Linear Relationships
Outcomes
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MA4-11NA
Creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane
- Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)
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Describe translations, reflections in an axis, and rotations of multiples of 90 degrees on the Cartesian plane using coordinates (ACMMG181)
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Use the notation P' to name the 'image' resulting from a transformation of a point P on the Cartesian plane
Examples
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Plot and determine the coordinates for P' resulting from translating P one or more times
Examples
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Plot and determine the coordinates for P' resulting from reflecting P in either the x- or y-axis
Examples
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Plot and determine the coordinates for P' resulting from rotating P by a multiple of 90 degrees about the origin
Examples
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Use the notation P' to name the 'image' resulting from a transformation of a point P on the Cartesian plane
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Plot linear relationships on the Cartesian plane, with and without the use of digital technologies (ACMNA193)
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Use objects to build a geometric pattern, record the results in a table of values, describe the pattern in words and algebraic symbols, and represent the relationship on a number grid
Examples
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Recognise a given number pattern (including decreasing patterns), complete a table of values, describe the pattern in words and algebraic symbols, and represent the relationship on a number grid
Examples
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Use a rule generated from a pattern to calculate the corresponding value for a larger number
Examples
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Form a table of values for a linear relationship by substituting a set of appropriate values for either of the pronumerals and graph the number pairs on the Cartesian plane, eg given y = 3x + 1, form a table of values using x = 0, 1 and 2 and then graph t
Examples
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Extend the line joining a set of points on the Cartesian plane to show that there is an infinite number of ordered pairs that satisfy a given linear relationship
Examples
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Derive a rule for a set of points that has been graphed on the Cartesian plane
Examples
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Use objects to build a geometric pattern, record the results in a table of values, describe the pattern in words and algebraic symbols, and represent the relationship on a number grid
- Solve linear equations using graphical techniques (ACMNA194)