish S.S.S. rule and explore A.A.A. and
work?                              revisit similarity.

Collect ideas.                     (Page 223)
                                   Is it possible to construct triangle ABC such that
Set a target of 10 ideas where     ………etc.
we use 360o.
                                   Divide class into pairs – allocate pairs different
Objective F                        starting questions so all questions are attempted.
Demonstrate (without
comment) constructions.

Pupils have to say what you
have done OR pupils have to
direct you in the construction
using precise language.
Oral and Mental                     Main Teaching (1 or 2 lessons)                          Notes                    Plenary
Objective u                         Objective G                                             Key Vocabulary            Why is the sum of external angle
Estimating angles (whiteboard       Discuss simple loci in 2 dimensions.                    Locus                       in a polygon always 360o.
responses)                          Pupils use constructions (sketch first) to complete     Loci                      What about internal angles in a
                                    question on 9SSM1b (loci) and discuss in pairs first.   Sphere                      polygon?
OR                                                                                          Plane                     Ask questions on conventions.
                                    Mini plenary                                                                      Discuss different types of locus
T = 2n – 180                        Discussion about how loci of multiple points in a                                   and phrases used – ‘equidistant
Substitute for different values     plane (2D shapes) can form 3D images might be           Dynamic geometry            from point-line’ etc.
of n. Pupils calculate to find T.   appropriate before attempting 9SSM1c                    package could be used.      Perpendicular to .. etc.
(Use negative fractions,            Pupils in 2s or 4s discuss further question on                                    Pupils model loci.
decimals etc.)                      9SSM1c on loci and try and sketch or describe loci.

Using integers show                 Mini plenary
relationship to sum of internal
angles in a polygon. (Use
regular polygons to
Proof comes later in scheme of
Oral and Mental                   Main Teaching (1 or 2 lessons)                          Notes            Plenary
Objective K                       Objective E                                             Key Vocabulary    When is a segment a sector?
How would you do the              Ask – what is a circle? – relate to locus.              Plane               (when it’s a semi circle!!!!)
following in your head?           Ask pupils to chant ‘A circle is the locus of a point   Equidistant       Test on names as you point to a
       398 + 1252                 moving equidistant from another fixed point in a        Cyclic              master diagram or draw in lines on
       648 – 329                  plane’.                                                                     a circle.
       17 x 25                    How can we draw/construct a circle?                                       Why are all regular polygons
       18 x 2.5                   Discuss types of equipment particularly string used                         cyclic?
       46.2 ÷ 0.2                 by grounds men to construct field markings.                               Explore some ideas on circle
       83 ÷ 0.5                   Ask pupils to imagine the line moving as below.                             theorems.
       21 ÷ 1.5

Offer each question separately,
followed by collecting answers
and methods.

If methods are ‘new’ to some
students set a similar question   Use to establish tangent, chord arc, segment semi
to practise.                      circle, diameter.
                                  Establish radius and sector.(mention major and
                                  minor segment and sector)

                                  Establish how regular polygon can be constructed
                                  using a circle (See page 195)

                                  Construct regular polygons particularly a hexagon
                                  (introduce cyclic).
                                  Produce a master diagram/poster identifying key
                                  parts of a circle.
Oral and Mental                  Main Teaching (1 lesson)                               Notes                     Plenary
Objective A and aa               Objective A & C                                        Key Vocabulary             Note down findings.
Ask pupils to sketch a nonagon. Establish convention for exterior and interior angles   Regular                    Establish understanding of
                                 of a polygon. Establish that exterior angles can       Irregular                    convention for interior and
Now score the nonagons using never by reflex. Address this misconception.               Polygon                      exterior angles of a polygon.
the following:                                                                          (names)                    Model solutions to difficult
Each internal acute angle = 20                                                                                       questions or set a difficult question
points.                                                                                                              and ask for ideas for a method or
Each right angle 15 points.                                                                                          solution.
Each pair of perpendicular lines                                                                                   Check names of polygons.
5 points (they don’t have to                                                                                       Check vocab. for angles work.
meet or cross)
                                                                                        Could use logo to draw
Check scores.                                                                           regular polygon. Using
                                                                                        exterior angle and side
Now try and produce the                                                                 length.
nonagon with maximum
points?                          Model a ruler turning through each exterior angle of
                                 a polygon. Note the ruler always rotates 360o.
Discuss outcomes
                                 Establish the sum of exterior angles = 360o.

                                 What about interior angles? Regular polygon and
                                 exterior angles – explore.

                                 Solve problems and questions using properties of
                                 shapes and exterior interior angles of polygon.
                                 Consolidate with SATs questions if time available

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