Creating programs for Teaching algebra is a difficult component of teaching numeracy, and planning usually focusses on simple patterning activities & “What comes next?” tasks. We have put together 5 simple steps and teaching algebra tips to help you plan and create successful algebra activities for your students.
Many teachers struggle with what algebra is all about at the primary school level and tend to think of it from a High School Perspective which makes it difficult for teachers to plan Learning Experiences that help students develop the language, strategies, skills & knowledge needed to “DO Algebra”.
The work of Dr.Paul Swan… can change this. His work includes simple hands-on activities that are motivating, engaging, and curriculum focussed.
Algebra Tip 1 – Planning
When Planning your program REMEMBER that Algebra is not reserved for High School it is for ALL Year Levels. It is part of the F to Y10 Number & Algebra Content Strand, more specifically it is part of the sub-strand Patterns & Algebra and includes a continuum of skills , knowledge & understanding that needs to be developed across all year levels, including:
- Apply number sense and strategies for counting and representing numbers
- Explore the magnitude and properties of numbers
- Apply a range of strategies for computation and understand the connections between operations
- Recognise patterns and understand the concepts of variable and function
- Build on their understanding of the number system to describe relationships and formulate generalisations
- Recognise equivalence and solve equations and inequalities
- Apply their number and algebra skills to conduct investigations, solve problems and communicate their reasoning
Algebra in the Australian Curriculum:
- Foundation – ACMNA005
- Year 1 – ACMNA018
- Year 2 – ACMNA035
- Year 3 – ACMNA060
- Year 4 – ACMNAo81 – ACMNA082 -ACMNA083
- Year 5 – ACMNA107 – ACMNA121
- Year 6 – ACMNA133 – ACMNA134
Algebra Tip 2 – Algebraic Thinking
Unfortunately Algebra has a very bad reputation and the mere whisper of the word can illicit a huge amount of fear and anxiety in adults & children alike. Math anxiety is a real condition that unfortunately exists in the majority of math classrooms around the world and has been inadvertently passed on to students & adults even before they have tried Algebra for themselves!
If truth be know children and adults ‘do algebra’ regularly, comfortably, and dare I say it, enjoyably without even realising they are ‘doing it!’ For most of us the idea of what algebra is, is actually built on a misunderstanding that it is hard maths with the numbers missing, & a series of complicated processes that involve the dreaded X, Y & even Z!
But fear not… The secret to Algebra in Primary years is not to emphasise the teaching and learning of formulaic algebra. Instead the emphasis is on developing the thinking needed to “do Algebra” or the ALGEBRAIC THINKING.
ALGEBRAIC THINKING focuses on doing, thinking & talking about patterns in maths. It involves identifying, investigating, generalising, reasoning, explaining, continuing, predicting & justifying patterns in numbers, pictures & music. Do not underestimate the importance of teaching Algebra in your classroom, even in Kindergarten & the Early Years. Experiences with patterns & pattern making allows students to see order in other areas of mathematics, particularly NUMBER! Dr Paul Swan describes the importance of pattern experiences and the thinking process that should be behind pattern activities, DSOP which he explains in his BOOK developing Mathematics with unifix cubes. You can also find out more in our FREE download.
Algebra Tip 3 – Making Patterns
Effective algebra teaching involves learning experiences that focus on the main idea or key understanding of Algebra. Research has identified that most mathematics programs are missing certain elements and may be overloaded in some areas. For example, many mental maths programs, designed for multiplication strategies, are heavily weighted towards rote & automatic recall of facts. They exclude strategies for when the memory fails, so students who can’t remember a number fact have no way of working it out, and are often, wrongly perceived as “not good at maths”. In the case of Algebra Programs they tend to overload on the same skill of copying Patterns!
The First Steps in Mathematics Program identifies the focus areas for Australian Curriculum Algebra:
- We use regularity or pattern to infer one thing from another & to make predictions
- Using numbers can make it easier to see patterns
- Describing a number pattern means describing a precise rule that will produce the pattern
- The number system has a lot of built-in patterns that make working with numbers easier
- Some numbers have interesting or useful properties. Investigation the patterns in these special numbers can help us to understand them better
Algebra Tip 4 – Hands-on Materials
We humans naturally to try and make sense of the world we live in by looking for patterns & regularities . Pattern is at the heart of mathematics and they come in many different forms including in numbers, sounds, pictures & objects. Teaching Algebra involves teaching the skills and strategies needed to see these regularities as well as linking and connecting mathematical concepts. Good Algebra knowledge & number sense are symbiotic, good mathematics requires harmony between these concepts. Physical hands-on experiences are the key to developing sound Algebraic Thinking. They are not just for the Early Years Classroom and are often omitted in later years. Individuals need the opportunity to physically experience, create, strengthen, talk & consolidate Algebra concepts. To achieve this Algebra programs need to include hands-on opportunities with concrete objects, or manipulatives. One such manipulative suited to Algebra is the Unifix Cube.
Planning learning experiences for F-Y6 using Unifx CubesDeveloping Mathematics with Unifix / Gr K-3 will allow students to:
- Recognise Patterns
- Sort & Classify Objects
- Explain Classifications
- Copy, Continue & Create Patterns
- Investigate & Describe Number Patterns
- Identify Missing Elements in Patterns
- Solve Problems using Numbers
- Describe, Continue & Create Number patterns
- Describe the Rule in Patterns
Algebra Tip 5 – Classroom Activities
Here are 2 of my favourite Teacher Resources to help plan curriculum focussed Algebra opportunities for your students from F -Y6
A whole book to help you plan purposeful UNIFIX activities, during our PD we tried:
- Snakes – A UNIFIX activity that allows students to recognise patterns & create patterns according to a rule (p.30)
- Making Long Trains – A UNIFIX activity to show students that patterns can go on forever (p.14)
- Carriages in the Train Shed – 1 – A UNIFIX activity to help students look for patterns, look for relationships between patterns & describe patterns P.20
- UNIFIX Stacks – A UNIFIX activity to help students use logic & patterns to solve problems (p.28)
- Number Patterns – A UNIFIX Activity for students to create & recognise number patterns (p.34) square numbers, triangular numbers etc…
Patterns & Algebra with Dr Paul Swan
More Algebra Resources…
Another favourite of mine is the ORIGO Algebra For All Series, from F-Y7. A fantastic set of books which includes activities & a teachers page with a script to follow. I love this as getting the language right is the thing I find the most difficult when it comes to Teaching Algebra and in this set of books the works are there for you to use if you want to. TOO EASY!
- Plan appropriate algebra activities linked to the Australian Curriculum for all year levels in Primary school (F-Y6)
- Know the continuum for Teaching Algebra across F-Y6 by Content Number & Content Description
- Teach Algebra using appropriate teaching Strategies based on Algebraic thinking NOT Formulaic Algebra using the DSOP model (Adapted from Dr.Paul Swan).
- Know the Key Focus Areas To Teach & The Main ideas of algebra (Adapted fro First Steps Mathematics)
- Allocate & Report ‘C’ Grades based n the Australian Curriculum Achievement Standards (F-Y6)