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Teaching and Learning Plan – Enlargements

Title of Class: Enlargements

Lesson Number: 2

Length of Lesson: 75 Minutes

Level of Class: Leaving Certificate.

Previous knowledge and experience of the material: From previous topics the students are

aware of similar shapes. They would need to e ale to construct rectilinear shapes !triangles and

rectangles"# and they would also need to understand the concept of ratios. $ote rectilinear shapes

are o%ects made up of straight lines.

Prior nowledge:

Capale of constructing triangles# s&uares and rectangles

'nowledge of similar triangles

!im of the Lesson: To introduce the topic of enlargements and enale students to accurately

construct an enlargement of a rectilinear figure y deducing the ray method.

"b#ectives:

• To enale students to e(plain and identify the concept of an )enlargement* and to recognise

associated terms.

• To enale students to identify similar shapes.

• To enale students to construct the rays on two similar shapes and hence calculate the centre of 

enlargement and the scale factor.

• To encourage and enale students to investigate and conclude that if the length of the sides of 

one triangle is + times the length of the other# that the scale factor is also +.

$ub#ect %atter:

Centre of enlargement.

 

,mage and -%ect

  cale Factor.

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&elationship to 'unior Certificate $(llabus

$tudents

learn about

$tudents working at )L

should be able to

*n addition

students working

at "L should beable to

*n addition

students working at

+L should be ableto

2./

Transformatio

n geometry#

enlargements

− investigate

enlargements paying

attention to

• centre of

enlargement

• scale factor + 0

1+3 #

  + 43 + ε 

• area

solve prolems

involving enlargements

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&esources re,uired:

- Coloured card !uggestion scrapoo+ with a variety of colours."

- cissors

- Math sets

- 6oster paper

- lue

- Long 8ulers

- 9hite oard and mar+er 

- 9or+sheet !ee :ppendi( :"

- ;emonstration triangles

- 8ussian ;olls- 6hotographs !ame photo# ut printed in different si<es"

- :lso possile items from supermar+et where small and large pac+ages are e(amples of 

enlargements# for e(ample Tolerone ars# cereal o(es# toothpaste o(es

-

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Pre-preparation

Cut scrap oo+ sheets in half and write on each half sheet instructions re si<es of triangles# s&uares

or triangles you re&uire the students to produce. $ote ma+e sure these are given out in pairs as

listed elow=

hape 3 hape 2

6air 3 Triangle angles /51# >51 and side ? cm Triangle angles /51# >51 and side 32 cm

6air 2 Triangle angle 511 and sides ? cm and > cm Triangle angle 511and sides ? cm and 32

cm

6air @ Triangle angle 3111# >51 and sides 7 cm and > cm Triangle angle 3111and side 3/ cm and 32

cm

6air / Triangle angles /51# >51 and side ? cm Triangle angles /51# >51 and side ? cm

6air 5 Triangle angles 711# 711 and side A cm Triangle angles 711# 711 and side 3> cm

6air > Triangle sides 5 cm# > cm and 7 cm Triangle sides 31 cm# 32 cm and 3/ cm6air 7 Triangle sides ? cm# 32 cm and 35 cm Triangle sides 32cm# 3> cm and 21 cm

6air A Triangle angles >11# >11 and side A cm Triangle angles >11# >11 and side 3> cm

6air ? &uare A cm y A cm &uare 3> cm y 3> cm

6air 31 8ectangle A cm y > cm 8ectangle 3> cm y 32 cm

  esson Interaction

Student Learning Tasks:Teacher Input

Student Activities: Possible andExpected Responses

Teacher’s Support and Actions

Task .

:rrange students into preBdecided

 pairs# ased on aility# !strong

student with a wea+ student".

tudents are unaware at this stage#

who their partner is.

;istriute paper# math instruments

and scissors to each student.

Ensure that clear and definite

instructions are given at the star

the lesson so as to avoid confus

and unnecessary &uestions.

Task /

ive each student a preBprepared

scrapoo+ sheet with the

dimensions of the triangles etc.

written on them. 6ut half the class

ma+ing smaller dimensions !hape

3" and the other half the larger

uestions regarding the method of 

construction.

:llow students time to construc

the shapes. 9al+ around the

classroom oserving the wor+

 eing carried out and offer help

re&uired.

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  esson Interaction

Student Learning Tasks:Teacher Input

Student Activities: Possible andExpected Responses

Teacher’s Support and Actions

dimensions !hape 2"# so as to

ensure that students are not aware

of the concept too early on.

;emonstrate and reBcap on the

method of construction# if

necessary.

Task 0

Find another person in the room

who has the same coloured sheet.

6rompt students to relate that the

angles are the same ut that one

shape is igger than the other.

ome students in the class

recogni<e that the shapes of the

corresponding figures are the same

shape ut different in si<e.

et the students to find another

 person in the room who has the

same coloured sheet and offer h

to those who cannot find their

 partner.

Encourage students to e(amine

shape they have constructed#

comparing and contrasting oth

shapes and hence motivate

students to deduce that the

triangles or rectangles are simil

in shape.

Task 1

how students the 8ussian ;olls#

6hotographs and supermar+et

items to further reinforce and

demonstrate the theory point and

elicit the term enlargement from

the pupils themselves.

tudents said various terms

relating to the concept

enlargement.

Dse all of the props to reinforce

the concept of enlargement.

The photographs were the est

resource when eliciting the term

enlargement students could li

the concept est to this resource

;raw the students* attention to

situation where the scale factorless than 3.

Task 2

;istriute poster paper to each pair 

of students. Lael the smaller

shape :# # C and larger shape

The students may have difficulty

understanding what the lines mean

and this may re&uire further

discussion and e(planation.

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  esson Interaction

Student Learning Tasks:Teacher Input

Student Activities: Possible andExpected Responses

Teacher’s Support and Actions

!the image" :3# 3# C3. et each

 pair of students to stic+ on their

shapes as on the ample :ctivities

on 6age ? of this TGL.

Hoin the points ::3# 3# and CC3 

and continuing these lines until

they intersect.

uestion students to predict the

result of %oining the correspond

 points ::3# 3# CC3 and

continuing these lines until they

intersect. Clarify any

misconceptions that students m

have.

Task 3

;emonstrate the calculation of the

scale factor and introduce the

concept of the centre of

enlargement. :llow students time

to construct the centre of

enlargement on their own shape#

and hence compute the scale factor 

on their poster.

ome students struggled with this

tas+ initially. They needed to

repeat the measurement of the

distances etween the centre of

enlargement to the o%ect and to

the image efore they recogni<ed

any relationship. tronger

students deduced the relationship

 etween the area of the o%ect and

the image at this point.

Monitor the class and aid stude

where difficulty arises

encouraging them to complete t

tas+.

Task 4

Iandout the wor+sheet !ee

:ppendi( :" to reBcap on the topic

and to reinforce the learning that

has ta+en place. :lternatively see

,nternet resources on page ?.

tudents read the wor+sheet

&uestions and as+ed for further

clarification where needed.

8eBcap on formulae and

definitions needed for the e(erc

in order to aid learning# e.g. ca

Factor J ,mage Length K -%ect

Length.

;raw the students* attention to

situation where the scale factor

less than 3.

+omework: Complete the

wor+sheet to reinforce the

learning.

N565 This T7L does not cover the following aspect of the Transformation geometr(8

enlargements section of the Leaving certificate s(llabus:

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  Area.

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*nternet &esources )urther exercises

http=KKwww.c.co.u+KappsKiflKschoolsKgcseitesi<eKmathsK&ui<engine

&ui<JtransformationshigherGtemplatetyleJmaths 

http=KKwww.channel/learning.comKsupportKprogrammenotesKnetnotesKcontentKpdfsKm/rKm/r2ws31.

 pdf  

$ample !ctivities

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!ppendix ! 9orksheet1. In the following iagra! A"#"$" i% the i!age of A#$ &ner an enlarge!ent with

'entre D an %'ale fa'tor 2. If A# ( 1.5 '!) #$ (1.6 '! an A$( 1.8 '!) *n

length% of A"#") #"$" an A"$". +how 'al'&lation%.

2. +how the i!age of A#$ &ner an

enlarge!ent with 'entre D an %'ale

fa'tor 3.

3. If A"#"$" i% the i!age of A#$ an the %'ale fa'tor i% 4) *n D the 'entre of

enlarge!ent.

 

4. ,in the i!age of A#$) if # i% the 'entre of enlarge!ent an the %'ale fa'tor i%

2.

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5. ,in the i!age of A#$ by a %'ale fa'tor of ) if the 'entre of enlarge!ent i% D.

 6. If A#$ i% 85/ an A$# i% 35/) 'o!0lete the following table.

:C

:**C*

:*C**

*:*C*

 

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8. © www.teachers.tv/system/files/13223_01.pdf  

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