HIGH SCHOOL GEOMETRY: BURIED TREASURE
UNIT OVERVIEW
Task Name: Buried Treasure
Grade: 10
Subject: Geometry
Depth of Knowledge: WILL FILL IN LATER
Task Description: Students find…ALSO FILL IN LATER
Standards:
G.? FILL IN LATER
Standards for Mathematical Practice:
MP.? FILL IN LATER
TABLE OF CONTENTS
HIGH SCHOOL GEOMETRY: BURIED TREASURE
PERFORMANCE TASK
Performance Task
Buried Treasure
Make sure to answer questions in complete sentences and explain fully. Label any unnamed points as 𝑋1 , 𝑋2 , 𝑋3 …
Pirate Albus is standing at the edge of Westend Bay (A), and his cohort, pirate Bluebeard, is 60 paces
to the north at point B. Each pirate can see Captain Coldhart off in an easterly direction burying a
treasure. With his sextant, Albus measures the angle between the Captain and Bluebeard and finds
that it’s 85°. With his sextant, Bluebeard measures the angle between the treasure and Albus and
finds it to be 48°. Albus and Bluebeard mark their positions with large boulders and return to their
ship, confident that they have enough information to return later and recover the treasure.
Can they recover the treasure? Explain why or why not. Support your answer with theorems and
postulates as appropriate. If it is possible, use your geometric tools to locate the position of the treasure on the map
and mark its location.
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Captain Coldhart, convinced someone in his crew stole his last treasure, has decided to be more careful about burying his
latest booty. He gives his trusted first mate, Dexter, two ropes, the lengths of which only the Captain knows. The Captain
instructs Dexter to nail one end of the shorter rope to Hangman’s Tree (H) and secure the longer rope through the eyes
of Skull Rock (S). The Captain, with the ends of the two ropes in one hand and the treasure chest tucked under one arm,
walks away from the shore to the point where the two ropes become taut. The Captain buries the treasure at the point
where the two ropes come together, collects his ropes, and returns confidently to the ship.
Has the Captain given himself enough information to recover the treasure? Explain why or why not. Support your
answer with theorems and postulates as appropriate. If it is possible, locate the position of this second treasure on the
map if the two ropes are 100 paces and 150 paces in length. Mark the treasure location on your map.
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After the theft of two very important ropes from his locker and the subsequent disappearance of his trusted first mate,
Dexter, Captain Coldhart is determined that no one shall find the location of his latest buried treasure. The Captain, with
his new first mate, Euclid, walks out to Deadman’s Point (D). The Captain instructs his first mate to walk inland along a
straight path for a distance of 130 paces. There Euclid is to drive his sword into the ground for a marker (M), turn and face
in the direction of the captain, turn at an arbitrary angle to the left, continue walking for another 60 paces, stop, and wait
for the Captain. The Captain measures the angle formed by the lines from Euclid to himself and from himself to the sword.
The angle measures 26°. The Captain places a boulder where he is standing (D), walks around the bay to Euclid, and
instructs him to bury the treasure at this point. Alas, poor Euclid is buried with the treasures.
Has the Captain given himself enough information to locate the treasure? Explain why or why not. Support your answer
with theorems and postulates as appropriate. If it is possible, locate the position of this third treasure on the map and
mark it. If it is not possible, explain how many possible locations for treasure there are, find and mark them on the map.
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HIGH SCHOOL GEOMETRY: BURIED TREASURE
RUBRIC
High School Geometry: Buried Treasure
Buried Treasure Rubric
The elements of performance required by this task are:
 FILL IN LATER
Possible Responses
1. a)Correctly state that they can recover the treasure
b) Support their answer with angle-side-angle, and explain that they are given
two angles and the side in between them.
c) Correctly construct and label a triangle which locates X on the map, which
accurately represents the situation.
Partial Credit
 State the postulate but do not support their answer.
 Construct the triangle correctly, but do not label it in a way that
represents the situation.
2. a) Correctly state that they he can recover the treasure
b) Support their answer with side-side-side, and explain that they are given the 3
distances, and will get the same triangle regardless of whether they are given any
angles.
c) Correctly construct the triangle which locates the treasure, and accurately
represents the situation.
Partial Credit
 State the postulate but do not support their answer.
 Construct the triangle correctly, but do not label it in a way that
represents the situation.
3. a) Correctly state that they cannot recover the treasure
b) Support their answer with SSA (non-theorem), or that the other two angles
are unknown, there are two possible locations.
c) Correctly construct and label the triangles to give the two locations of the
treasure, and accurately represent the situation.
Partial Credit
 Just state that SSA is not valid, but don’t explain.
 Only draw one triangle.
 Triangles are correctly constructed, but do not represent the situation.
Total Points
Points
Section
Points
1
2
2
5
(1)
(1)
1
2
2
5
(1)
(1)
1
2
3
6
(1)
(1)
(2)
16
High School Geometry: Buried Treasure
Rubric
Performance Level Descriptions and Cut Scores
Performance is reported at four levels: 1 through 4, with 4 as the highest.
Level 1: Demonstrates Minimal Success (0-3 points)
The student’s response shows few of the elements of performance that the task demands as defined
by the CCSSM. The student’s work shows a minimal attempt and lack of coherence. The student fails to
use appropriate tools strategically, such as a compass, protractor, postulates and theorems. The
student is unable to make sense of the problem and apply geometric concepts in this modeling
situation.
Level 2: Performance Below Standards (4-8 points)
The student’s response shows some of the elements of performance that the task demands as defined
by the CCSSM. The student might ignore or fail to address some of the constraints of the problem. The
student may occasionally make sense of quantities or relationships in the problem. The student
attempts to use appropriate tools, such as a compass, protractor, postulates and theorems, with
limited success. The student may recognize some characteristics of triangles, but has trouble
generalizing or applying geometric methods in this modeling situation.
Level 3: Performance at Standard (9-12 points)
For most of the task, the student’s response shows the main elements of performance that the task
demands as defined by the CCSSM with few minor errors or omissions. The student explains the
problem and identifies constraints. The student makes sense of quantities and their relationships in the
modeling situation. The student uses appropriate tools, such as a compass, protractor, postulates and
theorems. The student might discern patterns or structures and make connections between
representations. The student is able to make sense of the problem and apply geometric concepts to
this modeling situation.
Level 4: Achieves Standards at a High Level (13-16 points)
The student’s response meets the demands of nearly all of the tasks as defined by the CCSSM and is
organized in a coherent way. The communication is clear and precise. The body of works looks at the
overall situation of the problem and process, while attempting to the details. The student routinely
interprets the mathematical results, applies geometric concepts in the context of the situation, reflects
on whether the results make sense and uses all appropriate tools strategically.