Mathematics for Future Elementary Teachers
These lessons focus on understanding why mathematics works - not simply memorizing procedures. Explore mathematical ideas through models, multiple strategies, student thinking, and connections that can help you both understand mathematics and eventually explain it to others.
The three Math for Teachers courses build on one another, so topics may overlap. Use the course groupings below as a guide, or explore any module independently.
Math for Teachers 1
Numbers, operations, place value, and fractions
Modules 1–4
Math for Teachers 2
Geometry, measurement, ratios, proportions, and percent
Modules 5–7
Math for Teachers 3
Algebraic thinking, patterns, probability, data, and statistics
Modules 8–10
Jump to: 1 Number Sense | 2 Add/Subtract | 3 Multiply/Divide | 4 Fractions | 5 Geometry | 6 Measurement | 7 Ratios | 8 Algebra | 9 Probability | 10 Statistics
Module 1: Counting, Place Value, & Meaningful Number Sense
Goal: Build a conceptual understanding of how numbers are represented, organized, compared, and used.
How Counting Actually Works - Counting Principles
Understanding Quantity - Cardinality and One-to-One Correspondence
Why Digits Mean What They Mean - Place Value
Building Numbers in Base Ten - Composing and Decomposing Numbers
(COMING SOON) Which Number is Really Bigger? - Reading, Writing, & Comparing Numbers
Extending Place Value - Decimals and Powers of Ten
(COMING SOON) What If We Counted Differently? - Other Bases
(COMING SOON) Representing Numbers in Different Ways - Models, Words, Symbols, and Expanded Form
(COMING SOON) How Big Is It Really? - Estimation & Magnitude
(COMING SOON) Understanding Zero - Placeholder, Quantity, and Identity
Module 2: Addition & Subtraction - Concepts, Strategies, and Algorithms
Description coming soon
Module 3: Multiplication & Division - Meaning Before Procedure
Description coming soon
Module 4: Fractions, Factors, & Number Structure
Description coming soon
Module 5: Geometry - Shapes, Lines, & Angles
Description coming soon
Module 6: Measurement & Geometric Relationships
Description coming soon
Module 7: Ratio, Proportion, & Percent
Description coming soon
Module 8: Algebraic Thinking, Patterns, & Functions
Description coming soon
Analyzing Mathematical Equality
Keeping Both Sides Balanced
Finding Rules in Repetition
Inputs, Outputs, and Rules
Visualizing Relationships
Constant Rate of Change
Beyond Linear Relationships
Solving Problems with Shape
Using Precise Mathematical Language
Module 9: Probability & Randomness
Description coming soon
Understanding Chance
Combining Chances
How Data are Collected
Categorical vs Numerical Data
Modeling Randomness
Module 10: Data & Statistical Reasoning
Description coming soon
Bar Charts and Pie Charts
Histograms and Dotplots
Mean, Median, and Mode
When Values Don’t Count Equally
Visualizing Spread and Outliers
Measuring Variability