MATH – This lesson allows students to look at historical maps used in steamship travel to solve mathematical problems, finding the midpoint in ocean crossings.
Education Standards
Common Core: HSG-GPE.B.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Learning Objective
Calculate the midpoint in ocean crossings using a primary source map from the SSHSA Archives.
Vocabulary
- Midpoint
- formula
- distance
- slope
Question
How can we find the midpoint between two points on a map?
Sentence Stems
- We can find the midpoint by ____.
- We can use ___ formula to find the midpoint.
Materials Needed
- Printed map or digital map that students can mark up on the computer
- paper/notebook
- writing utensil
- pairs or groups to work with
Lesson Opening
This lesson allows students to look at historical maps used in steamship travel to solve mathematical problems, finding the midpoint in ocean crossings.
Give the scenario: You and your friend want to hang out but neither of you want to use too much gas to drive to the other’s house. What would be a good solution so that you are able to hang out with your friend but neither of you uses a lot of gas? Find a midpoint, meet halfway. How can you find the midpoint between your friend’s house and yours? Give the students time to try to figure out how they can find the midpoint. Challenge the students to come up with a formula to solve this problem.
Display this formula whenever you’re ready.
In order to solve the problems featured in Midpoint in Ocean Crossings, use this formula below.
To determine the midpoint, use this formula:
midpoint = a + b / 2
Lesson Body
Display the Azores map or upload to LMS for students to have access. Ensure that they are able to read the distances, enlarge or write on the board as needed.
Share this problem with the class: Distance from Santa Maria to Flores = 324 miles. Distance from Flores to Fayal = 130 miles.
Problem: Find the midpoint the steamship traveled from Santa Maria to Flores.
Problem: What would the midpoint be on a trip from Santa Maria to Fayal with a stop in Flores? Use the formula to solve this problem.
Extension
Draw a map showing the distance between your house and your friend’s house. Share your findings or ask others to solve the midpoint.
Additional State Education Standards
Texas – TEKS
111.41.c.2
(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures. The student is expected to:
(A) determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint;
(B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines; and
(C) determine an equation of a line parallel or perpendicular to a given line that passes through a given point.
Additional Resources
Geometry, Finding Distances and Midpoints, Math Planet.
Algebra, The Distance and Midpoints Formulas, Math Planet.
Education Standards
National Council of Teachers of Mathematics
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