Using tables to explore patterns and graphs

Use visual patterns, tables, formulae, and graphs to explore linear relationships, complete values, and make and test predictions.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA4-9
New NZC (2026)
  • NZC26-P4-ALG-ER-P-Y9-10
  • NZC26-P4-ALG-ER-P-Y9-08
  • NZC26-P4-ALG-ER-P-Y9-09
  • NZC26-P4-ALG-ER-P-Y9-07

Resources

  • Alpha textbook: Connecting rules, tables and graphs, Ex 18.03, pg 287-290
  • CorbettMaths on drawing linear graphs (table method)Questions PDF · Answers
  • CorbettMaths on drawing quadratics (table method)Questions PDF · Answers
  • Dr Austin Maths - Plotting Linear and Non-Linear Graphs Revision Practice GridQuestions PDF · Answers

Terminology

  • Table of values
  • Rule
  • Coordinate pair
  • Plot

Task goals

  • Complete a table of values by substituting given x-values into a linear rule.
  • Find the rule that generates a given table of x and y values.
  • Convert a row of a table into a coordinate pair, and use a table to predict the next point in a pattern.
  • Decide whether a table of values represents a straight-line graph, and if so, state the y-intercept and whether the graph rises or falls.
  • Recognise when a table of values does not lie on a straight line by checking whether the differences between successive y-values are constant.
  • Check whether a proposed rule correctly matches every pair of values in a given table.
  • Connect one growing visual pattern to its table, linear formula, and straight-line graph, treating the first displayed pattern as Pattern 0.
  • Use a formula to find Pattern 100 and solve backwards to decide whether exactly 100 shapes occurs at a whole-numbered pattern.

Where this fits

What leads into this objective, and where it goes next.

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Using tables to explore patterns and graphs

Using tables to explore patterns and graphs

Do

Using tables and graphs in the coordinate plane (showing all four quadrants), and diagrams to recognise the relationship between the ordinal position and its corresponding element in a linear pattern, developing a rule for the pattern in words and making conjectures about further elements in the pattern

Statement▸
Year 9 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y9-10
Do

Identifying the sign of m from tables of values, and linear graphs

Statement▸
Year 9 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y9-08

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