Treasure Island Estimation Center

Directions• Use the Guided Worksheet to make your way

through Treasure Island (It may contain some clues)– You will have to look up information online or use the

materials around you to complete some of the problems that you encounter

– You will also need to put into practice previous mathematical concepts

• Remember to Practice Estimating so your answers should be Approximations

• Good Luck Buccaneers!

Materials and Set-up Needed• Rulers• Sheet of Notebook

Paper • 7 Rolls of Quarters• 7 Bags of Marbles• 7 4 in. x 3 in. x 3 in.

Boxes

• Every student will have a ruler and a sheet of notebook paper.

• Every 4 students will have a roll of quarters, a bag of marbles, and a box to share.

• Students will work individually

Treasure Island• Please access the link below to begin your

journey!

Journey Through Treasure Island

• At each stop move your cursor over the picture and click play!

Congratulations! • Great Job! You made it and managed to find

the Treasure!

• Now let’s talk about everyone’s Journey!

Discussion• Discuss different approaches to each problem• Allow students to share their explanations on various

problems and compare and contrast student explanations• What are some of the similarities and differences that

you see among the problems?• Why is estimation important in these specific problems?

Why is estimation important in general? • Where do you see or use estimation in your daily life?• When should estimation not be used?

Solution to Ahoy Matey

Explanation of Ahoy MateyIn this problem students have to locate the exact dimensions

of Molokai and round those dimensions to get the Treasure Island estimated dimensions. Then students also have to employ the formula for surface area of a rectangle in a real world context. Generalizing the shape of Treasure Island as a rectangle also serves as an estimation. This allows students to relate the area of a land mass to surface area. Then using the total square mileage, students have to compute how long it would take for the crew to explore the island, by being provided a rate. This takes the problem one step further in that, students are practicing using a previously calculated estimated amount, the total square mileage, and implementing a rate, which they must form themselves.

Solution to Grub

Explanation of GrubThis problem allows students to practice estimating

weights of everyday food items. After selecting food items, students must piece together how to calculate the total weight each crew member will have to carry in snacks over the course of the journey. It is important here for students to realize that not only is the weight of the snacks an estimate, but they are also using a previous estimate. This allows for problems such as this one to be easier to manage calculations. This problem does not directly state to use the previous problem, so it requires students to conceptualize what the question is asking and to identify what is needed to calculate an answer.

Solution to The Fishing Hole

Explanation of The Fishing HoleIn this problem, students will actually have the task of measuring and

estimating a given measurement from the ruler. At first this problem seems difficult since the student will most likely measure the paper in inches, but the dimensions of the pond are in feet, so at some point a conversion will need to be made and students will need to explain their conversions. The problem employs the area of a rectangle, but also makes one consider the amount of a particular object that will fit into that area. Students in this problem will estimate the dimensions of the catfish and the pond, but will need to remember that only half of the pond is full of catfish. The half full aspect makes the problem a little more complex and gives each student one more component to consider. Here I want students to consider the relationship of how smaller objects fit into larger areas and also realize the importance of emphasizing “surface” in the question as a hint to needing area.

Solution to Are We There Yet?

Explanation of Are We There Yet?Although this is a fairly basic problem. I wanted

students to be able to conceptualize that as time progresses, land on Treasure Island will be explored and that after a certain period of time at a certain “rate of exploration,” one can estimate how much land is left to explore and how much land has been explored. This is a great exercise for students to put to practice an estimated amount , but also for them to measure progress. One key idea here is that student may believe that they are not actually estimating in this problem, but in fact they are using a previously estimated value to compute the answer, making the result an estimated value.

Solution to The Lost Lad

Explanation of The Lost LadHere students are confronted with a different

type of estimation problem. Students have been introduced to the formula of circumference before, but here they must consider Pi in a much different context than they are use to. Also students will need to notice that the length of the football field is used to represent the diameter at the very base of the volcano. This problem takes on a different role in estimating a distance and allows for students to understand another aspect of estimation.

Solution to X Marks the Spot

Explanation of X Marks the SpotThis problem is very involved and brings together a variety of concepts

as well as involves manipulatives. Students are given a rectangular box with dimensions proportionate to that of the treasure chest, which I want students to note. They are also given quarters and marbles which represent the contents of the chest and the students then simulate the chest with the materials provided. Using what they know about how many quarters and marbles fill half of the box, they will estimate the number of gold coins and jewels in the chest. Students must utilize volume in a way that they may have not seen before in that they have to fill a large volume with items of a smaller volume. In doing that I want students to realize that the treasure chest is the box, but on a much larger scale. All of these concepts combine to form this particular estimation problem, but students must pay attention to how each component of the problem leads the student to an appropriate estimation.

SourcesPowerPoint• Treasure Map Background: http://www.2020site.org/templates/Treasure-Map-Template.html

Prezi• www.prezi.com

The citations below correspond to the pictures in order as they appear on the Prezi• Sailing Ship: http://fiballouta.blogspot.com/2010/08/relation-ships-red-ocean.html• Treasure Map: http://www.123rf.com/photo_833892_old-map-showing-a-treasure-island-hand-painted-

illustration.html• Treasure Island: http://www.bdstudiogames.com/treasure-island.html• Molokai: http://www.bestofhawaii.com/map_molo.htm• Pirate Fishing: http://www.clipartof.com/portfolio/djholmes/fishing• Snacks: http://www.iupui.edu/~psyclubs/snack_sales.htm• Catfish Pond: http://www.floridafishfarms.com/game%20fish.htm• Skull Cave: http://www.worth1000.com/contests/5852/skull• Volcano: http://www.destination360.com/central-america/costa-rica/arenal-volcano• Football Field: http://www.krylon.com/projects/sports-recreation/football-field/index.jsp• Treasure Chest: http://depositphotos.com/11550860/stock-illustration-Treasure-chest-drawing.html