- 1. Constructing the Grid and First Quadrant Plotting
To construct the first quadrant of a Cartesian grid, correctly identify the x-axis, y-axis, and origin, and accurately read and plot coordinates using the 'across first, then up' rule.
- 2. Shape Deduction and Varying Scales in Quadrant 1
Read coordinates accurately on axes with varying scales, calculate segment lengths using visuals, and deduce missing vertices of 2D shapes.
- 3. Crossing the Axes (Four Quadrants)
Extend the Cartesian grid to include negative numbers, name the four quadrants, and accurately read and plot coordinates across all quadrants while avoiding the common coordinate reversal misconception.
- 4. Multi-Quadrant Shape Construction
Calculate horizontal and vertical distances across the axes and construct 2D shapes (rectangles, squares, triangles) that span across multiple quadrants.
- 5. Midpoint of a Line Segment (Direct)
Discover the midpoint of a line segment graphically, and use the mathematical formula (the average of the coordinates) to calculate midpoints across all four quadrants.
- 6. The Reverse Midpoint
Find the unknown endpoint of a line segment when given one endpoint and the midpoint, using visual "jumps" and algebraic inverse operations.
- 7. Discovering Additive Coordinate Patterns
I can find the additive relationship between x and y coordinates, write it as an algebraic rule ($y=x+c$ or $x+y=c$), and visualize the parallel, diagonal lines they form on a graph.
- 8. Discovering Multiplicative Coordinate Patterns
I can find the multiplicative relationship between x and y coordinates ($y = mx$) and visualize how changing the multiplier alters the steepness of a line anchored at the origin.
- 9. Horizontal and Vertical Lines
I can recognize, describe, and plot horizontal and vertical lines using their algebraic equations ($x=n$ and $y=n$).
- 10. Plotting Linear Graphs from Tables
I can use a linear equation to generate a table of values, write coordinate pairs, and plot them to draw a continuous straight line.
- 11. Formalizing Gradient (Rise over Run)
I can identify whether a line has a positive or negative gradient, and I can calculate the exact gradient by finding the vertical change for a given horizontal change (Rise over Run).
- 12. Writing the Equation of a Line ($y=mx+c$)
I can identify the gradient ($m$) and y-intercept ($c$) from a graph and use them to write the equation of any straight line in the form $y=mx+c$.
- 13. Introduction to Quadratics (Parabolas)
I can generate coordinate pairs from a quadratic equation, plot them to draw a symmetrical curve called a parabola, and identify its vertex.
- 14. Graph Reading Mastery and Interpolation
I can read coordinates and scales from non-linear graphs (piecewise, reciprocal, parabolas) and interpolate exact values between grid lines.
