●use ratio and rate reasoning to solve real-world problems
●use proportional relationships to solve multistep ratio and percentage problems
●explain the importance of real-world mathematics in the work of radiologic technologists
Common Core State Standards: 6.RP.A.3, 7.RP.A.3, 8.EE.A.2
Vocabulary: Radiologic technologist, sound wave, vibrate, rate, medium/media, density, metric system, English system, ultrasound waves, speed, frequency, hertz, diagnostic tool, sonogram, X-ray, computer tomography, magnetic resonance imaging, ratios, percentages, number operations, unit conversions
Materials: For the teacher: for demonstration purposes, severalX-ray images, use of whiteboard; per pair of students: Speed of Sound activity sheet; for teachers only: Speed of Sound Solutions answer key
1.Introduction (2 minutes, whole group)
Tell students that in this activity, they are going to learn what a radiologic technologist does and the real-life mathematics that radiologic technologists use to perform their jobs. Explain that before watching the video, they are going to talk about and perform some of the mathematics that a radiologic technologist may encounter in this medical profession.
Ask students, What is a sound wave? (Answer: A sound wave is produced when a source disturbs nearby molecules and causes them to vibrate. The vibrations disturb neighboring molecules, causing them to move back and forth as well. Sound waves travel in all directions from the source of the sound.)
Explain that sound waves, i.e., the vibrations that they make, travel at different rates through different media. Then, present the following chart containing average rates that sound waves travel through air, water, and steel:
Rate in meters/second
Note: The numbers noted are the averages, found in different citations. The actual speed of sound is also affected by other factors, such as density and temperature.
Ask students, What do these numbers tell you? (Answers may include that the numbers are written in the metric system and that sound travels faster through water and steel than through air.) Ask, Why do you think these rates are provided in metric units? (Answer: In science, the metric system is more commonly used than the English system.)
2.Sound Waves (15–20 minutes, pairs of students and whole class)
Explain to students that before we begin talking about one of the types of diagnostic assessments that a radiologic technician performs using ultrasound waves, we are going to perform various calculations, using information presented in the chart. Distribute the activity sheet to pairs of students. In order to complete the problems, students will also need to remember that distance = rate x time, 1 meter = 3.28 feet, and 1 mile = 5,280 feet.
Give students 10 to 15 minutes to complete the problems on the activity sheet. After students have completed them, take a few moments to discuss the solutions with the class.
3.Real-Life Math: Radiologic Technologist Video (5 minutes, whole class)
Explain to students that sound is measured not just by the speed at which it travels, but also by the frequency that it occurs, meaning the number of waves that pass through in a given amount. The human ear can hear sound waves that have a frequency of 20 to 20,000 hertz, or Hz. (A hertz is a unit of frequency in the International System of Units and is defined as one cycle per second.)
Ultrasound, however, refers to waves that have a higher frequency than 20,000 Hz and are therefore outside of our hearing range. Ultrasound equipment is one type of diagnostic tool that a radiologic technician uses. The sound waves travel through your skin and are focused on a certain part of your body by a scanning device called a “transducer.” It picks up the sound waves as they bounce back from organs inside the body. These are sometimes called echoes. This keeps repeating. The machine converts the echoes into electric pulses that are converted into computer graphic images, resulting in a diagnostic image called a sonogram.
Ask students, What do you think the average speed for ultrasound waves to travel through soft body tissue would be? (Answer: Because our bodies are made up of water, soft tissue is closest to water. The actual rate is closer to 1,540 meters/second.)
Explain, Another type of image taken by a radiologic technician is the following. (Hold up the pictures of X-rays.) Knowing that a radiologic technologist can take both ultrasound and X-ray images, what is a radiologic technologist? (You can explain that a radiologic technologist is a person trained to take various diagnostic images to help doctors see inside the body. Radiologic technologists use the following imaging equipment: X-ray generators, computed tomography (CT), and magnetic resonance imaging (MRI) machines. Technologists work with patients to educate them about how the images will be taken; make sure to position patients so that the best image can be create to assist doctors in making a diagnosis; and must know all safety precautions and effects that using the equipment may have on the patients, such as the use of radiation.)
Explain to students, As you watch the video on what a radiologic technologist does, think about the mathematics involved. Record at least five different ways that mathematics is used by a radiologic technologist.
Show students the video.
4.Discussion (5 minutes, whole group)
Ask students, What mathematics is involved in radiological imaging? (Sample answers will include: ratios and percentages, such as 15% of 70 kVp = 10,5 kVp*; number operations, such as multiplication, division, addition, and subtraction, such as 200 mA* x 0.083 second = 16.6 mAs; using complex equations and ratios, such as 240/I^2 = 40^2/20^2; calculating the proper dose of radiation; unit conversions, such as converting weight, as in pounds to kilograms (50 kg x 2.2 = 110 lbs); and measurement: measuring the distance of the patient to the source of the X-ray.)
*You may wish to note the following terms: kVp is the peak kilovoltage, or the energy of the X-rays that penetrate the tissue; mA is milliamperage per second, the unit of measure used in X-ray imaging diagnostics and radiation therapy.
5.Conclusion (5 minutes, whole group)
Ask students to write a reflection in response to the question: Why is mathematics important to the work of radiologic technicians? (Answers should include that math is important to ensure that a proper image is obtained the first time as well as for the safety of the patient so as not to apply too much radiation. Students should also identify the importance of proper calculations and the critical need for a radiologic technician to understand how to correctly convert numbers, take measurements, and apply formulas in order to successfully diagnose and support a patient.)
Activity Extension: You may wish to have students form groups to research some of the various diagnostic images that doctors need to obtain to help their patients and the math that is involved. They can include magnetic resonance imaging (MRI), computed tomography (CT scan), vascular ultrasound, X-ray, mammography, and bone densitometry.