ALG2 – Algebraic Thinking 2: Building Blocks
Welcome!
The aim of the ALG series is to support educators who are charged with advancing students’ development of algebraic thinking.
This is the second module in the algebraic thinking series, ALG2. In this module we focus on instruction that further develops students’ algebraic thinking. We also work with integers and exponents then use these skills to solve one-variable equations.
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: 4 hours
Recommended Prerequisites: ALG 1
To enroll in module ALG 2, click the button at the bottom of the page. 
ALG2 – Algebraic Thinking 2: Building Blocks
Module Description
In ALG2 we will work toward being able to manipulate equations to solve for one variable.
In the first part of the module, we focus on vocabulary and expanded symbol use as we progress in algebraic thinking. Additionally, we will work with integers and exponents. This module helps to build skills that will be needed later when working with functions.
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 blue arrow and the boxes below detail the math content and learning strategies that we discuss in the ALG2 module.
Math Content Focus
- Algebra-related vocabulary and symbols,
- Operations with integers and exponents,
- Multiple representations to solve equations with one variable, and
- Solving equations that require more than one step.
Learning Strategies
- Worked problems to shift from lower-level skills to critical thinking,
- Explicit teaching and modeling new math notation,
- Math Practice Standard 6: Attend to Precision,
- Parallel problems,
- Single-topic assessment and cumulative review, and
- Stepwise approach to solve equations.
ALG2 focuses on transitioning from arithmetic to algebraic thinking that can generalize math skills and properties to equations.
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.
ALG2 Module Objectives
Objective 1.
Describe how to solve equations that are missing one value. You will be able to do this for the four basic operations including when negative numbers are present.
Objective 2.
Discuss shifts in notation that may be misunderstood; these are best approached using explicit instruction to head off difficulties.
Objective 3.
Apply rules for four basic operations (addition, subtraction, multiplication, division) to exponents and incorporate exponents into equation solving repertoire.
Objective 4.
Apply content-specific tactics to intervene when students experience difficulties with content due to common misconceptions.
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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