MathsFreePrintable

Māori Patterns Geometry Shapes

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Māori Patterns Geometry Shapes

A community arts team is planning a geometric display inspired by tukutuku and kōwhaiwhai patterns. Use the diagrams and measurements provided to investigate shape, symmetry and transformations. Māori art forms carry cultural meaning: treat them respectfully, and make your own design rather than copying a specific pattern.

Shape and angle investigation

Use the information and measurements in Questions 1–4.

1.A repeating panel is made from a rhombus tile. How many sides and vertices does one tile have?

2.A regular hexagon tile is used in a border. Calculate the size of each interior angle. Show how you know using the interior-angle sum.

3.The three angles in a triangular motif are 48°, 67° and x°. Find x, then classify the triangle by its angles.

4.A quadrilateral tile has angles 90°, 90°, 110° and y°. Calculate y. What is the total interior-angle sum of any quadrilateral?

Transformations and symmetry

Use the descriptions in Questions 5–7 to analyse each transformation. Treat each motif as a shape that can be moved without changing its size.

5.A first triangle points upward, and a second triangle of the same size points downward. One possible transformation from the first to the second, about its centre, is a rotation. State the angle of rotation and explain why the size and shape stay unchanged.

6.A third triangle has the same orientation as the first and is shifted 6 cm to the right. Name the transformation and state what happens to its side lengths and angles.

7.A motif has one vertical line of symmetry. Hana reflects it across that line. What does the reflection do to the motif, and which properties are preserved?

Plan and create

Apply your geometry to a display design.

8.A rectangular display panel is 1.8 m long and 1.2 m high. Calculate its perimeter and area. Include units.

9.The panel will have a border made from 24 identical square tiles arranged in one row. Each tile has a side length of 7.5 cm. Find the total length of the row, in centimetres and metres.

10.Design a repeating geometric border in the drawing box. Include at least two types of polygon and show a translation and either a reflection or rotation. Add arrows or a short key to identify each transformation. Your pattern should be your own respectful design, not a copy of a culturally specific motif.

Draw your original repeating design here.