The following lesson plans are designed to be used in the science class in conjunction with the subject matter being studied. The main aim is to make the student feel comfortable with measurement, compilation of numbers, graphing, and looking at the results of the graph for interpretation. The techniques learned in math classes are easily carried over to science classes where the student can work with applications of the skills he has been taught. Practice in graph interpretation can also carry over to other subjects and areas. Emphasizing statistical concepts such as the average or mean, the normal distribution, and probability are a few of the ideas that are presented in these lesson plans.
Lesson Plan 1:
Measurement is Approximate
Purpose:
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To show students that measurement is approximate and show the variability of measurements obtained from each member of the class measuring only one sample. The graphing of the answers should produce a normally distributed histogram or curve which will be graphed. A similar experiment by J. S. Hunter, from an article in Science, “The National System of Scientific Measurement”, of one blood sample sent to 100 laboratories, showed the variability of lead concentration that was found by the different laboratories from the same sample.
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Materials:
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A lima bean and a metric ruler that each student has access to. NOTE: A maple leaf, pine needle, or any other biological specimen may be used instead of a lima bean.
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Method:
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1. Give out a paper with various length labelled lines, so you are sure each student can measure a line using metric scale.
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Example: (Have unlabelled line to check measure.)
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(figure available in print form)
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2. Have each student measure a sample lima bean length wise at its longest point, and pass this one sample around room. Ask each student to write down his answer on a little slip of unsigned paper and to hand in.
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3. The teacher can collect papers, and the next day post the cumulative results on the board from which the class can make a histogram.
(figure available in print form)
Lesson Plan lI:
Variability of Size Within One Type of Seed
Purpose:
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The purpose of this lesson is to show students that not only different measurements on one sample may vary, but the sizes of one type of biological entity such as a leaf, a seed, a human being, may vary when numbers of the sample are measured. So, human beings or lima beans come in different sizes, but all within certain normal limits, and the graphing of many measurements leads to a normal distribution curve or histogram that shows the range and the average or mean measurement.
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Materials:
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1. A box of dry lima beans, all of approximately the same size, from which 5 will be given to each student.
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2. A metric ruler
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3. Paper to record the size in cm. of each of the 5 beans, measured lengthwise through the longest distance.
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Method:
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1. Have students recheck Lesson Plan I so they are sure of measuring (in cm.) standard size lines.
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2. Give each student 5 lima beans and a metric ruler.
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3. Have the students record these 5 measurements on a piece of paper.
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4. Collect all the papers, and either compile the class results to post on the board for the next day’s graphing, or let the students help in putting all the results together.
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5. Give out graph paper and help the students to graph the results from the data on the board.
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NOTE: Also have students hand in their height, so a histogram of class height can be made.
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(figure available in print form)
Lesson Plan III:
Measuring and Graphing Rate of Growth
Purpose:
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To see that growth rate is not always linear, but often takes place in spurts. To see that growth can be influenced by other factors, for example, half the experimental seeds will be kept in the dark.
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Materials:
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1. Iima beans
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2. transparent plastic drinking cups
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3. towel paper
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NOTE: This experiment could also be done using soil to plant the lima beans, and watching and measuring their rapid rate of growth, but the plastic cups were chosen just so the student could see the first development that happens before the plant appears through the soil.
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Method:
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1. Have each student take a plastic transparent cup and line it with wet paper towel that is pressed all around the inside of cup.
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2. Give the students about 5 seeds each, which have been soaking overnight in water. Ask student to label cup with name.
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3. Then each student will tuck the seed inside the paper towel and pressed against the transparent cup, so it can be viewed and is held in place by the wet towel. (Sprinkle water on the towel if it dries up during the week.)
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4. Invert cup so the moisture will mostly be held inside the cup.
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5. Put in a place near a window.
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6. Repeat experiment, but this time put the seeds in a dark place, such as a cabinet.
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7. Each day have students record observations, and measure approximately the growth they see as the seed germinates.
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8. Pool class results and graph.
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NOTE: The experiment usually lasts only about a week because the wet paper towel starts to mold. If the seeds are planted a few cm. beneath soil they can be followed a much longer period of time.
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(figure available in print form)
Discussion:
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This type of study can also be done when biology students are studying reproduction. The size of the embryo and fetus is given in most biology books, and the rate of growth could easily be plotted using a curve or histogram. Also, highlight events happening at the same time as growth could be written directly on the graph, such as 4 months—the skin of the fetus is well formed. The heartbeat can be heard with a stethoscope. The students in the biology classes at McCabe Center enjoyed making this type of colorful histogram.
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Lesson Plan IV:
Measurement of Heart Rate Before and After Exercise
Purpose:
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To graph two distribution curves on the same graph as the pulse rate of the class with a normal distribution is graphed next to the higher rates of the pulses of the class after exercise, but still containing a normal distribution. These two groups would be interesting to compare, using a t test but the scope of this type of study would perhaps be better suited to a math class.
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Materials:
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Clock or watch with a second hand.
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Method:
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1. Have students seated and resting.
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2. Have them practice taking their own pulses with 1st, 2nd, and 3rd fingers lightly pressing the under side of the wrist near the thumb, or on neck.
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3. Time for 30 seconds and multiply by 2 to get pulse rate. Repeat a few times, check answer with previous answer, to make sure the students feel they are getting accurate counts. Repeat a third time, but this time ask the students to record the number on a paper in a table. (See example below.)
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4. Ask the students to walk, or jog, in place, for 2 minutes.
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5. After the 2 minutes, quickly repeat the pulse, taking procedure while standing.
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6. Have students record results in the table.
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7. The teacher can then collect papers, and post results on board. Students can help with the class tally. (See example.)
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8. Graph results of pulse when sitting to get histogram or curve, then graph results after class exercised to get histogram, or curve. Do on same graph.
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NOTE: The variations within certain limits should be discussed with the class so nobody worries about the variety of pulse rates obtained. Many variables could be added to this experiment. The average pulse rate of females is supposed to be slightly faster (by about 7 beats) than the average pulse rate of males. This would be fun to check in a laboratory lesson such as the above plan.
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(figure available in print form)
(figure available in print form)
Lesson Plan V:
Purpose:
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To see that if enough cases are studied, one has about a 50% chance of either having a girl or boy. The probability is 0.5. The empirical data gathered shows this is a little off because there are more boys born in this country every year, but this adjusted value is very close to 0.5. The main purpose of this exercise is to show the biology student that all eggs contain the X sex chromosome, and half of all the sperm contain the X chromosome, and the other half contain the Y sex chromosome. So the egg has a 50-50 chance of being fertilized by an X chromosome and producing a girl (XX) or fertilized by a Y chromosome and producing a boy (XY).
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Materials:
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1. a can of 50 pennies, half marked with a small X label, and half marked with a small Y label. This represents the sperm.
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2. a cardboard circle put on the desk of each student with an X label. This represents the egg.
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Procedure:
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1. Each student is told they will have 10 children, and the sex of the child will be determined by the sperm.
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2. Shake up the can of pennies, representing the sperm, and the student will take one without looking, then mark down XX-girl if she picks a X penny, and XY-boy if she picks a Y penny.
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3. Then she replaces the penny in the can, shakes the pennies to mix them, and draws again from this sperm bank.
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4. After everyone has had 10 draws, the results are tabulated on the board.
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Example:
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BOYS
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GIRLS
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Student 1
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7
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3
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Student 2
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4
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6
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Student 3
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5
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5
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Student 4
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6
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4
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etc.
The results can be graphed by placing number of students on the Y axis, and
either
boys
or
girls on the X axis. The columns could also be added to see if one approaches the same number of boy babies as girl babies.
(figure available in print form)