Envisioning a Computationally Enhanced Mathematics Curriculum in Hong Kong’s Primary & Secondary Schools
Pythagorean Theorem
Lesson Overview
This course aims to explore the Pythagorean Theorem with a visual representation by employing the simple underlying mechanism of moving and turning. By observing the speed of the construction of squares based on the three sides of a right triangle, students may infer the relationship between their areas, thus exploring the Pythagorean Theorem. The following task could employ these principles to find the distance formula in the coordinate system.
Learning Objectives

Use broadcast to connect the movement of different sprite, in order to draw any lines between two points.

Using “distance to object” to gain information of the length of the lines.

Use My block to create a function that can draw solid square with any length by move and turn with the length to be the parameter.

Use the created “My block” as a subroutine to draw solid square on the three sides of the right triangle.

Observe the drawing speed and make inference.
Task Description and Resources
Task 1: Draw Right triangles with two sprites
Purpose: Create a right triangle, which we can determine the length of the rightangle sides with one sprite and use another sprite to draw the hypotenuse.
Suggest Steps: by move XX steps and turn 90 degrees, we can create two mutually perpendicular line segments. Then use broadcast to connect to the other sprites to follow, we can create the hypotenuse.
Reference Code:
Task 2: Create solid squares
Purpose: Use move and turn to draw a solid square, set it as “My block”.
Suggest Steps: Determine how to use repeat, move and turn to scan a certain area (can refer to the scan task of drawing with conditions). Create the My Block and set the length (of the square) as the parameter that we can change. Then use the My Block function to draw solid square with different sizes in different positions (and directions).
Reference Code:
After simulation, reflect on the results:

What are the differences between Task 1 and Task 2, and why?

What can we infer from the results?
Task 3: Draw the Pythagorean Theorem
Purpose: Draw three solid squares based on the three sizes of the right triangle. Observe the time used for the sprites to finish drawing.
Suggest Steps: Draw the right triangle with two sprites in Task one. Use the created My Block to draw solid squares which equals to the length of the three sizes of the right triangle. Different colours can be used for the two sprites, and the triangle can be in any size or directions. This will result in one sprite drawing the solid square of the two rightangle sides, the other sprite drawing the solid square of the hypotenuse. Observe the time used and make inference from the outcomes. We can also consider other ways such as [touch colour] and [count] to make inferences of the areas.
Reference Code:
Link to Scratch: https://scratch.mit.edu/projects/1002756976
Summary
This course guides students to explore the relationship between the areas of squares based on the three sides of the right triangle. It is thought to be helpful to build inferences of the Pythagorean Theorem. The tasks involve various important CT concepts and practices such as subroutine, sequence, events. The decomposition of the task to achieve the final goals is also valuable for improving the problemsolving ability. The task can be used as a prerequisite task for the following learning including distance formula in coordinate systems.
Acknowledgement
The author would like to thank Zhi Hao CUI for designing this lesson and appreciate all the anonymous teachers and students who participated in this research.