The Warlord’s puzzle: A mathematical adventure

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This is an activity based on the picture book The Warlord’s puzzle: A mathematical adventure

Achievement Objectives
GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
GM3-3: Classify plane shapes and prisms by their spatial features.
Specific Learning Outcomes

Students will be able to use the fractional relationships between pieces of a tangram to solve problems involving area.

Description of Mathematics

Features of shapes can enable you to solve spatial problems.

Required Resource Materials
  • The Warlord’s puzzle: A mathematical adventure by Virginia Walton Pilegard
  • Several tangrams copied on coloured paper/card and cut into the 7 pieces (the master is located on the end pages of the book).

Fraction Action
This activity is based on the picture book The Warlord’s puzzle: A mathematical adventure

Author: Virginia Walton Pilegard
Illustrator: Nicolas Debon
Publisher: Pelican (2000)
ISBN: 978-1-56554-495-6

Set in ancient China, the story explores the puzzle of the tangram. A beautiful tile is dropped and breaks into pieces. The Warlord holds a contest to see who can put it back together and the unlikely hero is a peasant boy who sees the shapes within the puzzle representing silhouettes of familiar objects. The story is richly illustrated and a copy master of the tangram puzzle is on the endpapers for copying.

Lesson Sequence:

  1. Prior to reading, set the context fro the story by explaining the ancient tangram puzzle as being a “deceptively simple” puzzle that has fascinated people for generations. Ask students to brainstorm what they know about the features of a triangle, a square, and a parallelogram. Focus of their prior knowledge of angles, edges and vertices.
  2. Share the book with your students.
  3. Distribute a tangram to small groups of 2-3 students and ask them to solve the “broken tile puzzle” and make the pieces in to a square. Remind them about the characteristics of a square having 4 square corners and 4 equal sides, and the characteristics of the shapes with which they are working.
  4. After everyone has solved the puzzle (perhaps with some clues and prompts provided) ask students to work together to explore the tans with the following two activities:
    a. Fractions: What fraction of the whole does each tan represent? Students use their knowledge of halving to discover that the 2 large triangles together are ½ of the puzzle and therefore each represent ¼ of the whole. The middle sized triangle is half of a large one and therefore is 1/8 of the whole and the small triangles are each half of the middle sized one and therefore each 1/16. The two small triangles can be arranged to make the shape of the small square and the parallelogram so therefore those 2 shapes must also both be 1/8 of the whole.
    b. Area: Ask students to draw a tangram puzzle on 1cm grid paper. The puzzle needs to be in its square form with the dimensions 12cm x 12cm. Ask them to calculate the area of the whole puzzle and then each piece using what they know about the fractional relationship between each piece and the puzzle as a whole.
  5. Following on from this, students can be given tangram silhouettes to solve. There are many internet links for copies of these and many sites that have digital tangrams as well. Once students have become familiar with the puzzle they can then begin to create their own silhouettes or use 2 or 3 tangram sets to create larger figures.
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Level Three