Open Middle®
Directions: Make four points using the integers -4 to 4 at most one time each so that each point is in a different quadrant.
Hint
What happens if 0 is one of the coordinates?
Answer
Here is one potential answer: {(1, 2), (-1, 3), (-2, -3), (4,-4)}
Source: Robert Kaplinsky
Create the following Desmos activity to go along with this prompt.
https://teacher.desmos.com/activitybuilder/custom/56d8f5d853b64bfc0b47bd5b
Here’s a desmos graph to accompany this one: https://www.desmos.com/calculator/liwlurixhe
This problem is great for an enrichment activity in 5th grade, but for those that are struggling with the concept of plotting points in Quadrant I (which is the 5th grade standard and focus) this will be very challenging.
This is great for 5th grade enrichment but this is not in the 5th grade curriculum. Integers (positive and negative numbers) are a 6th grade skill.
Oh, good point. Thanks I didn’t think about that.
ok thank yo very much
I’m a 5th-grade teacher and the standard is only for quadrant 1. However, I teach the lessons using all 4 quadrants. No offense, but if they can learn how to do quadrant 1, you might as well teach the other 4 in the same process. If they can do all four, they can do one. Don’t hesitate to raise the bar!
very nice
There are 576 solutions. However, since you need 8 coordinates and 0 can’t be any of them, your points will always end up with the same 8 numbers as coordinates:
-4, -3, -2, -1, 1, 2, 3, 4.
You can always swap the y-coordinates of the points in the first and second quadrant (x2), the y-coordinates of the points in the first and third quadrant (x2), both (x2), swap the x-coordinates of the points in the first and fourth quadrant (x2), swap the x-coordinates of the points in the second and third quadrant (x2), or – again – both (x2), to get another solution.
You can also swap coordinates in the following 9 ways:
swap the x und y coordinates of A
swap the x-coordinate of A with the y-coordinate of B.
swap the y-coordinate of A with the x-coordinate of D.
swap the x-coordinate of B with the y-coordinate of C.
swap the x-coordinate of B with the y-coordinate of D.
swap the y-coordinate of B with the x-coordinate of D.
swap the x and y-coordinates of C.
swap the x coordinate of C with the y-coordinate of D.
So 1 * 2^6 * 9 = 576
Correction: Instead of “You can also swap coordinates in the following 9 ways:” it should say “You can also swap coordinates in the following 8 ways, resulting in the number of solutions being multiplied by 9”