8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Graphing points in all four quadrants of the coordinate plane? But wait, didn't students do that for 6.NS.6c? Yes. Yes, they did. So what's this standard all about?

This is about putting that graphing prowess to use. It's not enough to graph points; students should be able to solve problems (both real-world and mathematical) by graphing points. So bust out the atlases, the blueprints, and the treasure maps.

Students will also need to find horizontal and vertical distances on the coordinate plane, but they can't use (1) the distance formula, or (2) integer subtraction. They'll learn about the distance formula and Pythagorean theorem in eighth grade, and integer subtraction doesn't rear its ugly head until seventh.

"What?" you ask, horrified. "How on earth can students be expected to find horizontal and vertical distances without subtracting integers?!"

Well, they can count boxes. We seriously hope they can, anyway.

Or they can take the absolute value of coordinates, interpreting it as the distance between the point and one of the axes. For instance, they should reason that (-4, 2) has a horizontal distance of |-4| = 4 from the y-axis, and (2, 2) has a horizontal distance of |2| = 2 from the y-axis in the other direction. We can add these distances together to find that the distance between these two points is |-4| + |2| = 4 + 2 = 6. Boom.

Make sure to clarify that the negative signs tell us the direction of movement away from the axes, so the horizontal between (4, 2) and (2, 2) would not be 6 because they aren't on opposite sides of the y-axis! We seriously recommend having graphs here to help students out, here.