Corps of Discovery
How can we discover the information we need by exploring the information we have?
How can we use trigonometry and physics to better understand our world?
Unit Name
Mathematics Topic
Common Core
Preparation for Expedition
4 weeks
To Fort Mandan
6 weeks
From Starvation to Joy
4 weeks
Algebraic Geometry
Pythagorean Theorem Applied
3D Application and Reasoning
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
8.G.6
8.G.5
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8.G.6
8.G.7
8.G.8
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8.G.8
M.P.2
Essential Question
How can we use the information that we have to
find the information that we need?
How does trigonometry contribute to planning
a trip with a map?
How does trigonometry contribute to planning a trip in
the real, three-dimensional world?
Learning Outcomes
1. The sum of a polygons interior angles is (n2)180, where n = the number of sides of the
polygon.
2. The Pythagorean theorem says that
a2 + b2 = c2, where “c” is the hypotenuse of a
right triangle and “a” and “b” are the legs.
Students will use this to find the missing side of a
right triangle.
3. Students are able to find the distance between
two points of a coordinate plane using the
Pythagorean theorem.
1. Students will experiment with the
Pythagorean theorem and its converse using
the scale of a map.
2. Students will understand how the
Pythagorean theorem relates to distance in
the real world.
3. Students will be able to chart a course on a
map, using the Pythagorean theorem to
calculate distances.
1. Students will be able to find the distance between
two locations at different altitudes.
2. Students will use their knowledge and abilities with
algebraic geometry to solve complex problems.
3. Students will reason and make decisions based on
their calculations and estimations.
Enduring
Understandings
 Students will understand the explicit concepts of geometry and their application in new contexts, both real world and academic.
 Students will understand the relationship between algebra and geometry and their application to real work problems.
 Students will understand the value of organization and record keeping.
 Students will understand how to think, ask questions and analyze about their thinking when solving real world problems.
 Students will understand how to apply past knowledge to new situations.
 Students will understand how to think, reason and solve problems interdependently.
 The quantity of a polygons sides relates
 The Pythagorean theorem can be used to
 The Pythagorean theorem can help us to find the
definitively to the sum of both its interior and
estimate distances and estimate angles.
measures of three-dimensional objects.
exterior angles
 The skills used to find distance in the real
 Representing real world problems in explicit
 If we know most of the angles or sides of a
world on a map with a scale are the same as
mathematical form can help us to explore different
triangle, then we can usually find the remaining
finding the distance between two points on
solutions.
angles or sides of a triangle.
a coordinate plane.
 The Pythagorean Theorem applies to distance
as well as geometry.
- Selected Answer quiz over the explicit details of
- Performance assessment using standards
- Performance assessment using standards based
the content.
based observation tool. –Performance
observation tool.
- Daily formative assessments to monitor student
assessment in which students must verbally
–Performance assessment in which students must
learning.
explain and justify a course that they chart in a
verbally explain and justify a course that they chart in
-Extended written response about Pythagorean
teacher conference.
a teacher conference.
theorem applied to real world context
-Extended written response journals that record
-Extended written response journals that record and
and reflect student progress across the North
reflect student progress across the North American
American map.
map.
Summative
Assessments
Corps of Discovery
Major Learning
Activities
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Science
Social Studies

Direct instruction from lead teacher.
Exploration of explicit applications in
mathematics/academic contexts
through working on problems in small
groups.
Real world context research- students
will find a way to apply the
Pythagorean theorem to an element of
their weekly life in preparation for the
extended written response assessment.
Speed, Velocity and Acceleration
Community Connection:
Guest speaker from local community to teach
about mapping/orienteering

Guide Competition Project- students
will work in teams of two. The
teams will compete with each other
to find the “best”
(shortest/fastest/safest/least
expensive) route from St Louise to
Fort Mandan. Everyday the students
will plot their route on a map using
Geogebra as well as keep a
“journal” containing explicit
mathematical notations as a
reference to their Geogebra maps.

Presentation of Guide Routestudents will present their route, its
strengths, why they make certain
choices and why they deserve to be
“hired” as Lewis and Clark’s guide.
Exploring Velocity to Discover Time
Historical contexts and events of Lewis and
Clarke’s Expedition

Exploration Project- in a similar format to
the Guide Competition Project, students
will plot the remainder of Lewis and
Clark’s journey to the Pacific. Instead of
competing, they will collaborate in small
groups to solve the problem of calculating
distance over the Rockies. Students will use
small group discussions to discover how to
apply the Pythagorean theorem to threedimensional polygons.
Comparative Reasoning-students will
compare their team’s route from the Guide
Competition Project and the Exploration
Project to the actual route that Lewis and
Clark travelled. They will try to understand
Lewis and Clark'
Exploring Acceleration to Discover Time
Historical contexts and events of Lewis and Clarke’s
Expedition
Common Core Standards Referenced
8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when
parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the
same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
8.G.6. Explain a proof of the Pythagorean Theorem and its converse.
8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in
two and three dimensions.
8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
M.P.2. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in
problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to
decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life
Corps of Discovery
of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation
process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent
representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute
them; and knowing and flexibly using different properties of operations and objects.