Coordinates and graphs (four quadrants)

Practice 5 items →

The coordinate plane now has four quadrants, numbered counter-clockwise from the upper right. The signs of x and y are the quadrant: (−3, 4) has negative x and positive y, so it sits in Quadrant II. Horizontal and vertical distances between points come from absolute value — the distance from (2, 5) to (2, −1) is |5 − (−1)| = 6, not 4. Students plot polygons on the plane and find their perimeters, and represent a linear rule three ways: as a table, an equation, and a graph. Slope, as a number, waits for Math 7.

Specification · for a parent or teacher

Part no.: four-quadrant-plane
Course: Advanced Math 6 · Unit 10
Realm: Change
Difficulty: 2 of 4 — Grade 4–5. Two steps, or one idea in a story.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

plot $(x,y)$ in I–IV; horizontal and vertical distance as absolute value; polygons on the plane; a linear rule as table, equation, graph.

Ready when

they plot a rectangle with a vertex in each quadrant and give its perimeter.

Formulas

Vertical distance

d = \lvert y_2 - y_1 \rvert \quad (x_1 = x_2)

Horizontal distance

d = \lvert x_2 - x_1 \rvert \quad (y_1 = y_2)

Watch for

$(-3,4)$ in Quadrant III; distance between $(2,5)$ and $(2,-1)$ as 4.

Before · requires

Data analysis and coordinate graphsmean-quadrant-i · Math 5
Negative numbers and absolute valueintegers-absolute-value · Math 6

After · used by

Ratio, rate, and speed (motion graphs)speed-motion-graphs · Math 7
Coordinates and linear graphsslope-linear-graphs · Math 7
Coordinate geometrycoordinate-geometry · Math 1

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