Teaching with and through Maps

The Coordinate Plane is a grid map, right?

In writing this unit, I wondered if using ordered pair notation (x, y) instead of the grid reference system (A,1) on a grid map was heretical. I was assured by the seminar leader of “Teaching with and through Maps,” Dr. Ramachandran, that I was not breaking a cardinal rule.  After all, a coordinate plane is a type of grid map, differentiated in that it specifies its system of locating points based on their position horizontally on the x-axis, and vertically on the y-axis. Understanding how to plot and name ordered pairs is foundational to developing student understanding of proportional relationships in 7^th grade, finding slope in 8^th grade, and graphing more complicated functions in 9^th grade Algebra. Without this understanding, students will have difficulty manipulating formulas and writing equations of a line. While it is expected that incoming 7^th graders will have worked with coordinate planes during the ratio unit of 6^th grade, less than 10% of students in my 2024-2025 7^th grade class demonstrated the ability to plot points correctly on the proportional relationships pre-assessment when given a table of data points, especially when negative numbers and fractions were involved. To activate this necessary knowledge, provided grid maps and measuring tools, students will be tasked with overlaying a coordinate plane on a map by dividing the grid into quadrants, and labeling and numbering the x and y axes. Students will plot points on these coordinate plane overlay maps (CPOs), and after determining the distance between the two points in units by counting, they will use a given scale to determine the actual distance between the two points in the real world. Students will also use coordinate plane directions when giving instructions for navigating from a locale plotted at one ordered pair to another. Attending to precision, a student may respond for instance, “to navigate from the library plotted at (4, 7) to the grocery store plotted at (9, 10) on my map, you need to move 5 units to the right and 3 units up.” MLR 1- Stronger and Clearer Each Time should be employed here as student explanations become more precise in each pair share round. (See Table 1)

The Touchstone Atlas unit allows students to increase their familiarity with coordinate planes before reaching the graphing portion of the Proportional Relationships unit. Having practiced overlaying coordinate planes on maps, objects already associated with directionality, students are better positioned to associate coordinate planes with direction. They can refer to the How We Feel map they created during Unit 0, this time, noticing how the map is broken up into quadrants and how emotions intensify the further they move from (0,0). The color intensity also increases as the emotions move further from zero, giving an entry point for interpretation even for students who struggle with reading the words on the map. For further accessibility, the interactive map allows students to hover over a word to see the definition, lending itself to interdisciplinary usefulness in promoting vocabulary exposure and development.

FIGURE 2. Constructed collage of 5 screenshots taken on How We Feel App, July 9, 2025

Given this expanded coordinate plane context, students are encouraged to submit a revision to a previous atlas entry. Revisiting an earlier grid they used to determine triangle side lengths, they will create a CPO, assisting them in naming the coordinates of the vertices of the preimage and image. Students with dual enrollment in 7^th and 8^th grade math can make connections about coordinates and transformations on the coordinate plane. Meanwhile, all students will practice choosing a different scale factor and plotting the new triangle that results. Students will explain how they determined the coordinates of the new vertices and explain whether their new triangle is a scale copy of one or both triangles on their original grid.  Implementing MLR 3, students will critique whether their partners’ triangles meet the conditions. Constructing a shape on the coordinate plane previews Unit 7 content wherein students are expected to draw shapes with given conditions. This thoughtful previewing considers the reality that Unit 7 is often rushed as it falls right before end-of-year (EOY) state testing.

Coordinate plane practice is also beneficial for students who struggled with producing a number that falls between 0 and 1 when considering a scale factor that reduces the size of an image. Not only is a coordinate plane a grid map, but it is also two intersecting number lines. Highlighting this feature provides opportunity to develop rational number skills associated with the 7^th grade curriculum standards. While fractions can be off-putting for students, teachers must not avoid tasking students with plotting fractional values to make work more tenable. Repeated exposure to fractions across contexts is necessary to increase student familiarity and fluency with working with non-whole numbers.  Referring first to Quadrant I on their CPOs, students should consider where (¹⁄₂, ¹⁄₂) would lie on their map, in which locale will they find themselves? What about (¹⁰⁄₂, ⁵⁄₂)?

Referring to number lines is also invaluable in understanding additive operations with positive and negative numbers. Moving along number lines layered onto maps will strengthen the directionality association to assist students in intuiting the patterns for adding and subtracting positive and negative numbers. They will make use of the structure that they discovered when creating CPOs and recall that numbers increase as they move to the right or up on the grid and decrease as they move to the left or down on a grid. Students can extend their understanding by plotting a negative number on one of the axes and noticing the results when they are instructed to move in a more negative direction, effectively adding a negative number. They will discover that adding a negative number leads to a more negative number with a higher absolute value, in that it is now farther from zero. Students can use previous context to consider: In which city do we find ourselves if we start at (-2,1) and go 10 units to the west? What are the coordinates of that city? (-12, 1). What if we navigate 10 units to the west and 10 units north? How did the change in in y differ from the change in x? What words signify whether the number will increase or decrease, or whether the absolute value will increase or decrease? Uncovering these connections contextually will assist students when they reach the rational number unit which is loaded with integer rules.