This section introduces students to the coordinate grid. 

Students begin by drawing rectangles based only on verbal descriptions. They first do so without a grid, then on an unmarked grid, and finally on a coordinate grid. Along the way, they recognize that numbered grid lines allow them to locate points and communicate the features of shapes precisely. 

Students then learn to use the numbers on the horizontal axis and vertical axis to describe the position of points and plot them on the coordinate grid. They learn that pairs of numbers such as , called coordinates, describe the numbers of units a point is from the axes and the point , which is called the origin. 

For example, is 7 units to the right of and is on the horizontal axis. The point  is 1 unit to the right of and 4 units up.

In other words, the first number tells us the point’s horizontal position, and the second number tells us its vertical position.

Students then practice plotting points given their coordinates and identifying the coordinates of points on the grid.

In this section, students classify quadrilaterals and triangles into different categories and study the relationships between the categories.

They begin by sorting a large set of quadrilaterals in a way that makes sense to them, using attributes such as angle measures (especially right angles) and pairs of parallel sides. Then they focus on relating the attributes of trapezoids, rectangles, parallelograms, squares, and rhombuses.

Students explore two ways of defining trapezoids. One way is to say a parallelogram is a trapezoid, and the other is to say that a parallelogram is not a trapezoid. In this course, the former (inclusive) definition is used.

Students then study the relationship between squares and rhombuses, and between rectangles and parallelograms. They build these shapes with toothpicks, and see that a square is a special kind of rhombus and a rectangle is a special kind of parallelogram.

As they learn more about the relationships between quadrilateral categories, students use a Venn diagram to highlight their understanding.

In this section, students apply the concepts of this unit as they analyze numerical relationships between two quantities in different contexts.

Students begin by examining patterns in numbers generated by following a pair of rules. They record the patterns in a table and interpret the relationships between the pairs of numbers. Students learn that they can form ordered pairs using corresponding terms from each pattern. These pairs can be graphed on the coordinate grid, which allows them to better understand the behavior of the patterns.

Rule 1: Start at 0. Keep adding 10.
Rule 2: Start at 0. Keep adding 40.

Use the rules to complete the table.

	A	B	C	D	E	F
rule 1
rule 2

Plot the numbers in the table on the coordinate grid. Label the points.

Next, students use the coordinate grid to explore the relationship of pairs of values in different situations. For instance, they look at the numbers of heads and tails that result from flipping a coin a certain number of times, the number of coins and the value of coins, and the length and width of rectangles with a fixed perimeter or a fixed area.