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Operations with Fractions using Pattern Blocks

Overview and Objective

In this lesson, students practice four operations with fractions using pattern blocks by expressing one block in terms of the other.


The traditional pattern blocks are under the Polygon tiles of the Polypad. If students are already familiar with the blocks, you may want to change their colors to the original one be selecting Alternate Tile Colours in the settings

Start by inserting four pattern blocks into a blank canvas; the equilateral triangle, rhombus, trapezium, and hexagon. Ask students how many triangles, rhombuses, or trapeziums can be used to cover the hexagon?

Share this canvas with the students and let them express each block in terms of one another.

In the first part, where the triangle is assumed to be 1 unit, it is easy to express the others since we can use whole numbers to describe them. In the second section, where the rhombus is 1, students still can easily find the hexagon. Since the triangle is half of the rhombus, they might also find 1/21/2 by intuition. Remind them to write any fraction in the answer boxes as a/b format with no space in between.

Let them work on the possible ways to express the trapezium in terms of the rhombus. Remind them to make their thinking visible on the canvas using the blocks.

In the third section, where the trapezium is set to be 1, the hexagon and the triangle can still be found easily. Give students some time to work on the rhombus. There are many ways to find its value. Here are some possible expressions.

In the last section, where the hexagon is valued as 1, students can express the other blocks using unit fractions.

Main Activity

Share this Polypad canvas and allow students time to work on the questions.

Remind students that they may use the given block(s) to cover the asked shapes to help them work towards the solution. They may also change the transparency of the blocks when overlapping them. Here are some examples:

Share some student work with the class. Invite students to share which approaches they used to find the answers. There are several methods to find the answer; some might only consider the proportional relations between the given and asked fraction models. Some students might use different blocks as unit fractions to build up the given models.


To close the lesson, share this canvas with students and ask them to create fraction models using the four pattern blocks. At the end of the lesson, let them share their models with the class. Finally, compare and comment on different models that represent the same fractions.

Polypads for This Lesson

To assign these to your classes in Mathigon, save a copy to your Mathigon account.

Click here to learn how to share Polypads with students and how to view their work.

PB Fractions Warm up – Polypad – Polypad
Adding PB Fractions 1 – Polypad – Polypad
Adding PB Fractions 2 – Polypad – Polypad