Mapping Diagrams to Scatterplots

Unit Context

Unit: Exploring Functions and Relations
Lesson: 2 of 4
Grade: Algebra 1 (typically ages 13–15)
Duration: 90 minutes
Class size: 30 students
Curriculum Framework: International Baccalaureate (IB) Middle Years Programme - Mathematics

Learning Objectives

By the end of this lesson, students will be able to:

Identify and describe relations represented in different visual formats, specifically mapping diagrams and scatterplots.
Translate relations from mapping diagrams to scatterplots accurately, demonstrating understanding of input-output correspondence and coordinate representation.
Analyze visual representations to interpret domain, range, and patterns in relations.
Engage in collaborative problem-solving and communication as per IB learner profile attributes: Communicators and Thinkers.

IB MYP Mathematics 1-2 Criterion Alignment

Criterion B: Investigating Patterns
Students develop and describe patterns observed within relations shown in mapping diagrams and scatterplots.
Criterion C: Communicating
Students display mathematical communication by explaining their process in converting mapping diagrams into scatterplots.
Approaches to Learning (ATL)
- Thinking skills: Analysis and critical thinking when interpreting different representations.
- Collaboration skills: Working effectively in pairs or groups to create scatterplots.

Materials Needed

Whiteboard and markers
Student notebooks and graph paper
Pre-prepared sets of mapping diagrams on laminated cards (one per pair)
Transparency sheets with scatterplot grids (optional)
Colored pencils or markers
Tablets or laptops with spreadsheet software or graphing apps (optional, if tech available)
Exit ticket slips

Lesson Breakdown

Time	Activity	Description	IB Connections
0-10 min	Introduction & Recap	- Quick review of relations and functions from lesson 1 using probing questions. - Discuss how relations can be pictured in different ways including mapping diagrams.	Engage prior knowledge to activate conceptual understanding. Emphasize learner profile of Knowledgeable.
10-25 min	Teacher Modeling	- Project or draw a simple mapping diagram on board. - Model step-by-step how to convert it into a scatterplot. - Demonstrate identification of domain and range points as coordinates.	Modeling explicit thinking supports conceptual understanding and strategic thinking.
25-45 min	Guided Pair Activity: Convert & Plot	- Students work in pairs with different mapping diagrams. - Task: Determine pairs (input, output) and plot points on scatterplots. - Teacher circulates to scaffold and ask formative questions like “What does this arrow represent?” and “Where should this point go on your graph?”	Collaborative work develops communication and social skills alongside mathematical understanding.
45-55 min	Class Discussion on Patterns	- Review some examples, discuss any patterns, anomalies, or questions students encountered. - Highlight the connection between mapping arrows and coordinate points on scatterplots.	Develops global thinking and ability to communicate mathematical ideas clearly (Criterion C).
55-70 min	Individual Practice: Extended Tasks	- Provide a worksheet with 3 different mapping diagrams (increasing complexity). - Students independently convert and plot on scatterplots. - Challenge: For one relation, identify if it can be a function, and justify.	Independent skills build self-management and critical thinking (ATL), reinforcing Criterion B.
70-85 min	Technology Exploration (Optional)	- If technology available, students use graphing tools to enter coordinate pairs and view scatterplots digitally. - Encourage visual comparison between manual and digital outputs.	Integrates information literacy and fosters digital competence aligning with IB’s emphasis on technology use.
85-90 min	Exit Ticket & Reflection	- Quick written response: “Explain in your own words how a mapping diagram relates to a scatterplot.” - Collect exit tickets to assess understanding. - Brief homework assignment: find a real-world relation and draw a mapping diagram and scatterplot.	Reflection promotes metacognition and self-assessment, key IB learner traits (Reflective).

Differentiation Strategies

For students needing support: Use simplified mapping diagrams with fewer input-output pairs. Provide partially completed scatterplots as scaffolds.
For advanced learners: Challenge with non-linear or many-to-one relations, and introduce the concept of vertical line test to preliminarily assess if plotting creates a function.
Use of visuals and manipulatives: Mapping diagram cards and graph paper help concretize abstract concepts for diverse learners.

Assessment & Feedback

Formative: Ongoing questioning during pair work and class discussions; teacher notes on student misconceptions.
Summative: Accuracy and completeness of the individual practice worksheet.
Exit Ticket: Quick assessment of conceptual understanding to inform next lesson's focus.
Self-Assessment: In reflection, students describe relationships and assess their own grasp of the learning objective.

Reflection & Next Steps

The next lesson (Lesson 3) will focus on interpreting scatterplots to identify relationships, including direct and inverse variation patterns, further expanding students’ capacity to analyze functional relationships graphically.
Encourage students to continually connect visual and symbolic forms of relations, building toward a comprehensive understanding of functions as mappings with special properties.

Teacher’s Notes

Emphasize to students that a mapping diagram visually represents the relation as arrows from domain to range values, whereas the scatterplot represents the same pairs as coordinate points on a coordinate plane. Recognizing this equivalence fosters strong conceptual understanding of relations beyond procedural skills.
Use consistent vocabulary: domain for input values, range for outputs, and relation as the set of input-output pairs.
Highlight learner autonomy by encouraging students to verbalize reasoning during pair work.

This lesson leverages IB approaches — active inquiry, critical thinking, and communication — while deeply embedding key mathematics concepts appropriate for the Algebra 1 level. It uses visual and hands-on methods to build robust foundational skills in understanding relations and sets a strong base for future function work.