How to teach function tables and reading real-data graphs
Year 7 (ages 12 to 13)
A function rule like y = mx + c connects an input (x) to an output (y). This unit covers evaluating a rule at a given x, finding the rule from a table of values, and reading a real-world rate directly from a graph or description.
How to teach it
- Start with evaluating a given rule (substitute x, follow the order of operations) before working backward to find a rule.
- To find a rule from a table, show how y changes for each step in x (the gradient m), then read off y when x = 0 (the constant c).
- Connect function tables to real contexts (a tank filling, a taxi fare) so the gradient has a real meaning (a rate).
- Practise reading a rate directly from a worded description: total change divided by total time (or other input).
- Plot a few (x, y) pairs from a table on the Cartesian plane to connect the numeric table to its graph.
Worked example
A rule is y = 4x - 3. Find y when x = 5 y = 4(5) - 3 = 20 - 3 = 17
Common mistakes
- Substituting x incorrectly into the rule, e.g. forgetting the order of operations (multiply before subtract).
- Finding the gradient by looking at y-values alone, without checking that x increases by exactly 1 each row.
- Confusing the gradient (rate of change) with the constant (starting value, where x = 0).
- Reading a rate from a graph using two points that are not both clearly on the line.
Frequently asked questions
How do you find y from a linear rule like y = 3x + 2?
Substitute the given x-value into the rule and evaluate, following the order of operations. For x = 4: y = 3(4) + 2 = 12 + 2 = 14.
How do you find the rule from a table of values?
Find the gradient (m) by seeing how much y changes each time x increases by 1, then find the constant (c) as the y-value when x = 0. The rule is y = mx + c.
How do you read a rate from a real-world graph or description?
Divide the total change in the quantity by the total change in time (or whatever the other variable is). A tank that fills from 10 to 50 litres over 4 hours fills at (50-10)/4 = 10 litres per hour.
What year are function tables and reading real-data graphs taught?
In the Australian Curriculum both are Year 7 skills: reading graphs of real data (AC9M7A04) and making tables of values from patterns or function rules and plotting them (AC9M7A05).
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.