Envisioning a Computationally Enhanced Mathematics Curriculum in Hong Kong’s Primary & Secondary Schools
The Concert Hall Problem
Lesson Overview
This course is designed to guide students through the exploration of algebraic expressions and arithmetic sequences within the context of real-world problems, using Scratch programming activities. Starting with calculating the total number of seats in a concert hall, students will learn how to translate mathematical concepts into programming logic, progressing to more complex scenarios such as calculations of the seating capacities of concert halls and stadiums with various layouts. Through a series of incremental tasks, students will deepen their knowledge of arithmetic sequences, algebraic expressions, and computational thinking.
Learning Objectives
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Master the application of arithmetic sequences and algebraic expressions in solving practical mathematical challenges.
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Develop a robust understanding of computational thinking, encompassing abstraction, pattern recognition, and algorithmic thinking.
Task Description and Resources
Task 1: Calculating Seats in a Concert Hall
Problem Statement: Problem Statement: Tom is having a concert and wants to know how many seats are available in the concert hall. As far as he can count, there are 18 seats in the first row and 25 rows in total. There is one more seat in the row behind each row. Based on what Tom has observed, how would you use Scratch to help him calculate the number of seats in the concert hall?
Key Concepts: Loop iterations, variable manipulation, simple arithmetic operations.
Reference Code:
Link to Scratch: https://scratch.mit.edu/projects/1000913299
Task 2: A New Stadium Layout
Problem Statement: Tom’s next concert will be held in a concert hall with a layout like the one below (Fig. (a)). Write a Scratch program to calculate the number of seats in the stadium.
Key Concepts: Advanced loop usage, sectional analysis, cumulative addition.
Reference Code:
Link to Scratch: https://scratch.mit.edu/projects/1000913843
Task 3: A Bigger Stadium Layout
Problem Statement: Tom’s concert received high popularity, and he decided to hold a concert in a bigger stadium. The seat layout for the stadium is shown as Fig. (b). Write a Scratch program using My Blocks to help Tom calculate the number of seats in the entire stadium.
Key Concepts: Custom blocks (“My Blocks”), complex looping structures, conditional logic for pattern variation handling.
Reference Code:
Link to Scratch: https://scratch.mit.edu/projects/1000916265
Summary
These tasks not only teach mathematical concepts like arithmetic sequences and algebraic expressions but also crucial computational thinking concepts (e.g. variables, iterations, subroutines) and practices (e.g. abstraction, pattern recognition).
Acknowledgement
The author would like to thank Oi-Lam NG for designing this lesson and appreciate all the anonymous teachers and students who participated in this research.