ALG3 – Algebraic Thinking 3: Functions
Welcome!
The aim of the ALG series is to support educators who are charged with advancing students’ development of algebraic thinking.
This is the third module in the algebraic thinking series, ALG3. In this module we focus on learning about functions.
Audience: Educators interested in enhancing their algebraic thinking, math content knowledge, and teaching strategies to support their students’ learning – particularly those students who experience and/or learn math differently. Upper elementary and middle school grade educators will find the modules most-aligned to the math standards they teach.
Module time estimate: 3 hours
Prerequisites: ALG 1, ALG 2
To enroll in module ALG1, click the button at the bottom of the page. 
ALG3 – Algebraic Thinking 3: Functions
Module Description
In ALG3, we turn to the important topic of functions. While solving equations involved getting one (or two) correct answers, in functions we define a relationship between input quantities and output quantities. In other words, we begin to explore relationships between two variables.
The BRICK modules continue to intermingle content knowledge with common misconceptions and ways to teach. Our goal in this series of modules to help you build stronger connections to the content you teach and fill your “instructional toolbelt” with a wide variety of ideas for you to support your students to develop algebraic thinking.
Algebraic Thinking Builds from Kindergarten
Did you know that there are Ohio math standards that build algebraic reasoning as early as kindergarten? The learning progression map below (ODE, 2020) shows the progression of number, operations, and algebraic thinking strands that are built on over time toward algebra 1. The purple arrow and the boxes below detail the math content and learning strategies that we discuss in the ALG3 module.
Math Content Focus
- Defining and describing functions and comparing them to equations,
- Examples of simple math functions – from scenario to three representations: equation (rule), table, and graph,
- Focus on linear equations,
- Analyzing linear equations to understand how changes in equations impact the slope and the y-intercept,
- Cycling through noticing, conjecturing, and investigating in math.
Learning Strategies
- Explicitly teaching by using stepwise guides,
- Explicitly teaching with side-by-side comparisons,
- Using solved problems as the basis for problem analysis,
- Drawing out noticings and conjectures from students, and guided investigations in response to conjectures,
- Employing gradual increase in problem difficulty using guided and independent practice to inform educators’ decisions regarding timing for leveling up,
- Leveraging real-life examples to bridge understanding of solutions to decontextualized math functions.
ALG3 focuses on understanding and using functions.
Who is the audience for this module series?
The ALG module series is designed for educators who are responsible for teaching algebraic thinking to upper elementary and middle school students and intervention specialists who are responsible for supporting upper elementary and middle school students with disabilities, but who may feel under-prepared to do so. What do we mean by under-prepared?
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- Perhaps your background isn’t in mathematics, but you are charged with teaching math: this series will help you to both bolster your understanding of math concepts and think about how to teach them.
- Perhaps you have a strong math background but are unsure how to support students who struggle: this series will help you to think about how you can apply evidence-based practices aligned with Universal Design for Learning (UDL) to support your students who may experience/learn math differently.
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Emphasis for this series is placed on educators of upper elementary and middle school students, as the lessons in the ALG series align most directly with grades 6, 7, and 8 mathematics standards. While ALG1 focuses on earlier foundations in algebraic thinking, educators in grades 6-8 will benefit from a review of the ways algebraic thinking is developed in earlier grades so they may a) build on that learning and b) intervene in topics not mastered during those earlier grades.
Teachers of grades 4 and 5 may also benefit from the modules to better understand how their instruction impacts the progression of algebraic thinking beyond their grade level.
ALG 3 Module Objectives
Objective 1.
Describe what a function is and compare and contrast a function with an equation.
Objective 2.
List and define key terms and identify symbolism associated with functions.
Objective 3.
Describe common misconceptions students often hold that may influence their learning about functions and list strategies to eradicate them.
Objective 4.
Model functions using three key representations: mathematical equations, tables, and graphs.
Use of People-First Language
The BRICK Science and Mathematics modules have been created to support intervention specialists (aka special education teachers) and teams of general and special education personnel in more effectively delivering science and mathematics content to students with disabilities and learning difficulties who need additional support. In these modules, we have opted to follow the general guideline of using person-first language. While we are sensitive to the evolving nature of preferred terms for the various communities impacted by naming conventions (e.g., Woodridge, 2023), we have opted to use the term Students with Disabilities, or SWD, throughout the modules when referring to students who receive special education services, regardless of their specific disability condition.
Policies and Navigating the Course
The BRICK (Building Robust Intervention Specialist Content Knowledge) project’s primary goal is to enhance the content knowledge and teaching practices of Ohio educators with a particular emphasis on educators whose primary role is to teach and support students with disabilities and/or learning difficulties. Increased content knowledge in evidence-based math practices will support intervention specialists and other educators (general education teachers, paraprofessionals, school-based tutors, instructional specialists) in making such content more accessible for students with disabilities and learning challenges. BRICK online learning modules aim to develop educators’ content knowledge as well as content-specific pedagogical knowledge, particularly in the use of UDL 3.0, to support student learning. The project focuses on supporting educators to use explicit, systematic instruction, emphasizes the connections between achievement in literacy and achievement in math, offers a virtual community of practice for educators, and provides family materials that students and their family members can use to talk about math content at home.
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