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Introduction to Algebra - Coggle Diagram
Introduction to Algebra
Variables
Key ideas
Letters represent unknown numbers
Variables can change value
Difference between variable and label
Using boxes → letters progression
Multiple values for same variable
Notation conventions (e.g. 3a not 3 × a)
Common misconceptions
Letter is an object
Letter has only one fixed value
3a means 3 + a
Links to→ substitution→ expressions→ equations→ patterns
Language
Core terms
Variable
Constant
Coefficient
Term
Expression
Equation
Simplify
Substitute
Teaching supports
Vocabulary wall
Frayer models
Sentence frames
Say–write–explain routines
Expressions
From words to algebra
“more than”
“less than”
“times”
“sum of”
“difference between”
Strategies
Highlight key words
Build expression step-by-step
Function machines
Bar models (optional)
Common errors
reversing order
writing full sentences
missing multiplication
Links to→ interpreting expressions→ substitution→ real-world problems
Interpretations
Understanding meaning
What does 3a represent?
Verbalising algebra
Tables of values
Matching expressions to contexts
Comparing two expressions
Sense-checking answers
Unifying Strands→ U.1 Understanding→ U.8 Problem solving→ U.13 Communication
Subbing
Core process
Replace variable with number
Use brackets correctly
Follow order of operations
Evaluate expressions
Check reasonableness
Progression
single substitution
multi-term expressions
negative values (later)
Common misconceptions
dropping brackets
incorrect order of operations
arithmetic slips
Links to→ number skills→ simplifying→ equations
Simplifying
Key skills
Identify like terms
Combine coefficients
Recognise structure
Use algebra tiles (if available)
Simplify step-by-step
Conceptual focus
Why only like terms combine
Structure of expressions
Maintaining meaning
Common errors
adding unlike terms
combining incorrectly
sign errors
Links to→ expressions→ equality→ solving equations
Equality
Core ideas
Meaning of equals sign
Balance model
True/false statements
Missing number sentences
Maintaining equality
Pedagogical focus
Move from operational → relational view
Use balance diagrams
Use number sentences
Forming Equations
From contexts
Word problems
Function machines
Diagrams
Real-life scenarios
Number patterns
Key steps
Identify the unknown
Represent relationship
Write equation
Common difficulties
choosing variable
translating wording
structuring equation
Solving
Methods
Inverse operations
Balance method
Maintaining equality
Checking solutions
Progression
addition/subtraction
multiplication/division
word problems
Common misconceptions
operating on one side only
arithmetic errors
not checking
Links to→ equality→ number operations→ problem solving
Representations
Words ↔ algebra
Tables ↔ algebra
Diagrams ↔ algebra
Function machines
Patterns
Visual models
Purpose
deepen conceptual understanding
support mixed ability
strengthen connections
Real World Connections
Age problems
Cost problems
Perimeter formulas
Mobile phone plans
Simple finance contexts
Growing patterns
Goal→ make algebra meaningful→ build transfer