Year level: Year 5

Strand: Number

Lesson length: 75 min

In this first lesson in the series, students investigate fractions through the relationships between various shapes. They then use tangrams to puzzles to explore fractions. 

This lesson was developed in collaboration with the Australian Association of Mathematics Teachers (AAMT).

Fraction shape puzzles Image

Achievement standard

Students order and represent, add and subtract fractions with the same or related denominators.

Content descriptions

Solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies. AC9M5N05

Solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions. AC9M6N05

General capabilities

General capabilities

  • Numeracy: Interpreting fractions (Level 7 and Level 8)
  • Critical and Creative Thinking: Generating: Create possibilities
  • Literacy: Speaking and listening

Cross-curriculum priority

Asia and Australia’s engagement with Asia: Understanding Asia’s global significance

  • Reserve time at the end of the lesson for students to reflect and demonstrate their learning.
  • Use the Fraction shape puzzles exit ticket on the teacher's slides (slide 6): ‘If the blue triangle is worth 1, what are the other shapes “worth”? Show your working.’
  • Expect responses such as: Inability to get started; students are unsure of which shape to do next or equivalent fraction shapes.
  • Basic arithmetic skills (addition, subtraction and multiplication).
  • Some background information about numerators, denominators and other basic fractional knowledge, including equivalent fractions.
  • Exposure to tangrams or the relationships between shapes is advantageous.

Some students may:

  • find the introduction of shapes like triangles, squares and parallelograms used as representations of fractions somewhat abstract (particularly for younger students), leading to potential confusion. Refer to real-life examples like 1 2 of a sandwich and 1 4 of an orange to emphasise that they have seen fractions in different shapes before. Encourage students to draw the whole square and divide into halves, quarters etc and compare with the tangram pieces
  • find it challenging to grasp that different visual representations can still represent the same fraction, for example, that different puzzles could both represent 1 2 , even if they look different. Encourage students to replicate equivalent fractions using smaller pieces to confirm that they cover the same area or can be comprised of the same smaller pieces
  • struggle to add fractions with different denominators even using the tangram pieces. Encourage them to subdivide larger pieces and label each part in terms of sixteenths, for example, marking the two halves of the medium triangle and labelling each part  1 16 .

What you need:

  • Lesson plan (Word)

  • Teacher's slides (PowerPoint)

  • Fraction shape puzzles worksheet (Word)

  • Fraction shape puzzles tangram template (Word)

  • Scissors

Preparation tips

  1. Tangram required: one copy (A4) for each students and one teacher copy (A3), pre-cut for demonstration (or physical tangram pieces if available).