Graphing Linear Patterns

Overview

In this Lesson 11 of 26, students connect a pattern rule and its table of values to points on a coordinate grid. Using concrete floor coordinates, linking cubes, guided notes, and independent practice, students identify that a constant change produces points that form a straight-line graph. This builds on earlier work with patterns, input-output tables, ordered pairs, and coordinate planes.

Learning intentions

Students will:

• Represent a linear pattern in a table, as ordered pairs, and on a coordinate grid.
• Plot points accurately in the correct order.
• Explain how constant change is connected to a straight-line graph.
• Predict the next output from a pattern and justify the prediction.

Success criteria

• I can identify the input and output in a pattern.
• I can write and plot ordered pairs correctly.
• I can label both axes, choose a suitable scale, and plot points accurately.
• I can describe the constant change and predict the next output.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — constructing tables of values, graphing relations, and drawing conclusions.
• Shape and Space — identifying and plotting points in all four quadrants of a Cartesian plane.
• Mathematical processes — communication, connections, problem solving, reasoning, visualization, and mental mathematics and estimation.

Lesson structure (50 minutes)

1. 0–5 min · Attention hook and retrieval. Display a visual of a staircase made from linking cubes and ask, “If the pattern keeps growing by the same amount, what might its graph look like?” Open with the pattern hook and prediction slide. Students complete a quick oral retrieval: identify the input, output, and next term in (2, 5, 8, 11), then share a prediction using a sentence frame: “The next output is ___ because ___.”

2. 5–12 min · Concrete coordinate model. Place large floor coordinate axes and model the table (y=2x+1) for (x=0,1,2,3), using linking cubes to build outputs 1, 3, 5, and 7. Students physically stand at or point to the coordinates ((0,1),(1,3),(2,5),(3,7)), reading each ordered pair aloud as “across, then up.” Use tactile coordinate cards and explicitly correct common errors, including reversing coordinates and beginning at the wrong axis.

3. 12–20 min · Explicit teaching and guided notes. Use the ordered-pairs and straight-line teaching slides and distribute the guided notes and graphing practice sheet. Model how to make a table, write ordered pairs, label the horizontal input axis and vertical output axis, select a scale, plot points, and describe the constant change. Students complete the guided notes with the teacher, answering: “What stays the same?” and “What does a constant change look like on the graph?”

4. 20–30 min · Supported partner investigation. Give each pair one pattern card or teacher-provided pattern, such as “Start at 4 and add 3 each time.” Students build the first four outputs with linking cubes, record the table and ordered pairs on the worksheet, and plot them on enlarged grids. Partners take turns as Plotter and Checker. Pause for a brief Mathology graphing activity or a carefully selected classroom video segment using the investigation directions and discussion prompt. Students discuss whether their points form a straight line and explain why.

5. 30–43 min · Independent graphing and practice. Students complete the independent section of the independent graphing questions. Include three accessible patterns: start at 1, add 2; start at 5, add 4; and start at 10, subtract 2. Students must complete a table, write ordered pairs, label axes, plot points, state the constant change, and predict the next output. Students who finish may practise a related skill in Mathletics while the teacher conferences with students needing support.

6. 43–50 min · Evidence checkpoint and closure. Display the final check and reflection slide. Each student submits or shows one completed graph and answers: “What is the next output, and how do you know?” Students complete a brief confidence rating and correct one error after feedback. The teacher records evidence for Knowledge and Understanding, Mental Math, and Problem Solving.

Resources

• the complete linear-pattern graphing slide deck
• the guided notes and independent graphing worksheet
• Linking cubes
• Large floor coordinate grid and masking tape
• Enlarged coordinate grids
• Tactile coordinate cards
• Mathology graphing activity
• Mathletics access
• Pencils, rulers, coloured pencils, and erasers

Assessment

• Knowledge and Understanding: During modelling and conferencing, check whether students identify input/output, write ordered pairs in the correct order, label axes, and plot points accurately. Record progress as beginning, developing, or demonstrated.
• Mental Math: Listen for accurate identification of the constant change and prediction of the next output without recounting every term. Record whether the student identifies, explains, or requires prompting.
• Problem Solving: Review the independent graph and explanation. Record whether the student connects the table, ordered pairs, graph, and prediction, including a reasonable justification.
• Use the final graph as the evidence checkpoint: assess ordered pairs, labelled axes, plotted points, constant change, and the predicted next output. Note results in the PowerSchool descriptors for Knowledge and Understanding, Mental Math, and Problem Solving.

Differentiation

• Provide enlarged grids, pre-labelled axes, highlighted origin points, tactile coordinate cards, and a reduced-point version with only two or three ordered pairs.
• Offer guided notes with partially completed tables, colour-code inputs and outputs, and use the sentence frames “Across ___, up ___” and “The pattern changes by ___.”
• Read all written directions aloud, use a dyslexia-friendly sans-serif font, generous spacing, uncluttered pages, and allow students to respond orally or point before recording.
• Work beside students with modified programs or a math disability using one pattern at a time. Pre-assign partner roles, use brief timed tasks, and provide quiet individual seating or a movement break for distractable students.
• Extend ready students by asking them to plot a fourth-quadrant pattern or explain how the graph would change if the constant change were doubled.