Function 2
Overview
In this Phlow, students are introduced to evaluating a simple linear function, y = 2x, by substituting values for x into the equation. The exercise is structured step by step, using a table to guide learners through the process of calculating corresponding y values.
First, students are shown how to substitute x = 1 into the expression 2x, recognising that it is written as 2(1).
They then calculate the resulting value of y = 2.
The process is repeated for x = 2, where learners substitute into the formula as 2(2). They confirm that the correct output for y when x = 2 is 4.
The task combines substitution, functional notation, and evaluation, helping students build a concrete understanding of how equations define relationships between variables. By completing the table, they see the function in action and connect the algebraic representation to numerical outcomes.
This Phlow develops early algebraic thinking, reinforces function notation, and prepares students for working with more complex functions and graphs in later levels.
Prerequisite Knowledge Required
- Understanding of multiplication and simple algebraic notation (e.g., 2x means 2 × x).
- Familiarity with substitution from Algebra 2B – Substitution into an Expression.
- Recognition of ordered pairs (x, y) and their meaning.
Main Category
Algebra
Estimated Completion Time
Approx 6-10 seconds per question. 20 questions total. Total time: 2-4 minute.
Cognitive Load / Step Size
Low to moderate — each step adds a single new input while reinforcing the same substitution rule. The predictable pattern keeps working memory demands minimal and supports fluency.
Language & Literacy Demand
Low — concise mathematical language with clear symbolic structure (x, y, 2x). Instructions rely on visuals (tables and arrows) more than long sentences, supporting accessibility for weaker readers.
Clarity & Design
Strong visual clarity — a simple function table links input (x) and output (y) with arrows showing substitution. Step-by-step progression highlights the relationship between multiplying by 2 and the resulting values.
Curriculum Alignment
Irish Junior Cycle Mathematics – Algebra Strand:
- “Explore linear relationships; represent relationships using tables, equations, and graphs.”
Engagement & Motivation
Learners see immediate cause-and-effect feedback between inputs and outputs, reinforcing a sense of discovery. The regular pattern encourages prediction and curiosity about what comes next.
Error Opportunities & Misconceptions
- Adding instead of multiplying (e.g., thinking y = x + 2).
- Substituting incorrectly (e.g., writing 2 + 2 instead of 2 × 2).
- Confusing input–output order when completing tables.
Transferability / Real-World Anchoring
Applies directly to contexts such as cost per item, speed = distance/time, and other proportional situations — helping students see that algebra models real-world relationships.
Conceptual vs Procedural Balance
Balanced — procedural fluency in substitution builds alongside conceptual awareness of how x and y vary together in a linear pattern.
Learning Objectives Addressed
- Understand and apply substitution to evaluate a linear function.
- Recognise y = 2x as a rule connecting two variables.
- Identify patterns in input–output tables that represent linear growth.
- Strengthen the link between algebraic expressions and numerical reasoning.
What Your Score Says About You
- Less than 5: Needs more practice applying substitution correctly.
- 6–7: Understands the rule but sometimes mixes operations.
- 8–9: Consistently substitutes and multiplies correctly.
- 10/10: Fully fluent — recognises linear patterns and can predict future values confidently.