This worksheet connects algebra and geometry, teaching students to generate a table of values from a rule or growing pattern and to locate points on the Cartesian plane. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A rule (e.g. y = x + 2) connects an input value x to an output value y — substitute x to generate a table of values.
- A coordinate pair (x, y) locates a point: x tells you how far along, y tells you how far up or down.
- The Cartesian plane is divided into four quadrants by the x-axis and y-axis, numbered 1 to 4 anticlockwise from the top right.
- Quadrant 1: x>0, y>0. Quadrant 2: x<0, y>0. Quadrant 3: x<0, y<0. Quadrant 4: x>0, y<0.
- A growing pattern's terms can be modelled by a rule connecting the term number n to the term's value.
What your child will practise:
- Substituting a given x-value into a rule to find the matching y-value.
- Writing the result as a coordinate pair (x, y).
- Identifying which quadrant a point lies in from the signs of its x- and y-coordinates.
- Finding the constant difference in a growing pattern's terms, and use it to find the rule or predict further terms.
- Checking whether a table of values is linear by confirming the differences between consecutive y-values are constant.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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