Effective: 2024-05-01

Course Description

The course outline below was developed as part of a statewide standardization process.

General Course Purpose

The purpose of this course is to provide a comprehensive and conceptual understanding of fundamental mathematical concepts covered in VDOE K-8 mathematics Standards of Learning (SOLs). This course is intended to cover the content of the first semester of a two-course lower-level math for elementary educators sequence, with the second semester of the course taken at the four-year college after transfer.

Course Objectives

• Quantitative Literacy
• Use problem-solving skills and quantitative reasoning to solve problems, explore new ideas, and improve your understanding of mathematics
• Critical Thinking
• Formulate multiple solution paths for mathematical problems and describe connections between and within these paths
• Written Communication
• Demonstrate proper use of terminology, notation, and/or written conventions used in the field of mathematics and mathematics education
• Professional Readiness
• Analyze and evaluate the mathematical thinking of K-8 students expressed in their oral and verbal reports, written work, and authentic representations
• Design strategies to develop positive math beliefs, including growth mindset, persistence in work, and productive student struggle

Major Topics to be Included

• Problem Solving and Quantitative Reasoning Skills
• Identify connections between conceptual knowledge and standard algorithms
• Generate meaningful mathematical representations using algorithms, employing both written formats and physical manipulatives
• Counting and Number Systems
• Describe quantities across multiple number systems, encompassing natural numbers, whole numbers, integers, and rational numbers
• Establish connections between concepts such as place value and regrouping, explaining their relationship within the base-ten number system
• Analyze similarities and differences between the base-ten number system and numbers in alternative bases
• Integers and Rational Numbers
• Apply fundamental understanding of whole numbers to grasp integers and their associated operations
• Utilize core principles of number theory, such as prime factorization, divisibility, greatest common factors, least common multiples, etc., to examine the structure of integers
• Generate multiple representations for rational numbers and justify their equivalence in various forms
• Comparing Fractions and Arithmetic Operations
• Make valid comparisons between rational numbers and model arithmetic calculations with them
• Utilize various reasoning approaches to justify arithmetic operations involving whole numbers
• Develop standard and non-standard algorithms for addition, subtraction, multiplication, and division by drawing on principles of counting, place-value grouping, and partitioning
• Base Ten and Other Bases
• Exhibit adaptable and conceptual thinking while exploring numbers, operations, and their interconnections
• Investigate the concepts of place value and regrouping within the framework of the base-ten system and alternative numerical bases
• Addition and Subtraction
• Use, compare, and mathematically justify different strategies and representations to solve addition and subtraction problems
• Develop versatile computational skills across all number categories, using and articulating various methods for addition and subtraction
• Multiplication and Division
• Formulate multiple solution paths for multiplication and division problems and describe connections between and within these paths
• Assess and explain the mathematical ideas and reasoning used in multiplication and division
• Formulating Solution Paths and Beliefs about Mathematics
• Embrace a growth mindset to reflect on personal beliefs regarding mathematics and the teaching and learning processes, fostering an open exploration of mathematical concepts.
• Generate comprehensive mathematical representations for the course content, incorporating written formats (such as area models, number lines, scaled diagrams, strip diagrams, etc.) and tangible manipulative tools (like base-ten blocks, Cuisenaire rods, linking cubes, pattern blocks, etc.), to enhance understanding and engagement.