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Mathematics in Science and Research

Data Analysis and Problem Solving
Tabor Boy

Sail

Use the data from the Tabor Boy cruise for the analysis and calculations in Section 1 (below).

In Sections 2 and 3, calculate the answers based on the information and data given.

1. Use geometric models and ratios to analyze the Tabor Boy cruise sighting data.

Data analysis

Create, compare, and evaluate different graphic representations of the same data.

1.1 - Use the chart to plot the fixes of the cruise. Draw a line on the chart to show the course. Use an effective wide of the transect of two miles to either side of the research vessel. Draw, with dotted lines, lines parallel to the research cruise and at a distance of two miles.

Calculate the study area of the research cruise.

  • How many miles did the cruise travel?
  • Estimate how many square miles was studied.
  • How many sightings of each species of whale did we observe?
  • How many whales per square mile did we see?

    1.2 - Use the data table to estimate the amount of time that was effectively spent on the research cruise.

  • How many sightings per hour of each species did we observe?

    1.3 - Using the data that you calculated in 1.1 and 1.2, how might these ratios be useful in data analysis?

    1.4 - Create two different displays using the data in 1.1 and 1.2, showing the differences in sighting frequency for each of the species of whales.

  • Which is easiest to understand?
  • What are the advantages of each display? Disadvantages?
  • 2. Use models to develop the concept of operations with variables.

    2.2 Create a graphic representation of the data.

    2.4 Create a graphic representation of the data.

    3. 2. Use models to develop the concept of operations with variables and percent.

    Use of scientific notation in calculations if needed and appropriate for your level of mathematics.

    2.1 - Growth of a Blue Whale. At the moment of birth a blue whale calf averages 23 feet in length and 3 tons in weight. For the first six months of its life its average weight gain per day is 200 pounds. (assume that every month has 30 days)

  • What is the estimated weight at the end of:
    1 month (30 days)?
    2 months (60 days)?
    3 months (90 days)?
    4 months (120 days)?
    5 months (150 days)?
    6 months (180 days)?

    2.2 - Create a display using the data in 2.1 to show the growth (in weight) of a blue whale calf over time from birth to six months of age.

    2.3 - At 200 pounds per day, what is the percent weight gain of the whale's total weight at the age of:

    1 day ?
    1 month ?
    2 months ?
    3 months ?
    4 months ?
    5 months ?
    6 months ?

    2.4 - Create a display using the data in 2.2 to show the rate of growth (in weight) of a blue whale calf in relationship to the time it grows.

    2.5 - How does the growth rate change as the calf grows? Why does the growth rate change if the weight gain remains the same?

    3.1 - If a blue whale eats food equivalent to 4% of its body weight each day how much would a whale eat if it weighed:

    20 tons?
    45 tons?
    50 tons?
    70 tons?
    80 tons?
    100 tons?

    3.2 - How much would a group of three whales eat in a day if they one weighted 70 tons, the second weighed 47 tons, and the third weighed 67 tons?

    How much would they eat in a:

    week?
    month?
    year?

    3.3 - If a herring weighs an average of _____pounds each, how many herring would the three whales eat in a:

    day?
    week?
    month?
    year?
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