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1.1 Sequences
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Unit objectives
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• Understand a proof that the angle sum of a triangle is 180° and of a
quadrilateral is 360°; and the exterior angle of a triangle is equal to the sum
of the two interior opposite angles
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• Distinguish between conventions, definitions and derived properties
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• Use a ruler and protractor to measure and draw angles, including reflex
angles, to the nearest degree; and construct a triangle, given two sides and
the included angle (SAS) or two angles and the included side (ASA)
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• Use straight edge and compasses to construct triangles, given right angle,
hypotenuse and side (RHS)
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• Solve geometrical problems using side and angle properties of equilateral,
isosceles and right-angled triangles and special quadrilaterals, explaining
reasoning with diagrams and text; classify quadrilaterals by their geometrical
properties
• Solve problems using properties of angles, of parallel and intersecting lines,
and of triangles and other polygons
• Use straight edge and compasses to construct the mid-point and
perpendicular bisector of a line segment; the bisector of an angle; the
perpendicular from a point to a line; the perpendicular from a point on a line
• Know the definition of a circle and the names of its parts
• Explain how to find, calculate and use the sums of the interior and exterior
angles of quadrilaterals, pentagons and hexagons; and the interior and
exterior angles of regular polygons
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Get in line
Website links
• Opener
Online angle puzzles
• 2.5 Geometry
resources, including
interactive explanations
LiveText resources
Notes on the context
Recreational maths (puzzles and games that relate to maths) can intrigue and
inspire those who are not naturally drawn to maths as a subject. The Englishman
Henry Dudeney and the American Sam Loyd, who worked on and published
puzzles at much the same time, did not have strong mathematical backgrounds
but both found puzzles irresistible. Dudeney and Loyd collaborated for a time,
but their working relationship broke down when Dudeney accused Loyd of
stealing his ideas and publishing them as his own.
Paper
planes
• Use it!
• Games
• Quizzes
• ‘Get your brain in Gear’
• Audio glossary
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Dudeney’s original instructions for solving the Haberdasher’s problem included
constructions using ruler and compasses, e.g. for the bisection of two sides of
the triangle. The base of the triangle is cut in the approximate ratio 0.982 : 2 :
1.018. A simplified solution is given here:
•
• Skills bank
• Extra questions for
each lesson (with
answers)
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• Worked solutions for
some questions
• Boosters
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Bisect AC; bisect BC. Roughly divide AB into three in the ratio 0.982 : 2 : 1.018.
Draw the lines as shown – lines meet at right angles inside the triangle. Then
rearrange the pieces.
For a range of other fun dissection puzzles, which can be downloaded as
resource sheets, please visit the relevant unit section at www.heinemann.co.uk/
hotlinks.
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Discussion points
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What mathematical skills are used in activities A and B?
Activity A
b)
The Online Assessment
service helps identify
pupils’ competencies and
weaknesses. It provides
levelled feedback and
teaching plans to match.
• Diagnostic automarked tests are
provided to match this
unit.
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Activity B
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a)
Level Up Maths Online
Assessment
b)
c)
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a)
Answers to diagnostic questions
1 Pupil’s line 6.3 cm long
2 31°
3 Pupil’s angle of 87°, labelled ‘acute’
4 a) rectangle
c) square
b) equilateral triangle
d) scalene triangle
5 Square, rectangle, trapezium, parallelogram, rhombus, kite, arrowhead
Opener
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2.1 WGM pages to come
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Get in line
Sequences
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2.2 Angles and proof
Objectives
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• Understand a proof that: the sum of the angles
of a triangle is 180°; and of a quadrilateral is
360°; and the exterior angle of a triangle is
equal to the sum of the two interior opposite
angles
• Distinguish between conventions, definitions
and derived properties
PR
Starter (1) Oral and mental objective
120
40
170
43
72
84
140
38
145
135
78
90
94
165
127
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Display this table and ask pupils to find complements
to 180.
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Starter (2) Introducing the lesson topic
EC
Recap alternate and corresponding angles on parallel
lines. Using mini whiteboards, ask pupils to draw a
pair of parallel lines with a transversal.
Resources
Main lesson
Starter (2), Main: mini
whiteboards
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Ask pupils to mark a pair of corresponding angles and a pair of alternate angles.
1 Interior and exterior angles
Functional skills
Which of these angles is an interior angle?
(angles BAC, ACB, CBA) Exterior angle?
(angle BCD)
Make an initial model of
a situation using suitable
forms of representation
C
Display this diagram.
A
C
D
Framework 2008 ref
Angle BCA is 50°. Calculate angle BCD. (130°)
1.3, Y8 1.2, Y8 4.1, Y9
4.1, Y9 4.3
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What is the sum of the interior angles in a triangle?
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Repeat with other values of angle BCA. Give other interior angles in the
triangle to check pupils are able to find missing interior and exterior angles.
Repeat for a quadrilateral. Q1–3
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2 Proof of sum of interior angles in a triangle
Display this diagram.
Ask pupils to copy the diagram on mini
whiteboards and label the other angles
which are equal to the circle and triangle.
Lead pupils through the proof that if angles on a
straight line add up to 180°, then the angles in the triangle must also sum to
180°. Q4, 6
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Activity B: dynamic
geometry software
Intervention
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– Explain that pupils will be using what they know about angles on parallel lines
to prove that the interior angles in a triangle sum to 180°.
Get in line
PoS 2008 ref
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3 Proof of sum of interior angles in a
quadrilateral
Model how pupils can prove that the sum of the
exterior angles in a quadrilateral is 360° by drawing
a diagonal from a vertex to the opposite vertex,
and finding the sums of the angles in the two
triangles formed. Q5
Activity A
Activity B
Pupils investigate the interior angles in a triangle
using dynamic geometry software.
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Plenary
ED
Pupils make up their own triangles and give the sizes
of two of the interior angles. They challenge their
partners to find the missing interior and exterior angles.
PR
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– Explain the difference between conventions,
definitions and derived properties. Many pupils
struggle with this so try to provide as many examples
as possible and ask pupils to suggest their own
examples. Display a simple shape such as a square.
How could this shape be defined? What conventions
are used to show that the angles are 90° and the
sides are the same length? What derived properties
can be deduced from the definition of the shape? Q7
Display a right-angled triangle.
Homework
Homework Book section 2.2.
EC
Ask pupils how they would prove that a + b = 90°.
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Challenging homework: Pupils investigate finding the proof that the sum of the
exterior angles of a triangle is 360°.
Answers
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1 p = 100°,
2 a) i) An exterior angle ii) An interior angle
b) 75° i) 96° ii) 82° iii) 63°
Related topics
Symmetry and art
Discussion points
Discuss what constitutes
a proof and the difference
between demonstrating
a rule works and proving
that the rule is always
true.
Common difficulties
iii) An exterior angle
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3 a) x = 91°, interior angles in quadrilateral sum to 360°;
y = 89°, angles on a straight line add up to 180°.
b) s = 55°, t = 55°, angles in a triangle sum to 180°, isosceles triangle has two equal angles;
u = 125°, angles on a straight line add up to 180° or exterior angle of a triangle equals the
sum of the two interior opposite angles.
c) q = 75°, angles on a straight line add up to 180°; p = 47°, angles in a triangle sum to 180°,
or exterior angle of a triangle equals the sum of the two interior opposite angles.
d) d = 88°, interior angles in quadrilateral sum to 360°;
e = 82°, angles on a straight line add up to 180°.
4 Angle x is equal to angle a because they are alternate angles.
Angle y is equal to angle c because they are alternate angles.
x + b + y = 180° because they lie on a straight line.
Since x = a and y = c, a + b + c = x + b + y.
This proves that angles in a triangle sum to 180°
Pupils can find moving
to formal proof difficult
so encourage the use of
symbols before moving
onto letters.
LiveText resources
Explanations
Booster
Extra questions
Worked solutions
5 a + b + c = 180° because angles in a triangle sum to 180°.
d + e + f = 180° because angles in a triangle sum to 180°.
Therefore (a + b + c) + (d + e + f ) = 360°.
6 a + b + c = 180° because angles in a triangle sum to 180°.
c + x = 180° because they lie on a straight line.
a+b+c=c+x
7 a) Derived property
b) Convention
c) Definition
d) Convention
2.2 Angles and proof
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2.3 Constructing triangles
Objectives
Starter (1) Oral and mental objective
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Ask pupils to visualise a square piece of paper. I fold
it across one of the diagonals. What shape is made?
What are the angles in the shape? I fold the resulting
shape in half. What shape do I get? What angles
are in the new shape? Ask pupils to explain their
reasoning.
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• Use a ruler and protractor to measure and
draw angles, including reflex angles, to the
nearest degree
• Construct a triangle given two sides and the
included angle (SAS) or two angles and the
included side (ASA)
• Use straight edge and compasses to construct
a triangle, given right angle, hypotenuse and
side (RHS)
Starter (2) Introducing the lesson topic
EC
Display angles on the board and ask pupils to identify
whether they are acute, obtuse or reflex angles.
Resources
Ask pupils to draw an acute angle of 72°. Pupils check their angle drawing with
their partner.
Starter (2): compasses,
ruler, protractor
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Main lesson
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Ask pupils to estimate the size of the angles.
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– Explain that pupils will be constructing triangles using a protractor and a
ruler and also compasses and a ruler. They should already have done this, so
some of this lesson will be revision.
1 Construct a triangle given two sides and an angle (SAS)
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Recap on how to draw a triangle given two sides and an angle using a
protractor and a ruler. What will you measure and draw first? Q1–2
2 Construct a triangle given two angles and a side (ASA)
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How do I draw a triangle given two angles and a side using a protractor and a
ruler? Q3–4
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3 Construct a triangle given three sides (SSS)
I know the lengths of all three sides of a triangle. How do I use compasses
and a ruler to draw the triangle? Model how to draw a triangle, for example
with sides 8 cm, 5 cm, 6 cm.
Advise pupils to draw the longest side first. Ensure that they can use
compasses correctly. Q6–7
– Display a straight line. How do I construct a line perpendicular to this line?
Check that pupils know how to do this. Q8
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Get in line
Intervention
Functional skills
Use appropriate
mathematical procedures
Framework 2008 ref
1.3, Y8 1.2, Y8 4.3, Y9 4.3
PoS 2008 ref
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4 Construct a right-angled triangle using
compasses
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Display a right-angled triangle. Which side is
the hypotenuse? How can you draw a rightangled triangle when you know the length of the
hypotenuse and one of the other sides? Model
how to use compasses and a ruler to do this. For
example draw a sketch of a right-angled triangle
then model how to draw the right-angled triangle
with a hypotenuse of 15 cm and one side 9 cm.
Repeat with another triangle if appropriate.
What is the length of the unknown side? Q5, 9–11
Activity A
Activity B
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Pupils practise drawing a right-angled triangle using
compasses and a ruler and then describe it for their
partner to draw.
PR
Pupils practise drawing a triangle using a protractor
and ruler and then describe it for their partner to
draw.
Plenary
Homework
Homework Book section 2.3.
EC
Write a selection of answers on the board.
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Ask pupils which triangles are impossible to draw.
Give them two minutes to discuss in small groups and then share their answers
with the rest of the class.
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Challenging homework: Pupils construct nets using compasses and a straight
edge.
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1 Correct angles drawn.
a) obtuse
b) reflex
c) reflex
Discussion points
Common difficulties
Encourage pupils
to check their
measurements using a
ruler as sometimes the
compass can slip.
LiveText resources
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Answers
Related topics
Explanations
d) obtuse
Booster
Extra questions
3 Accurate drawing of triangles.
Worked solutions
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2 Correct triangles drawn.
4 b) 10 + 11 = 21 m
b) d
c) i
d) j
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5 a) b
6 Accurate drawing of triangle.
7 Accurate drawing of triangle.
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8 Perpendicular line drawn.
9 a) Correct scale drawing.
10 a) Correct scale drawing.
b) 6 m
b) 3.9 m
11 The two shorter sides are 5 cm and 3 cm. These add up to 8 cm, which is shorter than the third
side 9 cm. Therefore the shorter sides will never meet.
2.3 Constructing triangles
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2.4 Special quadrilaterals
Objectives
• Begin to identify and use angle, side and
symmetry properties of triangles and
quadrilaterals
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• Solve geometrical problems using side and
angle properties of equilateral, isosceles
and right-angled triangles and special
quadrilaterals; explaining reasoning with
diagrams and text; classifying quadrilaterals by
their geometric properties
270
143
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84
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145
135
78
90
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265
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EC
180
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240
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Display the following target board and ask pupils to
find complements to 360.
ED
Starter (1) Oral and mental objective
PR
• Solve problems using properties of angles, of
parallel and intersecting lines, and of triangles
and other polygons
Starter (2) Introducing the lesson topic
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Ask pupils to draw a rectangle on a piece of paper and cut it out. Pupils draw
and measure the diagonals of the rectangle.
Resources
Starter (2): mini
whiteboards, paper,
scissors
Main: poster paper
Intervention
Functional skills
In pairs, ask pupils to write three sentences to describe the rectangle. Explain
that they can comment on things like the sides, angles and symmetry.
Use appropriate
mathematical procedures
Take feedback about the sentences they have written. Write a selection on the
board.
Framework 2008 ref
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What do you notice about where the diagonals cross? (bisect each other)
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Main lesson
– Explain that pupils will be investigating the properties of special
quadrilaterals.
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1 Special quadrilaterals
Display a rectangle, square, parallelogram, rhombus, isosceles trapezium, kite
and arrowhead and ask pupils to name the ones that they already know.
Ask pupils to work in groups – each group focuses on a specific quadrilateral
and finds its properties. Each group could make a poster of the properties of
their shape and this could be displayed during the lesson for the class to use.
Share the findings of each group with the rest of the class and summarise the
findings on the board. Q1–5
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Get in line
1.3, Y8 1.4, Y8 4.1, Y9 1.2
PoS 2008 ref
Display this shape and model
how to find the missing angles.
During each step of their
working, ask pupils to explain
their reasoning and show
this on the board. Q6–10
b
a
120°
35°
c
Activity A
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Pupils work in pairs, using the properties of
quadrilaterals to identify the shape.
Activity B
In this activity pupils set problems for their partner to
solve within a parallelogram.
Plenary
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Give pupils the following description: I am a special
quadrilateral. I have one line of symmetry and two
pairs of equal sides. I have no parallel lines. Which
special quadrilateral am I? (kite)
ED
Repeat with other descriptions.
Homework
Homework Book section 2.4.
Answers
EC
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Challenging homework: Pupils could identify impossible quadrilaterals if sides
and angles are given.
Number
of pairs of
parallel sides
Is a rectangle a square?
Is a parallelogram a
rhombus?
Lines of symmetry
0
0
4
Common difficulties
isosceles
trapezium
parallelogram
rectangle
rhombus
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2
2
kite, arrowhead
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1
1
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3
square
C
4 b) Parallelogram
c) Opposite sides are equal and parallel; diagonals bisect each other; rotation symmetry of order 2.
5 a) Rhombus
LiveText resources
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x = z = 140°, y = 40°
8 a) ⬔TUV = 45°
b) ⬔TVU = 105°
Explanations
c) ⬔SVU = 150°
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9 ⬔ABE = 180° − 90° − 72° = 18°.
⬔CBD = 180° − 90° − 56° = 34°.
(Angles in a triangle sum to 180°.)
⬔ABC = 90°, therefore ⬔EBD = 90° − 18° − 34° = 38°.
There are other valid approaches.
10 a)
b)
c)
d)
When pupils are asked to
describe the properties
it is useful to display key
words and a list of what
to comment on when
describing their shapes.
b) A, C
6 a = 60°, b = 30°, c = 60°
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Art and Design
Technology.
Discussion points
1 Yes – a square is a rectangle with all sides of equal length.
2 C
Related topics
Booster
Extra questions
Worked solutions
⬔FAB = 65° (Opposite angles in a parallelogram are equal.)
⬔ABE = 70° (Alternate angles are equal.)
⬔CBE = 110° (Angles on a straight line sum to 180°.)
⬔BCD = 115° (Angles in a quadrilateral sum to 360°.)
There are other valid approaches.
2.4 Special quadrilaterals
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2.5 More constructions
Objectives
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• Use straight edge and compasses to
construct: the mid-point and perpendicular
bisector of a line segment; the bisector of an
angle; the perpendicular from a point to a line;
the perpendicular from a point on a line
• Know the definition of, and the names of parts
of a circle
PR
Starter (1) Oral and mental objective
Starter (2) Introducing the lesson topic
EC
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Ask pupils to draw a circle on mini whiteboards.
Ask them to draw and label the diameter, radius,
circumference, chord, arc, sector, tangent. Check
pupils’ drawings and identify the parts of a circle on
the board.
ED
Introduce the term ‘bisect’. Practise finding halves
of numbers and measures, for example 5 cm,
3.3 cm, 45°.
Main lesson
– What does the term ‘perpendicular’ mean? Check that pupils know.
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Explain that pupils will not be using a protractor to measure angles but that
they will be drawing perpendicular lines using compasses and a ruler only.
Most of this is revision of earlier work.
1 Construct the perpendicular bisector of a line segment
2 Construct the angle bisector
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How do you draw the perpendicular bisector of a line segment? Take
instructions from pupils to check that they know how to do this – remind them
if necessary. Also check that they keep the compasses rigid while drawing the
perpendicular bisector. Q1–3
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How do you draw the bisector of an angle using compasses only? Remind
pupils, if necessary (they should have done this in earlier work), and give them
an opportunity to practise. Pupils can check they have bisected the angle
accurately by checking with a protractor. Q4
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3 Construct the perpendicular from a point on a line segment
How do you construct the perpendicular from a point on a line segment? Take
instructions from pupils to check that they know how to do this – remind them
if necessary. Q6, 7
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4 Construct the perpendicular from a point to a line segment
How do you construct the perpendicular from a point to a line segment? Take
instructions from pupils to check that they know how to do this – remind them
if necessary. Q5, 8
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Get in line
Resources
Starter (1): mini
whiteboards
Main: compasses, rulers,
protractors
Activity A: dynamic
geometry software
(optional)
Intervention
Functional skills
Use appropriate
mathematical procedures
Framework 2008 ref
1.3, Y8 1.2, Y9 1.1, Y9
4.1, Y8 4.3
PoS 2008 ref
Website links
www.heinemann.co.uk/
hotlinks
Activity A
Pupils practise drawing the perpendicular bisector for
a triangle in a circle. If available, dynamic geometry
software is useful for this activity. In a triangle, the
perpendicular bisectors meet at the circumcentre of
the triangle.
Activity B
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Pupils draw polygons within circles and investigate
where the perpendicular bisectors of the sides
intersect.
Plenary
PR
Ask pupils how you can draw a circle whose
circumference passes through each vertex of a
triangle. Give them a few minutes to discuss their
ideas in groups and then report back to the class.
Write a summary on the board. Pupils will find this
easier if they have done Activities A and B.
Homework Book section 2.5.
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Challenging homework: Pupils could make other
constructions such as the centroid of a triangle, or
use perpendicular bisectors to find the centre of a
circle.
ED
Homework
EC
Answers
1
Perpendicular bisectors correctly drawn.
2
b) Perpendicular bisector correctly drawn.
c) It is an equal distance from both houses.
3
Circle with radius, diameter, chord, arc, tangent, circumference correctly labelled.
Related topics
Loci
Common difficulties
Encourage pupils
to check their
measurements using a
ruler as sometimes the
compasses can slip.
Perpendicular bisectors correctly drawn.
5
Perpendicular correctly drawn.
6
Perpendicular correctly drawn.
LiveText resources
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Perpendicular correctly drawn.
Explanations
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a) b) Circles correctly drawn.
c) It is a rhombus.
Booster
Extra questions
Worked solutions
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2.5 More constructions
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2.6 Angles in polygons
Objectives
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• Explain how to find, calculate and use: the
sums of the interior and exterior angles of
quadrilaterals, pentagons and hexagons; the
interior and exterior angles of regular polygons
• Solve problems using properties of angles, of
parallel and intersecting lines, and of triangles
and other polygons
PR
Starter (1) Oral and mental objective
Ask pupils to add and subtract pairs of numbers, for
example the answer is 149 – what is the question?
Starter (2) Introducing the lesson topic
ED
Ask pupils to list pairs of numbers that you can add to
make 149. Repeat for numbers such as 8.6, 0.4, 0.12.
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Recap the sum of the interior angles in a triangle.
Which of these sets of angles are angles in a triangle?
Explain your reasoning.
A 36°, 72°, 93°
B 59°, 73°, 48°
EC
Two angles in a triangle are 48° and 87°.
Calculate the missing angle.
Main lesson
1 Proof of sum of interior angles in a quadrilateral
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2 Sum of the interior angles in polygons
C
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Remind pupils that they proved that the sum of angles in a quadrilateral is
360°. Display an irregular quadrilateral. How can you split it up into triangles?
Label the angles in one triangle a, b and c and in the other triangle d, e and
f. Show how a + b + c = 180° and d + e + f = 180° and therefore angles in a
quadrilateral must sum to 360° Q1
Number of
sides
Number of
triangles
Sum of interior
angles
triangle
3
1
1 × 180° = 180°
quadrilateral
4
2
2 × 180° = 360°
U
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Shape
hexagon
Ask pupils to complete the missing values.
For an n-sided polygon, how would you find the number of triangles? (n − 2)
Sum of interior angles? ((n − 2) × 180) Q2–4
3 Sum of the exterior angles in polygons
Display a quadrilateral. What is an exterior angle? How would you work out
the sum of the exterior angles in a polygon? What is the sum?
Get in line
Intervention
Functional skills
Make an initial model of
a situation using suitable
forms of representation
1.3, Y8 1.2, Y9 1.2, Y9 4.1
pentagon
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Activity A: materials for
poster making
Framework 2008 ref
Display this table:
–
Resources
PoS 2008 ref
Explain that in a regular polygon all the sides have
the same length and the angles are equal. How
would you calculate one of the interior angles in a
regular hexagon? (720 ÷ 6 = 120°)
What is the size of one of the exterior angles? (60°)
Discuss both of the following methods:
Method (1): 360 ÷ 6 = 60°
Method (2) 180 − interior angle Q5–11
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Activity A
Pupils make a poster explaining what they know
about interior and exterior angles in polygons.
Activity B
PR
Pupils try to explain which regular polygons tessellate
by looking at their interior angles.
Plenary
ED
Ask pupils if it is possible to draw a polygon whose
interior angle sum is 1400°. Give them a short time
to discuss this in small groups and report back to the
class. Repeat for other values.
Homework
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Homework Book section 2.6.
EC
Challenging homework: Pupils could find examples of real-life regular polygons,
and calculate interior and exterior angles.
Answers
LiveText resources
Explanations
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2 a) Find the sum of the interior angles by dividing the pentagon into three triangles, then divide by 5.
b) Subtract the interior angle from 180°.
Booster
Extra questions
iii) 720°
Worked solutions
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ii) 540°
Art and design, design
technology, ICT
Common difficulties
1 a) Split the shape into two triangles.
b) Spit the shape into three triangles.
3 a) i) 360°
b) 1440°
Related topics
4 The interior and exterior angles lie on a straight line. Angles that form a straight line sum to 180°.
6 a) 60°
Number
of sides
Sum of
interior angles
C
Size of each
interior angle
Sum of
exterior angles
Size of each
exterior angle
equilateral
triangle
3
180°
60°
360°
120°
square
4
360°
90°
360°
90°
regular
pentagon
5
540°
108°
360°
72°
regular
hexagon
6
720°
120°
360°
60°
regular
octagon
8
1080°
135°
360°
45°
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Regular
polygon
d) Sum of exterior angles is always 360°.
b) 120°
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c) 360°
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5 b) 360°
8 a (n − 2) × 180°
b) Interior 157.5°, exterior 22.5°
9 a) i) 20
b) 15
ii) 162°
10 No. The sum of the interior angles in a multiple of 180° and 1300 is not divisible by 180.
11 a) 135°
b) 45°
c) 22.5°
Sequences
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Puzzle time
What does the arrow notation represent?
How can this be used to solve problems?
It would be beneficial to summarise the learning in
this unit by highlighting the important angle facts
– producing a checklist for angle problems could also
be useful.
Solutions to the activities
ED
1 a = 135°
2 b = 30°
3 c = 142°, d = 65°
4 e = 71°
T
5 f = 104°, g = 96°, h = 84°
8 l = 45°, m = 65°, n = 70°
9 o = 105°, p = 75°, q = 105°
R
10 r = 170°
EC
6 i = 119°, j = 61°
7 k = 234°
R
Number grid:
O
Answers to practice SATs-style questions
C
1 a) Angles on a straight line sum to 180°. 180° – 70° = 110°,
so Sally is correct.
b) a = 45° (1 mark each)
2 a = 40°, b = 140°, c = 20° (1 mark each)
N
3 a) Angle BCD = 105°
b) Angle BAD = 75° (1 mark each)
U
4
6 cm
6 cm
8 cm
8 cm
8 cm
6 cm
(1 mark per triangle)
32
Get in line
PR
The activities cover a range of missing angle
problems. It would be useful to discuss pupil
methods for the latter questions, particularly activities
8 and 9. Emphasise that surplus details are not given
in these types of problems – all information given will
and should be used to reach a solution.
O
O
F
Notes on plenary activities
5 a) 3y = 90°, so y = 30° (2 marks)
b) 2x = 30°, so x = 15° (2 marks)
6 a) ABCD: interior angles sum to 360°, so angle
ADC = 96° and angle EDC = 48° (2 marks)
b) Angle DEB = 132° (1 mark)
c) DAE is an isosceles triangle: angle DAE = 84°,
angle ADE = 48° and angle AED = 48° (1 mark)
Functional skills
The plenary activity practises the following functional
skills defined in the QCA guidelines:
• Select the mathematical information to use
• Use appropriate mathematical procedures
U
N
C
O
R
R
EC
T
ED
PR
• Find results and solutions
O
O
F
7 a) s = 32°
b) t = 56° (2 marks each)
Puzzle time
33