Effective mathematics instruction requires knowledge of both mathematics pedagogy and mathematical content. Yet many elementary teachers express lack of confidence in their mastery of math skills and concepts which may be rusty or were never fully understood in the first place. These self-directed modules are intended to support primary- and junior-grade teachers who seek to solidify or extend their mathematical knowledge for teaching. They include key concepts and procedures in Ontario’s elementary math curriculum. Each module concludes with an interactive problem-solving slide deck that provides an opportunity to apply and practice relevant concepts in different contexts.

### Working Through the Modules

We encourage teachers to complete the modules and practice problems at their own pace. While the modules were designed to build upon one other, they can also stand alone, depending on your needs. Interconnections among mathematical concepts make some degree of overlap among topics inevitable. The list of modules and topics will help users to locate particular pieces of missing knowledge.

Starting with the interactive problems at the end of a module may be another effective strategy for identifying areas for learning.

In our experience, group tutoring sessions strongly confirmed the value of collaborative problem-solving and exchange of strategies with peers. You might find it especially fruitful to work through the modules with colleagues.

The order of the modules as laid out below provides a logical progression of skills and concepts.

### Learning Modules and Problem Sets

Module 1 - Whole Numbers and Operations

- Place Value
- Multiplying Whole Numbers
- Dividing Whole Numbers
- Factors and Prime Numbers

Module 2 - Rational Numbers (Fractions)

- Representing Fractions
- Simplifying Fractions
- Converting Fractions
- Operations with Fractions
- Greatest Common Factor (GCF)
- Least Common Multiple (LCM)

Module 3 - Algebra (Patterns and Equations)

- Place Value
- Multiplying Whole Numbers
- Dividing Whole Numbers
- Factors and Prime Numbers

## Module 4 - Integers and Operations

- Order of Operations
- Positive and Negative Numbers
- Decimal Numbers
- Exponents

Module 5 - Rational Numbers (Fractions, Decimals, and Percents)

- Converting Among Fractions, Decimals, and Percents
- Working with Ratios, Proportions, and Rates
- Proportional Reasoning
- Probability

Module 6 - Algebra (Linear Relationships and Coordinate Graphing)

- Identifying Dependent and Independent Variables
- Linear Relationships
- Linear Equations

Module 7 - Measurement

- Common Units of Measurement
- Volume and Capacity
- Metric Orders of Magnitude: Standard Prefixes
- Converting among Metric Units
- Converting between Units Using a Conversion Factor

Module 8 - Geometry

- Defining and Understanding Shapes
- Classifying Angles and Triangles
- The Pythagorean Theorem
- Perimeter and Area
- Surface Area and Volume

This set of learning modules developed out of group tutoring sessions held at the Dr. Eric Jackman Institute of Child Study between 2019 and 2021. The sessions offered support to teacher candidates in the Master of Arts Child Study and Education program at the Ontario Institute for Studies in Education as they practiced solving problems based on fundamental ideas in elementary mathematics. They were designed to supplement existing mathematics pedagogy courses for prospective teachers who sought additional reinforcement of basic mathematics skills and knowledge.