Transitions in the Conception of Number: From Whole Numbers to Rational Numbers to Algebra

Introduction

I firmly believe that instilling good math and money skills in students will lead them to greater happiness and better health.

Teaching students about the benefits of money doesn’t have to be “the root of all evil.” Many researches have shown that wealth and social prestige are often the driving forces to greater happiness and even better health.¹ In fact, money does matter, especially for many marginalized groups in the United States where the striking wealth and health disparities between the haves and have-not continue to rise.² In a 2021 published study, about 6,000 Americans of diverse backgrounds were surveyed about their wealth and happiness, and also were given a math test with 8 questions that varied in difficulty to get a sense of their math skills.³ The study shows that on average people who are better at math make more money, and are happier than people who are less mathematically inclined.⁴ Because money can make a person’s life easier, in terms of providing better shelter, education, healthcare, and access to more opportunities, I would argue that good money skills must be taught at an early age, especially in schools with a high population of underprivileged and underserved students. Let’s prepare students to gain control of money instead of money controlling their destinies.

With the use of U.S. coins and decimal fractions, my curriculum unit aims to strengthen 3^rd to 5^th grade students’ grasp of equivalency and place value among whole numbers, decimals, fractions, and percentages. For instance, a quarter can be represented as $0.25 or 25¢, and it is also equivalent to the fractions: 25/100, 5/20, ¼, as well as the percent: 25% of one dollar.

The unit is developed for 5th Grade U.S. History, and addresses the Math Common Core Standards 5.NBT.A.1 (place value), 5.NBT.A.3 (decimals), and 5.NF.A (fractions). The goal is to deepen students’ concepts of rational numbers and better prepare them to transition to more abstract thinking involving the use of algebraic signs, symbols, number variables, number expressions, and equations. This curriculum unit is designed for 3^rd to 5^th grades with two main learning objectives:

• familiarize students with the history of U.S. coins;
• guide students to use coins like quarters, dimes, nickels, and pennies to develop greater understanding of place values.