# Problem Solving on the Wildlife Refuge

## Super Value Kit

### Materials Included In Kit

(for each student group)
Wildlife Puzzle Cards, set of 6
Wildlife Ratio Cards, set of 8

Calculator (optional)

### Prelab Preparation

Photocopy enough Problem Solving on the Wildlife Refuge Student Instructions handouts and the accompanying worksheets for each student.

1. Distribute the student instructions and worksheets, Wildlife Puzzle Cards and Wildlife Ratio Cards to each student group.
2. Go through the instructions and the sample problem with the students.
3. Show students how the Wildlife Ratio Cards may be turned upside-down if needed in order to have the animal units placed correctly. Note: Just as with playing cards, the numerals will always be right-side up on the left side of each card even when the animal pictures are upside-down.

### Teacher Tips

• Introduction to Unit Factoring. This kit contains enough reusable materials for 15 student groups: 15 sets each of the Wildlife Puzzle and Ratio Cards.
• This is a good activity to do early in the school year and may be revisited often as various types of problems are encountered in the curriculum.
• Enhance the experience by decorating the classroom with stuffed animals and playing appropriate music as the students enter or even by wearing a safari hat. Let your imagination be your guide.
• The Wildlife Puzzle Cards are designed to allow the instructor flexibility. All six puzzles do not need to be completed by each group. The Wildlife Puzzle Cards are numbered in order of degree of difficulty (puzzles 1 and 2 require two ratio cards, puzzles 3 and 4 require three, and puzzles 5 and 6 require four ratios cards). The odd-numbered puzzle cards have whole number solutions and the even-numbered puzzle cards have solutions that require rounding to the nearest whole number. Certain puzzles may be omitted depending on the ability of the students or if time is a factor.
• The event described in Question 1 of the student worksheet is true. Visit the Mars Climate Orbiter website for more detailed information at http://marsprogram.jpl.nasa.gov/msp98/orbiter/ (accessed August 2009).
• Units are commonly forgotten by students when doing calculations or recording measured data. If this ever happens in your classroom (and it will), simply tell the forgetful student that you would like to borrow \$10 and pay back with 10 cents. After all, units do not really matter, do they?

Puzzle 1

Puzzle 2
Puzzle 3
Puzzle 4
Puzzle 5
Puzzle 6
1. In 1999, the Mars Climate Orbiter spacecraft was lost as it attempted to orbit Mars. According to the investigative report, the main cause was the failure of one team to convert English units to metric. Given the ratios of 1 inch/2.54 centimeters and 10 mm/1 cm, determine how many millimeters are in 8 inches.
2. Rudy is attending a party for 15 people, and offered to bring BBQ chicken wings. One bucket of wings has 45 pieces, and Rudy figured on an average of six pieces per person. To find out how many buckets of wings to buy he divided 45 by 6 to get the number of servings in each bucket, and then multiplied that answer by 15 people. His final answer was 112.5. He knew that couldn’t be right. What did Rudy do wrong? How many buckets of wings does Rudy need?
Rudy did not use the correct ratios—his “units” did not cancel out. Following his reasoning, his equation would appear as follows.
Rudy should have done the following calculation.

### Discussion

Since units give dimension to a number, the technique used in this activity is often called dimensional analysis. Some refer to the technique as the factor-label method while others use unit analysis or unit-factor method. No matter what this problem-solving method is called, it is an important tool to use whenever calculations need to be made with measured values.

Whether problems are simple or complex, asking students to simply “label the answer” will not ensure the method used to obtain the solution to the problem was correct. Teachers can reinforce good practice by consistently modeling unit factoring whenever solving problems in front of the class. As students employ the technique of unit factoring—identifying the unknown (target units), specifying what is known (values and units along with relevant conversion factors and units), developing an equation with the appropriate conversion factors, and performing the calculations—they will be developing an essential skill that has many applications in the science classroom and everyday life.

### References

Special thanks to Sue Bober, Schaumburg High School, Schaumburg, IL, for sharing this activity with Flinn Scientific.

Herr, N.; Cunningham, J. B. Hands-On Chemistry Activities with Real-Life Applications; Jossey-Bass: San Francisco, 1999.

# Problem Solving on the Wildlife Refuge

### Introduction

Students often forget to include units when solving problems or recording measurements, yet numbers without units are usually meaningless. Help your students develop the habit of using proper problem-solving techniques as they enter the wildlife “unit-factoring” refuge.

Welcome to the wildlife refuge where spectacular animals live together on the beautiful savanna! The savanna has two main seasons—wet and dry—and large numbers of animals migrate during the dry season in search of food and water. Scientists need to keep careful count of endangered species present on the refuge throughout the year. Since the animals continue to migrate in the dry season, scientists are not able to count each animal by sight. An indirect and practical means of counting these animals must be used and the wildlife refuge needs your help!

A series of wildlife ratios has been prepared that help to estimate the number of animals on the refuge. When a particular species has migrated far from the observation area, scientists are still able to predict the number of animals present on the refuge based on the observed population of another species.

An example of a wildlife ratio card is shown in Figure 1. This ratio means that for every 4 zebras observed, 3 hippos may be found on the refuge. Conversely, for every 3 hippos, there are 4 zebras. Using the ratio cards, the number of one type of animal can be predicted based on observation of another type of animal.

{11981_Introduction_Figure_1_Ratio card}

### Concepts

• Problem solving
• Measurement units
• Dimensional analysis
• Conservation factors

### Experiment Overview

Determine the population of various types of animals on the wildlife refuge by using the ratio cards provided.

### Materials

Calculator (optional)
Wildlife Puzzle Cards
Wildlife Ratio Cards, set of 8

### Procedure

1. Spread all eight ratio cards face up on the top half of the work space.
2. Select the first puzzle card. See Figure 2 for a sample puzzle card. Working with your partner, describe the “problem” or question that is illustrated on the card. In Figure 2, the problem might be stated, “Knowing that two cheetahs are observed or found on the refuge, how many hippos are present?”
{11981_Procedure_Figure_2_Puzzle card}
3. Place the puzzle card at the left side of the work area.
4. Find a ratio card that has the animal on the puzzle card with the known population. In the sample given, the known animal is a cheetah.
5. Place the ratio card with the known animal as the denominator (bottom half) of the ratio next to the puzzle card. Note: If necessary, turn the ratio card upside-down so the known animal is on the bottom (see Figures 3 and 4).
{11981_Procedure_Figure_3}
6. Determine the target animal—the animal whose population is unknown. In the sample in Figure 2, the target animal is a hippo.
7. Find a ratio card that has the target animal. Place this ratio card at the right side of the work area with the target animal as the numerator (top half).
8. Select other ratio cards as needed so the type of animal cancels out in a “top–bottom” fashion until only the target animal remains on both sides of the equation (the equal sign) (see Figure 4). Remember that the target animal must appear in the numerator (top half).
{11981_Procedure_Figure_4}
9. If a solution is not found, try a different ratio card that has either the target animal or the known animal and repeat steps 5–8. Remember that the ratio cards may be turned upside-down so that “units” (the animals) cancel out.
10. Record the series of ratio cards in word form on the Problem Solving on the Wildlife Refuge Worksheet, including the known animal and number from the puzzle card (see Figure 5).
{11981_Procedure_Figure_5}
11. Draw a line through each animal name that cancels out (this should be all except the target animal).
12. Now factor the numbers to simplify the math (see Figure 6). Note: This step may be omitted.
{11981_Procedure_Figure_6}
13. Multiply the numbers on the top half of the cards and then divide by the product of the numbers on the bottom half to determine the population of the target animal. Round to the nearest whole number if necessary. Record the answer on the worksheet (see Figure 7).
{11981_Procedure_Figure_7}
14. Repeat steps 1–13 for each puzzle card.

### Student Worksheet PDF

11981_Student1.pdf

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