The purpose of this Warm-up is for students to find the distance between two points on the same horizontal or vertical line in the coordinate plane. Students are intentionally given only the coordinates and no graph. This encourages them to reason about the relative locations of the points, which will help them determine the distance between two points in the coordinate plane using the Pythagorean Theorem in a following activity.
Arrange students in groups of 2. Give students 2 minutes of quiet work time followed by 1 minute to compare their responses with a partner. Follow with a whole-class discussion.
(2,4) and (2,10)
(-3,6) and (5,6)
(-12,-12) and (-12,-1)
(7,0) and (7,-9)
(1,-10) and (-4,-10)
Invite students to share how they ordered the pairs of coordinates from closest to furthest apart. Record and display the responses for all to see. After the class agrees on the correct order, ask students to share the distance between a few of the pairs of coordinates and their strategy for finding that distance. Ask 2–3 students to share pairs of coordinates they found that would have a closer or further distance than the ones in the list.
If not brought up in students’ explanations, consider asking the following questions:
“What does it mean that each pair has one coordinate that is the same?” (The two points are either on the same horizontal or vertical line.)
“How did you decide on which coordinate to subtract?” (I subtracted the coordinates that were different.)
“Why didn’t you need to subtract the other?” (The difference would be 0.)
“Could we represent this distance with a line segment? (Yes, we could draw in a line segment that connects the two points.)
“Would your strategy work for any pair of coordinates?” (No, it would only work for a pair of coordinates that both lie on the same horizontal or vertical line.)
“Which pairs would it work for? Which pairs are we not sure if it would work for?” (It would not work for pairs of coordinates that are not on the same horizontal or vertical line.)
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The purpose of this Warm-up is for students to find the distance between two points on the same horizontal or vertical line in the coordinate plane. Students are intentionally given only the coordinates and no graph. This encourages them to reason about the relative locations of the points, which will help them determine the distance between two points in the coordinate plane using the Pythagorean Theorem in a following activity.
Arrange students in groups of 2. Give students 2 minutes of quiet work time followed by 1 minute to compare their responses with a partner. Follow with a whole-class discussion.
(2,4) and (2,10)
(-3,6) and (5,6)
(-12,-12) and (-12,-1)
(7,0) and (7,-9)
(1,-10) and (-4,-10)
Invite students to share how they ordered the pairs of coordinates from closest to furthest apart. Record and display the responses for all to see. After the class agrees on the correct order, ask students to share the distance between a few of the pairs of coordinates and their strategy for finding that distance. Ask 2–3 students to share pairs of coordinates they found that would have a closer or further distance than the ones in the list.
If not brought up in students’ explanations, consider asking the following questions:
“What does it mean that each pair has one coordinate that is the same?” (The two points are either on the same horizontal or vertical line.)
“How did you decide on which coordinate to subtract?” (I subtracted the coordinates that were different.)
“Why didn’t you need to subtract the other?” (The difference would be 0.)
“Could we represent this distance with a line segment? (Yes, we could draw in a line segment that connects the two points.)
“Would your strategy work for any pair of coordinates?” (No, it would only work for a pair of coordinates that both lie on the same horizontal or vertical line.)
“Which pairs would it work for? Which pairs are we not sure if it would work for?” (It would not work for pairs of coordinates that are not on the same horizontal or vertical line.)