Open Middle®
Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to find the greatest and least possible slope.
Hint
What creates a large (or small) slope?
Answer
Greatest: 8
Least: -8
Least: -8
Source: Dane Ehlert
Slope From Two Points
I can make a slope of 8 (which is larger than 7/3) using (2,1) & (3,9). Similarly with the smallest.
My students came up with 8 and -8 today as well!
Great catch you two! The correct solution has been updated, thanks!
How did you get the lowest slope
As I look at this, I wonder if we should consider 8 and -8 the same slope. One just being a positive and the other negative. They both have the same steepness. I was thinking 8 and 1/8. I am going to change the directions to read, Create a slope with the greatest steepness and one that is the least steep. Wondering what you all think…
Very interesting Jeanmarie. I think it highlights the mathematical precision issues with “biggest and smallest” and I really like your version. Thanks so much for adding it to the conversation.
I did the same thing Jeanmarie! I think there are more meaningful conversations around the fact that the kids that found 8 and -8 are both correct because they have the same steepness!
(0,-8) (1,9)
good but there is no 0 allowed in this question
Also, no negative numbers. We get the negative by the direction we subtract to get the slope.
Can you explain how you did this?
I was thinking the same thing.