Elementary Algebra: Operations and Fractions
Welcome!
The aim of our mathematics modules is to support educators who are charged with advancing students’ development of algebraic thinking.
Algebraic thinking begins well before middle school or high school. In fact, it begins in the elementary grades. This module is designed as one of two pre-cursor modules to ALG1, ALG2, and ALG3. In this module, we focus on helping students understand the concepts of the operations (i.e., addition, subtraction, multiplication, and division) as well as understanding of fractions, comparing and ordering of fractions, computation with fractions, and ratios.
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. Elementary grade
educators will find the modules most-aligned to the math standards they teach.
Module time estimate: 5Â hours
Elementary Algebra: Operations and Fractions
Module Description
In Elementary Algebra: Operations and Fractions, we will work toward understand of two major domains within the elementary grades. First, we will focus on number and operations in base ten. We will overview the concepts of addition, subtraction, multiplication, and division. We will review computation with each operation and word-problem solving across the operations.
Second, we will focus on number and operations with fractions. We will highlight three models of fractions. Then, we will discuss how to use the models to compare, order, add, subtract, multiply, and divide fractions. We will finish with a focus on ratios and proportions.
This module helps to build skills that lay the foundation for success with later algebraic thinking in middle school and high school.
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 yellow arrow and the boxes below detail the math content and learning strategies that we discuss in this module.
Math Content Focus
- Concepts of addition, subtraction, multiplication, and division
- Fact fluency
- Whole-number computation strategies
- Word-problem solving
- Models of fractions
- Comparing and ordering fractions
- Fraction computation strategies
- Ratios and proportions
Learning Strategies
- Focus on math vocabulary
- Explicit teaching and practice on math concepts and procedures
- Use of representations (i.e., concrete hands-on tools, virtual manipulatives, drawings)
- Fluency building activities
- Word-problem solving.
Elementary Algebra: Operations and Fractions focuses on major content related to arithmetic that is foundational for later success with algebra.
Who is the audience for this module series?
The math modules are designed for educators who are responsible for teaching math and algebraic thinking to elementary and middle school students and intervention specialists who are responsible for supporting elementary and middle school students with disabilities, but who may feel under-prepared to do so. What do we mean by under-prepared?
- Perhaps your background isn’t in math, but you are charged with teaching math: this series will help you to both bolster your understanding of math concepts and procedures 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 or learn math differently.
Emphasis for this series is placed on educators of elementary and middle school students, as the lessons in the ALG series (ALG 1, ALG2 and ALG3) align most directly with grades 6, 7, and 8 math standards. However, this module focuses on earlier foundations to algebraic thinking and will most likely be appropriate for elementary educators who support the early learning of algebraic thinking that occurs across Kindergarten through Grade 5. This module may also be appropriate for middle grade educators who work with students with unfinished learning from the elementary grades.
Module Objectives
Describe the concepts of addition, subtraction, multiplication, and division. Explain how the concepts of the operations relate directly to common word-problem schemas.
Demonstrate different ways to add, subtract, multiply, and divide using computation.
Use the length, area, and set models to represent fractions. Use the models to compare, order, add, subtract, multiply, and divide fractions.
Demonstrate how to use models to show different types of ratios and proportions.
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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