Algebra 1C
This Phlow introduces learners to the concept of simplifying algebraic expressions by combining like terms. Rather than focusing on numbers alone, it helps students see how repeated variables can be collected into a single term.
Building Understanding Through Visuals
Students begin with expressions such as 2c + c, where they must recognise that the coefficients of the same variable can be added together to give 3c. The visual cue of a hand writing reinforces the step-by-step simplification process.
Exploring Patterns
The Phlow then reinforces the pattern with x + x, guiding learners to see that adding two of the same variable doubles it, giving 2x. Finally, learners are challenged with a + a + a, extending the concept to three terms and showing that they can be grouped into 3a.
From Repetition to Generalisation
By presenting progressively more complex but still familiar examples, learners build confidence in generalising: any repeated variable can be simplified by adding its coefficients.
This sequence supports the development of early algebraic fluency, laying essential groundwork for later topics such as simplifying longer expressions and solving equations. It balances symbolic practice with conceptual clarity, making the abstract idea of “like terms” tangible and accessible.
Prerequisite Knowledge Required
Learners should already understand what a variable represents, and be familiar with substitution and basic addition of numbers.
[Link to Add 1 Phlow] [Link to Algebra 1 and Algebra 1B Phlows]
Main Category
Algebra – Simplifying Expressions
Estimated Completion Time
Average 20–30 seconds per step. Total: ~3–4 minutes.
Cognitive Load / Step Size
This Phlow introduces a new but manageable step: combining like terms. The leap from substitution (Algebra 1B) to simplification (e.g., 2c + c → 3c) is moderate, but clearly scaffolded with multiple examples. Step size feels appropriate for learners consolidating early algebra.
Language & Literacy Demand
Minimal language is used. Key terms like “equal to” and “+” are consistently reinforced with symbols and visuals. Questions are short and clear, making the focus almost entirely mathematical rather than linguistic.
Clarity & Design
Design is clean and effective. The variable plus terms are written large, supported by handwriting graphics to show working. Multiple-choice answers are uncluttered. Visualisation genuinely supports understanding by reinforcing the idea of combining identical symbols.
Curriculum Alignment
This Phlow directly aligns with the Number Patterns and Algebra strand of the Irish Junior Cycle specification, specifically the learning outcome: “Recognise equivalent forms of expressions involving variables and simplify where appropriate.”
Engagement & Motivation
The activity is short, focused, and clear. Immediate feedback keeps learners in flow. While not highly gamified, the quick pace and simplicity make it accessible and confidence-boosting.
Error Opportunities & Misconceptions
- Students may mistakenly write 2c + c = 2c (forgetting the extra coefficient).
- Some might misinterpret variables as separate objects (e.g., thinking c and 2c are unlike terms).
- Miscounting repeated terms (e.g., treating a + a + a as 2a).
Transferability / Real-World Anchoring
The skills are abstract but transferable within mathematics, preparing students for equations, factorising, and algebraic manipulation. No explicit real-world context is given, but the core skill is foundational.
Conceptual vs Procedural Balance
This Phlow leans procedural but also develops conceptual understanding of coefficients as counts of variables. It balances the “why” (variables are like units that can be added together) with repeated procedural practice.
Learning Objectives Addressed
- Understand that like terms can be combined by adding coefficients.
- Simplify algebraic expressions such as 2c + c → 3c.
- Recognise that x + x = 2x and a + a + a = 3a.
- Build fluency in transitioning from repeated addition to algebraic shorthand.
What Your Score Says About You
- Less than 5: You may still be mixing up numbers and variables, or not yet confident in combining like terms.
- Between 6–7: You can handle some basic simplifications but are inconsistent — more practice will strengthen fluency.
- Between 8–9: You understand the process well, with only minor errors.
- 10/10: You can confidently combine like terms and are ready for more complex algebraic simplifications.