Grade 10 · Core Mathematics · Lesson 11 of 11

Appreciating Similarity and Enlargement in Real-Life Applications

A Grade 10 Core Mathematics CBE lesson from the sub-strand Similarity and Enlargement. In it, learners construct and evaluate scale nets and models of physical structures using a linear scale factor.

Strand Measurements and GeometrySub-strand Similarity and EnlargementLesson code 10CM-21-L1140 minutes · 2 slides

KICD learning outcome (f)

Appreciate the use of similarity and enlargement in real-life situations.

By the end of this lesson, learners should be able to

Construct and evaluate scale nets and models of physical structures using a linear scale factor.
Apply linear, area, and volume scale factors to solve practical real-life problems involving marketing models and geometric figures.

Key vocabulary

Scale model: A three-dimensional representation of an object maintaining exact proportional dimensions of the original.; Learners created a scale model of the school hall using card paper and linear ratios.
Area scale factor: The square of the linear scale factor relating corresponding surface areas of similar geometric figures.; With linear scale ratio 3 to 5, the area scale factor is 25 over 9.

Lesson preview

Slide 1 · Modelling Physical Structures with Scale NetsModel · 18 min

Figure 1: A flat net on a grid showing dimensions for a room, alongside the folded three-dimensional replica.

Applying scale enlargement concepts in practical contexts allows architects, builders, and designers to construct precise scaled prototypes. Learners construct a flat net of classroom walls, floor, and ceiling on thick paper using a proportion of $1 : 100$ . Folding this 2D pattern yields a 3D physical replica of the room. By comparing their structures across working groups, learners observe how linear ratios preserve proportional dimensions and spatial relationships accurately. Use Figure 1 to see how flat dimensions form a three-dimensional physical room.

Scale drawings allow large physical structures to be represented accurately on portable sheets of manilla paper.
A linear scale factor of 1 : 100 converts each actual metre into exactly one centimetre on the net.
Folding the net creates a three-dimensional model that visually mimics the actual room geometry.
Group discussions help learners appreciate practical applications of scaled models in construction and architectural design.

Worked example. Convert actual dimensions to centimetres:

12 m = 1200 cm

and

9 m = 900 cm

. Apply linear scale factor

k = \frac{1}{100}

to find model dimensions: length

= 1200 \times 0.01 = 12 cm

and width

= 900 \times 0.01 = 9 cm

. Calculate model floor area:

Area = 12 cm \times 9 cm = 108 {cm}^{2}

. Calculate volume scale factor:

k^{3} = {(\frac{1}{100})}^{3} = \frac{1}{1 000 000}

or ratio

1 : 1 000 000

. Answer: Model floor area is $108 {cm}^{2}$ and the volume scale factor is $1 : 1 000 000$ ..

Check question: A rectangular store room measures $10 m$ long, $5 m$ wide, and $3 m$ high. If learners construct a model using manilla paper at a scale of $1 : 50$ , what is the area of the model floor in ${cm}^{2}$ ?

$1 {cm}^{2}$
$50 {cm}^{2}$
$200 {cm}^{2}$
$10 000 {cm}^{2}$

Show answer

$200 {cm}^{2}$ . First, convert the actual floor dimensions into centimetres: $10 m = 1000 cm$ and $5 m = 500 cm$ . Next, apply the linear scale factor of $1 : 50$ to find the model dimensions. The model length is $1000 \div 50 = 20 cm$ and the model width is $500 \div 50 = 10 cm$ . Finally, calculate the model floor area: Area $= 20 cm \times 10 cm = 200 {cm}^{2}$ .

Slide 2 · Industrial and Commercial Applications of Scale FactorsClosing · 22 min

Figure 2: A diagram comparing a standard tea tin to an enlarged version, demonstrating different scale factors.

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This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

Both slides with diagrams and class activities
Teacher notes, SNE adaptations and assessment checks
Homework and the other 10 lessons in this sub-strand

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Appreciating Similarity and Enlargement in Real-Life Applications

By the end of this lesson, learners should be able to

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 11 lessons in Similarity and Enlargement