Year 7–8 Mathematics · Geometry & Coordinate Grids

Lesson 4: Scale, Enlargement & Zoo Enclosure Design

Using scale factors to enlarge and reduce enclosure designs — connecting proportional reasoning to the real engineering challenge of designing animal habitats.

🎯 Ngā Whāinga Akoranga | Learning Intentions

🧠 Students will know:

How scale factors work for enlargement and reduction; how to apply a scale factor to all coordinates of a shape; why scale and proportion are fundamental to design and architecture.

📐 Students will demonstrate:

Enlarge a zoo enclosure design by a scale factor of 2 and 3; reduce a given enclosure by a scale factor of 0.5; explain the relationship between scale factor and area.

🎥 Media Anchor & Mathematical Scaffold

Scale Factors & Similarity

Video Anchor: Year 9 Lesson 8: Scale Factors & Similarity — Mathspace Academy (Runtime: 9:00).

🧠 1. Before Viewing

If a miniature zoo model has an enclosure measuring 3cm × 4cm, and the scale is 1:100, how large is the real enclosure? Show your calculation.

👁️ 2. During Viewing

  • Full Watch: This video runs just over an hour in full — play a segment in class, or set it as homework. As you watch, record: (1) What is a scale factor? (2) How do you enlarge a shape by a scale factor? (3) How does the area change when you scale a shape? Work through at least one example from the video yourself.

🗣️ 3. After Viewing — Kaiako Move

Kaiako Move: Model the enlargement of a simple zoo enclosure shape using a scale factor on the coordinate grid. Show the before and after coordinates. Prove: area scales by the square of the scale factor.

Task: Enclosure Redesign: Take a small enclosure design (3×4 coordinate units). Enlarge it by scale factors of 2 and 3. Calculate the original and enlarged areas. Explain the pattern you observe.

⚡ Whakaoho | Do Now (5 mins)

If the kiwi house measures 4 coordinate units × 5 units, what would it measure after applying a scale factor of 3? What is the new area?

📐 Activity 1: Guided Mathematical Exploration (25 mins)

Design comparison: given a budget that allows a maximum area of 200m², and the current enclosure is 80m² (scale factor applied from your coordinate grid), what scale factors are possible for a redesign?

✍️ Activity 2: Application & Reflection (20 mins)

Scale factor summary: write a rule explaining how scale factor affects linear dimensions and area. Include a worked example from today's zoo context.

🏫 Kaiako Planning & Pedagogy Notes

Curriculum Alignment: Te Mātaiaho Mathematics Phase 3/4 — Geometry: apply scale factors to coordinate shapes; understand the relationship between linear scale and area scale.

Hamilton Zoo Context: All tasks use authentic zoo spatial data. Print the map to a stated scale and say what that scale is — ākonga cannot check an enlargement against an unstated one.

Cultural Connection: Enclosure design is where the maths meets manaakitanga: the scale drawing determines whether an animal has enough space. Ask ākonga what the enclosure would need to be if the animal's needs, not the site's limits, set the size.