Linear Graphs Connections

Year Group

Year 7 (Aged 11-12)

Duration

55 minutes

Class Size

33 students

National Curriculum Alignment

Mathematics Programme of Study – Key Stage 3, Years 7–9

Year 7
- Pupils should be taught to:
  - Use coordinate geometry to draw and measure line segments and triangles, and explore their properties (Geometry - Position and direction)
  - Understand and use the concepts and vocabulary of coordinates in the first quadrant (Number - Fractions, decimals and percentages)
  - Plot graphs of linear functions and find coordinates of points on a graph (Algebra)

Lesson Title

Linear Graphs: The Connection Between Equations and Coordinates

Learning Objectives

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

Generate coordinate pairs by substituting x-values into linear equations (NC M7 - Algebra)
Plot points accurately on Cartesian grids to draw linear graphs (NC M7 - Geometry)
Verify whether given points lie on a specific linear graph by substitution (NC M7 - Algebra and Geometry)
Identify and understand horizontal and vertical lines as special cases where either x or y is constant (NC M7 - Geometry)
Use appropriate mathematical vocabulary relating to coordinates, lines, and equations (NC M7 - Communication)

Success Criteria

I can substitute x-values into a linear equation to find corresponding y-values.
I can plot points onto a graph correctly using coordinate pairs.
I can join plotted points to draw straight lines representing linear equations.
I can check if a point lies on a line by substituting its values into the equation.
I can explain when a line is horizontal or vertical and describe its equation form.

Resources Needed

Graph paper (printed with grids)
Whiteboards and markers (for group work)
Calculators (optional)
Worksheets with linear equations and coordinate tables
Rulers and pencils
Projector or interactive whiteboard
Dyslexia-friendly coloured overlays and accessible fonts versions of printed materials
Angle measurers from previous lessons, if tying to quadrilaterals and algebra

Lesson Structure

1. Starter Activity (10 minutes)

Objective: Revise plotting points and coordinate pairs

Give students a quick warm-up: Substitute values into the equation y = 2x + 1 for x = 0,1,2,3 and plot the points on a mini grid (provided on handout).
Use mini-whiteboards for students to write their coordinate pairs.
Whole-class short discussion: What shape do these points form? (A straight line)
Refer back to the success criteria for clarity.

Differentiation: Provide number line aids for students who find substitution challenging.

2. Introduction & Modelling (10 minutes)

Objective: Introduce y = mx + c and explore horizontal and vertical lines

Using the interactive whiteboard, model plotting a graph from y = 3x - 2.
Demonstrate substitution step-by-step for three x-values (-1, 0, 1).
Show how to join plotted points to form a straight line.
Define and illustrate:
- Horizontal lines (y = k, where y is constant)
- Vertical lines (x = k, where x is constant)
Plot examples of each and explain: horizontal = slope 0, vertical lines not functions but important in coordinate geometry.

Dyslexia-friendly tip: Present text in Arial font, larger size, and provide verbal explanation alongside visuals.

3. Main Activity: Pair Work (20 minutes)

Objective: Practice plotting and verifying points on linear graphs

Hand out worksheets: Each pair receives 2 linear equations and a table template to fill in values and plot points.
Task 1: Fill in the tables with x and y values by substitution.
Task 2: Plot their points and draw the line accurately on graph paper.
Task 3: Given 3 points per equation, determine by substitution if these points lie on the graph (true/false).
Circulate, offer support, and use questioning to promote reasoning.

Differentiation:

Support groups receive pre-filled tables with fewer points to plot.
Advanced learners get challenge equations like y = -0.5x + 4 and identify slope and intercept.

4. Plenary and Reflection (10 minutes)

Objective: Consolidate understanding & peer assessment

Invite some students to plot their graphs on the whiteboard for discussion.
Whole class discussion: How do graphs change with different m (slope) and c (intercept)?
Exit ticket (on mini-whiteboards or paper):
- Write the equation of a horizontal line through y = 5.
- Check if (2, 7) lies on y = 2x + 3.
- Plot the point for x = -1 on y = -x + 4.

Extension Activities (For Advanced Learners)

Investigate and plot graphs of parallel and perpendicular lines using equations.
Explore the algebraic connection between the slope of lines and angle between them, linking back to previous angle lessons.
Begin simple combinations of angle properties with linear equations to predict coordinates under transformations.

Differentiation Strategies

Group	Support Strategies	Challenge Strategies
Learners needing help	- Provide substitution scaffolds (step-by-step clues) - Use visual supports, number lines, and working with one coordinate at a time - Allow pair work for confidence building	- Provide non-integer slopes - Encourage predicting trends in the line before plotting - Start questions hinting toward algebraic reasoning and gradient impact
Dyslexic learners	- Use dyslexia-friendly fonts and coloured worksheets - Provide oral instructions and visual examples - Break tasks into small, manageable steps with checklists	- N/A but can pair with peers to peer-teach graphs and patterns

Cross-curricular Links

Geometry and Algebra: Reinforces plotting and understanding linear equations physically connected to algebraic concepts.
English: Emphasises mathematical vocabulary (coordinates, gradient, intercept, horizontal/vertical).
ICT: Use of interactive whiteboard enhances engagement and visual learning.

Assessment for Learning

Ongoing questioning during collaborative tasks.
Marking completed coordinate tables and graphs on worksheets.
Exit tickets provide quick informal assessment on the day's key objectives.

This highly interactive and scaffolded lesson builds a deep conceptual understanding of linear graph plotting and coordinates, preparing students for more complex algebraic graphs and integrating their previous knowledge on angles and shapes.

Teaching Instructions