Name_____________________ Class_____________ Date__________
Problem Solving Connections
UNIT
2
COMMON
CORE
Treasure Hunt Carlos has heard stories about buried treasure near his CC.6.NS.6b,
hometown. According to local legend, a pirate buried his treasure, drew CC.6.NS
a map, and hid clues at various locations. He planned to reclaim his
.6c,
treasure one day, but never returned, and the map, clues, and treasure
CC.6.NS.7a,
have never been found. Recently, Carlos bought an old map at an antique CC.6.NS.7b,
store. Could this be the legendary treasure map?
CC.6.NS.8
1 Locations in a Coordinate Plane
A Carlos copies the old map
onto
a coordinate plane.
Directions on the back of the map describe distances in steps, so Carlos
measures the length of his step and sizes his grid so that each unit represents 1
step. The starting point on the original map corresponds to (−5, −4) on Carlos's
copy of the map. Graph this point on the coordinate plane and label it “Start”.
B Carlos reads the back of the original map.
1.FROM THE START:
15 STEPS NORTH
THEN 15 STEPS EAST
LARGE CRACK IN NEARBY ROCK
What are the coordinates of Carlo's location after he follows the directions?
Graph this point on the coordinate plane and label it “Rock”.
C Carlos finds an old piece of paper inside the rock and follows the directions on
it.
2. 6 STEPS WEST, THEN 16 SOUTH
UNDER THE ROOTS OF AN OLD TREE
What are the coordinates of Carlos's new location?
Graph this point on the coordinate plane and label it “Tree”.
2 Distance in a Coordinate Plane
A Carlos measured his step length as 3 feet. How many steps has Carlos walked
so far? What is this distance in feet?
B Under a tree root, Carlos finds second map. This map shows a church, a well,
and a dry creek bed. Carlosgraphs these locations on his copy of the first map
as shown.
Give the coordinates of each location.
Church
Well
Dry creek bed
C How far is the dry creek bed from the church?
steps, or
feet
How far is the church from the well?
steps, or
feet
D Carlos finds these directions written on the back of the second map.
3. WALK NORTH 12 STEPS IN ALL,
THEN GO TO THE NORTHEAST WALL.
UNDERNEATH THE TILED FLOOR –
BURIED TREASURE? OR CLUE 4?
Carlos walks 12 steps north to find the ruins of an old church.
How many steps has Carlos walked from the starting point to the church?
What is this distance in feet?
E The crafty old pirate has sent Carlos on a long winding route to the old church.
Find a shorter path from Carlos's starting point tothe church, assuming that
Carlos can walk only north, south, east, or west. Draw your path on the
coordinate plane.
Describe how to follow your path from the starting point, and find the distance
in steps and in feet.
____________________________________________
____________________________________________
____________________________________________
____________________________________________
3 Comparing and Ordering
A The church's roof has collapsed and the tile floor is cracked. Carlos locates the
northeast wall and begins to dig. Soon he uncovers an old wooden chest. Has he
found the treasure?
Carlos opens the chest and finds' several rocks and another piece of paper.
4. CASTLE ISLAND'S EGHHIST INOPT
AT THE TOP, USE YER SCOPE.
LOOK TO THE SOUTH.
GO TO THE PLACE YOU SEE
AND FIND ITS MOUTH.
Carlos knows that Castle Island is nearby, but he does not fully understand the
clue. Two of the words are scrambled. Carlos turns the paper over and finds a
table:
T O N P T H S I G H E I
0 5 10 3 12 −9 −1 8 −6 −4 −2 −7
To unscramble the words, first write the numbers in the table in order from
least to greatest.
________________________________________________________________
______
Now replace each number in your list with the corresponding letter from the
table.
The scrambled words are
B When Carlos arrives at Castle Island, he sees this sign.
List the locations on the sign in order from the least elevation to the greatest
elevation.
________________________________________________________________
______
________________________________________________________________
______
The highest point on Castle Island
is
Its elevation is
feet.
C From the island's highest point, Carlos looks south through his binoculars and
sees a small remote beach.
Write an integer to describe Carlos's descent to this beach.
(Assume that the beach is at sea
level.)
D On the beach, there is an old wooden sign with faded letters. Carlos can barely
read Captain's Cave, Elev. -3 ft. He sees the opening of a cave nearby. Could
this be the beach's “mouth” described in Clue 4?
Is Captain's Cave above or below sea
level?
Write an inequality using the elevations to justify your answer.
________________________________________________________________
______
Is Captain's Cave higher or lower than Bilge
Basin?
Write an inequality using the elevations to justify your answer.
________________________________________________________________
______
D At the back of the cave, Carlos moves several large loose rocks to reveal a
small recess in the cave wall. He reaches in and pries out another old wooden
chest, similar to the one he found at the church. Is this the treasure at last?
Carlos slowly opens the lid and...
IT'S THE TREASURE!!!!
To find the treasure's value, first rearrange the numbers in the table in order
from least to greatest. Then replace each number with its corresponding letter.
2 −9 5 −6 −1 9 0 −4
U A T B O E L S
The treasure has
value!