The Quantum To-Go program goal is to match scientists, engineers, and professionals in the field of Quantum Science, Engineering, and Technology with classrooms across the country to introduce the importance of quantum science and technologies and increase student...

# QIS Key Concepts for Early Learners: K-12 Framework

## High School Math

## Incorporating QIS into High School Math

For each key concept, the group identified the mathematics required to understand the concept presented. While there are a total of nine QIS Key Concepts, we only included the subset that had clear mathematical content covered in middle school and beyond in the framework. Some key concepts include multiple concepts, so if a single key concept has multiple individual applications of mathematics, it is included multiple times.

Once the mathematical concepts for each key concept were identified, the group identified the **Common Core State Standard** associated with the mathematical concept as well as the **course** in which that content is typically taught. (The Common Core State Standards for Mathematics are available here: https://www.nctm.org/ccssm/)

Individual courses were then identified that commonly teach that common core state standard. However, there were two circumstances in which multiple courses were identified for the same learning goal. First, not all states and school districts cover the same standards in the same courses, so the same standard might be taught in different courses (e.g. Algebra 1 or Geometry). Second, some concepts are introduced in one course and might be covered in more depth in a follow-on course, so instructors could choose to cover the Quantum concept in either course (e.g. Algebra 1 or 2).

To create relationships between different concepts, we considered whether the mathematics or QIS material being covered in one key concept was then used in a subsequent one. In the learning trajectory, there are two kinds of learning goals, both of which we had to consider.

- Mathematical concepts that will be used in quantum later (e.g. the probability of two independent events is their product).
- Applications of mathematical concepts to quantum (e.g. entangled qubits’ outcomes are not independent).

Document organization:

This document has several pieces of information associated with each learning goal of the learning trajectory.

- QIS Key Concept
- Relationship of Key Concept to mathematical concept
- Common Core State Standard associated with the mathematical concept
- Course that in which the concept is typically taught
- Relationship between this learning goal and any pre-requisite learning goals

The purpose of the QIS K-12 Key Concepts Math Focus Group was to create a document that would be useful to curriculum developers and teachers, providing guidance about places where high school mathematics learning goals can be satisfied at the same time as content in the QIS K-12 Key Concepts.

The focus group brought together experts, educators familiar with teaching and research of mathematics concepts at high school and/or university levels. The members were:

- Eugenie Alvares, Simpson Academy for Young Women, Chicago, IL
- John Brown, Lake View High School, Chicago, IL
- *Diana Franklin, University of Chicago, Chicago, IL
- Kit Golan, Lesley University, Cambridge, MA
- Maajida Murdock, Baltimore County Public Schools, Baltimore, MD
- *Brent Yen, University of Chicago, Chicago, IL

*Designates working group leads, conveners, and/or framework editors.

The result is a set of activities that both teach mathematics skills typically taught in high school as well as very early QIS concepts. These are not meant to be full activities or lesson plans – different instructors may use different languages, choose to go into different amounts of depth, etc. We hope, however, that by providing examples of synergistic activities, curriculum developers will be able to use these (and their own ideas) to create either individual activities or sequences of activities that build math skills and knowledge while, at the same time, introducing students to some basic QIS concepts.

The output is downloadable via the following link. We are releasing this first version for feedback from the community. Please reach out to us with your comments/questions at edwardse@illinois.edu.

#### DOWNLOAD THE FRAMEWORK FOR QIS + K-12 MATH (updated 12-7-2023)

# Resources and Tools

The resources in this repository are created and submitted by members of the quantum education community. We review them prior to posting and provide information on suitability for different audiences. We also note when teachers have either co-developed or reviewed the resource. Did we miss anything? Contact our team to let us know!

## Textbook: Introduction to Classical and Quantum Computing

This resource is a textbook was used in an undergraduate course at Creighton University. It is based on lecture notes and homework problems from a course taught by Prof. Thomas Wong during 2018 and 2020. Some of the introductory material may be appropriate for AP High...

## EPIQC informal activities for early ages

EPiQC is an NSF-funded quantum computing research program. As part of their education effort, experts in computer science education and early education have developed activities to introduce children and their families to quantum computing topics. The website of the...

## Lecture notes: The Mathematics of Quantum Mechanics

The Mathematics of Quantum Mechanics is a set of notes aimed at high-school students, and provide the necessary mathematical background to dive into quantum information science. Through this three-chapter introduction, students will gain the necessary background in...

## QBraid

qBraid.com offers an online platform for learning about quantum information and programming on quantum computers. It is targeted at different levels, spanning high school, undergraduate. For example, non-quantum learners may visit qbook.qbraid.com/learn to access an...

## Quantum Country

This resource is an online self-guided set of essays about quantum computing, quantum mechanics, and other quantum topics. It is similar to an online textbook and includes some Q & A for the reader to help reinforce concepts. The authors describe the resource as...

## EdX Course: Introduction to Quantum Computing for Everyone

This is an online course offered on EdX. It is an introduction to quantum computing aimed at novices and requires learners to have an understanding of basic algebra. The course covers the future impacts of quantum computing, provides intuitive introductions of quantum...

## Lesson Modules by the Institute for Quantum Computing

The University of Waterloo’s Institute for Quantum Computing (IQC) has created five lesson plans for senior (12th grade) high-school Physics classes, including introductions to superposition, wave-particle duality, the uncertainty principle, quantum computing, and...

## Quantum Computing Zines

Zines are short, comic-book-style pamphlets that fit on an 8.5”x11” piece of paper and intended for general non-expert, informal learners. The zines cover a number of quantum computing topics ranging from superposition to quantum notation. These begin with analogies...

## EdX Course: Quantum Mechanics for Everyone

This is a quantum mechanics (physics) course aimed at non-scientists and is intended to be accessible to high school level students and above who have studied Algebra II and Trigonometry. It introduces the concepts of superposition and entanglement, as well as others....