# Algebraic Thinking

This page is a collection of my posts about teaching algebra and algebraic thinking. Although the concepts in the lessons/ activities are algebra concepts, they are always link to concepts in geometry, numbers, measurement, etc. The main teaching approach is Teaching through Problem Solving (TtPS) or via mathematical investigation. The objective is always dual: the learning of the mathematical concepts and the development of higher-order thinking skills/mathematical habits of mind.

### What is algebra?

- What is algebra? Can you teach it without the
*x*‘s? - The biggest idea in algebra is algebraic thinking
- Arithmetic versus Algebra
- What is algebraic thinking?

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**Teaching Algebra to Year 7 – 10**

Algebraic expressions

- Counting Smileys
- PCK Map for Algebraic Expressions
- Polygons and algebraic expressions – Part 2
- Polygons and algebraic expressions – Part 1

Equations

- Solving systems of equation by elimination – why it works
**How to teach the properties of equality through problem solving****The Properties of Equality – do you need them to solve equations?**

Functions

- How to introduce the concept of function
- Evolution of the definition of function
- Assessing understanding of graphs and function
- A framework for assessing understanding of function in equation form
- Zeroes of Polynomial Functions
- Graphs of rational functions
- Trigonometric functions

PreAlgebra

- PCK Map for Integers
- Who says subtraction of integers is difficult?
- A problem solving approach for introducing positive and negative numbers
- Assessing operations involving integers
- Algebraic thinking and subtracting integers – Part 1
- Algebraic thinking and subtracting integers – Part 2
- Subtracting integers using numberline – why it doesn’t help the learning
- What is an integer?
- Teaching absolute value of an integer
- Patterns in the table of integers

**Algebra lessons for K-Year 6**

- What is algebra? Can you teach it without the
*x*‘s? - Teaching for conceptual understanding of equal sign
- Pupil’s understanding of equal sign

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