Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Tables and Cartesian graphs

Tables and Cartesian graphs

Generate tables, plot ordered pairs and describe relationships between variables in authentic graphs.

Updated 2026-07-24 - 7 min read

Generate tables, plot ordered pairs and describe relationships between variables in authentic graphs. This draft teaching resource is aligned to the cited Year 7 content descriptions and still requires named human curriculum approval.

Define each variable before operating. Every symbol, table entry and graph coordinate should retain one consistent meaning and unit.

1. Generate tables and ordered pairs

A table organises corresponding input and output values. Coordinates are always written horizontal value first, vertical value second.

Text-equivalent representation: Text table for y = 2x + 1: x values 0, 1, 2, 3; matching y values 1, 3, 5, 7; ordered pairs (0,1), (1,3), (2,5), (3,7).

Decision check: Apply this lesson's rule to the worked example: Keep each input paired with the output generated from the same row. Identify the exact value, label or property that satisfies the rule.

2. Plot and interpret authentic graphs

A graph shows how one variable responds as another changes. A useful description names direction, amount of change and units.

Text-equivalent representation: Graph text equivalent: horizontal axis = distance k in kilometres; vertical axis = cost C in dollars; points (0,5), (1,7), (2,9); cost rises $2 for each 1 km.

Decision check: Apply this lesson's rule to the worked example: Read axes and units before describing the shape or rate of a graph. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: For y = 2x + 1, find y when x = 3.

  1. Substitute 3 for x.
  2. The output is y = 7.

Answer: 7

Check: Each x-value has a corresponding y-value from the rule.

Worked example 2

Question: Which statement correctly describes the point (3, -2)?

  1. Coordinates are written (x, y).
  2. Therefore x = 3 and y = -2.

Answer: x = 3 and y = -2

Check: Read horizontally first, then vertically.

Worked example 3

Question: A graph represents a taxi fare with a $5 start fee and $2 per kilometre. Which description should match the graph?

  1. Identify the independent variable and what changes for each unit.
  2. The graph increases by $2 for each kilometre.

Answer: increases by $2 for each kilometre

Check: Describe direction and amount of change, with units.

Method map for this topic

  1. Generate tables and ordered pairs: Keep each input paired with the output generated from the same row.
  2. Plot and interpret authentic graphs: Read axes and units before describing the shape or rate of a graph.

Common mistakes and how to correct them

  • table output: Not yet. Each x-value has a corresponding y-value from the rule. Recheck the table output step, then try again.
  • coordinate order: Not yet. Read horizontally first, then vertically. Recheck the coordinate order step, then try again.
  • table to points: Not yet. Keep the original x-value as the first coordinate. Recheck the table to points step, then try again.
  • graph interpretation: Not yet. Describe direction and amount of change, with units. Recheck the graph interpretation step, then try again.
  • point on graph: Not yet. A point lies on a graph only when its coordinates satisfy the rule. Recheck the point on graph step, then try again.
  • inverse table: Not yet. Use the output to form an equation. Recheck the inverse table step, then try again.

Guided interactive lesson studio

The Learn lesson for this topic includes a structured action rather than asking you only to read an explanation or select an answer.

Build a table and matching Cartesian graph

Complete every output in the table for y = 2x + 1, then enter the four ordered pairs. Plotting is optional because coordinate fields provide the same assessable response.

You will complete: Table outputs for x = 0, 1, 2, 3; Ordered pairs; Describe how y changes when x increases by 1.

Accessible route: The table and grid communicate identical values. A learner may complete number and coordinate fields without dragging or interpreting colour.

Evidence boundary: the automatically checkable fields give immediate formative feedback. Explanation and reflection fields remain formative and require rubric or teacher review; this action cannot create mastery evidence by itself.

Practice

  1. For y = 2x + 1, find y when x = 3.
  2. For y = 4x - 2, find y when x = 5.
  3. Which statement correctly describes the point (3, -2)?
  4. Which statement correctly describes the point (-4, 5)?
  5. A graph represents a taxi fare with a $5 start fee and $2 per kilometre. Which description should match the graph?
  6. A graph represents water draining from 40 L at 3 L per minute. Which description should match the graph?

<details> <summary>Answers and reasoning</summary>

  1. 7 — Substitute 3 for x. The output is y = 7.
  2. 18 — Substitute 5 for x. The output is y = 18.
  3. x = 3 and y = -2 — Coordinates are written (x, y). Therefore x = 3 and y = -2.
  4. x = -4 and y = 5 — Coordinates are written (x, y). Therefore x = -4 and y = 5.
  5. increases by $2 for each kilometre — Identify the independent variable and what changes for each unit. The graph increases by $2 for each kilometre.
  6. decreases by 3 L each minute — Identify the independent variable and what changes for each unit. The graph decreases by 3 L each minute.

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | generate table ordered pairs | Generate a table of values and express its rows as ordered pairs. | | plot read cartesian points | Plot and read coordinates accurately on the Cartesian plane. | | describe variable relationship graph | Describe direction, rate and context in a graph of related variables. |

Retrieval prompts

  • State the defining relationship for each method above without looking.
  • Give one example where two visually similar representations mean different things.
  • Diagnose one misconception from the list and explain the first corrective step.
  • Name a check that is independent of simply repeating the same calculation.

Teach-back and self-check

Close the worked examples and explain tables and cartesian graphs as if you were helping another Year 7 student. Begin by naming the clue that tells you which relationship, representation or operation is needed. Then show one complete example with labels and units where they matter. At each line, explain what stayed equivalent and why the next step is allowed.

Use this four-part check before calling the method secure:

  1. Identify: What information is given, and what must be found or justified?
  2. Represent: Which number line, diagram, table, expression, graph or organised list makes the relationship visible?
  3. Reason: Which rule connects the representation to the required answer?
  4. Verify: Can you check by estimation, substitution, an inverse operation, a second representation or the original context?

If the explanation depends on “I just knew”, return to the method map and name the missing decision. A durable method is one you can explain, check and use in a changed context after a delay.

Transfer task

Model a changing school or household quantity using tables and cartesian graphs. Define every variable and unit, test at least two inputs, and explain what the outputs mean.

Sources