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(Download as Microsoft Word documents: Skeletal Math, Data Recording, Dem Bones, Follow Up Questions, Rubric, Student Directions, Vocabulary)

An Integrated Activity for 6^th - 8^th Grade Math and Science

Barbara Arvin Delia Edling Bruce Lightner Barb Sleith

Concepts Used: data collection, recording, and organization; measuring, prediction, graphing (scatter plots, best fit, linear equations)

PA Standards Addressed: 2.1.8 A, D, 2.2.8 B, 2.3.8 D,

2.4.8 A, B, C, D, F 2.5.8 B, C 2.6.8 A, C, F

2.7.8 B, D 2.8.8 B, C, D, G, H

NCTM Standards Addressed:

Number and Operations

· Understand numbers, ways of representing numbers, relationships among numbers and number systems.

· Compute fluently and make reasonable estimates.

Algebra

· Understand patterns, relations, and functions.

· Use mathematical models to represent and understand quantitative relationships.

· Analyze change in various contexts.

Measurements

· Understand measurable attributes of objects and the units, systems, and processes of measurement.

· Apply appropriate techniques, tools, and formulas to determine measurements.

Data Analysis and Probability

· Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

· Select and use appropriate statistical methods to analyze data.

· Develop and evaluate inferences and predictions that are based on data

· Understand and apply basic concepts of probability.

Introduction/Applications:

Science Tie-ins (this as our introduction but the remaining are additional suggestions)

· Use the song “Dem Bones” which introduces the connections of the bones in the body. Discuss the visual difference in lengths of several bones. Pose the questions to the students: “What is the connection between the length of certain bones of the body and your overall height?”

History Tie-ins

· Use the song “Dem Bones” which introduces the connections of the bones in the body. Discuss its origin as an African- American spiritual. Talk about their use of oral history and learning because they were denied a formal education.

· Discuss change in average height over the past two centuries due to dietary change.

· Discuss famous people in history of exceptional height.

Health Tie-ins

· Discuss the nutritional evolution from the past and the present.

· Compare and contrast the physical structure of male and female bodies.

· The increase in medical technology that may improve the quality of life.

Questions:

· What is the connection between the length of certain bones of the body and your overall height?

· Is there a difference between males and females?

Model:

· Using students’ physical features to collect data.

Resources and Materials (estimated cost):

Procedures & Activities:

· Grouping Students: Students are to be split into groups of boys and girls (size of group can be determined by teacher based on size of class). The data collected by each individual will be recorded collectively by gender.

· Collection and Recording of Data: Each student will use a metric tape measure and metric ruler to measure his/her height along with the lengths of his/her tibia, foot, and radius. These measurements are to be recorded in the teacher generated tables.

· Creating List: Students will create four lists in their graphing TI-83 calculator by selecting STAT, followed by Edit. In L1 will be the students’ heights, in L2 will be the lengths of their tibiae, in L3 the lengths of their feet, and in L4 the lengths of their radius bones.

· Scatter Plots: Next the STAT PLOTS will be turned on by selecting 2^nd STAT PLOT.

· Then turn Plot 1 on, select scatter plot, and the Xlist will be L1 and Ylist will be L2;

· then turn on Plot 2, select scatter plot, and the Xlist will be L1 and Ylist will be L3;

· then turn on Plot 3, select scatter plot, and the Xlist will be L1 and Ylist will be L4.

· These will produce scatter plots of the lengths of tibia, foot, and radius bones with respect to the students’ height.

· Line of Best Fit: Students are then to find the line of best fit by selecting STAT, CALC, LinReg(ax+b). The students will then enter LinReg(ax + b)L1,L2,Y1 - this will create a line of best fit between the students’ heights and the lengths of their tibiae.

· Regrouping: Combine at least two groups of girls or boys into a new larger group. Have them compare their own graphs to the other group’s graph. Then mix up the groups so that the males and females may compare their results. Students will generalize the formulas for height based on all three body parts measured.

· Discussion: As a group, have students respond to the teacher generated questions. Provide students with the previously verified formulas that are used by scientists for the tibia, the radius, and the foot.

· Follow- up Activities –

· Use collected data to determine a range, median, mean and mode for the tibiae, radii, feet and height for each gender as a whole.

· Have students convert all measurements from centimeters to inches.

Answers/Rubric:

Data Collection:

5 – All data measured and recorded correctly and done neatly.

4 – One mistake in recording and measuring data and done neatly.

3 – One mistake in recording and measuring data but not completed neatly

or few mistakes in recording and measuring data and completed neatly.

2 – Several mistakes in recording and measuring data.

1 – Numerous mistakes, not legible.

0 – No responses in recording data.

Graphing Data

5 – Lists, scatter plots, and line of best fit completed correctly and cooperatively.

4 - Lists, scatter plots, and line of best fit completed correctly with minimal outside assistance.

3 - Lists, scatter plots, and line of best fit completed correctly with some outside assistance

2 - Lists, scatter plots, and line of best fit incomplete or inaccurate.

1 - Lists, scatter plots, and line of best fit attempted but completed with major misconceptions and mistakes.

0 - Lists, scatter plots, and line of best fit were not attempted.

Data Analysis

5 – Responses to questions answered correctly with insight and mathematical comprehension.

4 – Responses to questions answered with minimal mistakes with insight and mathematical comprehension.

3 – Responses to questions answered with some misconceptions and some insight and some evidence of mathematical comprehension.

2 – Responses to questions had many misconceptions and lacked insight and little evidence of mathematical comprehension.

1 – Responses to questions had serious misconceptions and provided no insight or mathematical comprehension.

0 – Questions not attempted.

Cooperation

5 – All students participated within groups with no outside assistance needed

4 – Students participated within groups with minimal outside assistance.

3 – Students required some guidance in staying on task and required some outside assistance in completing tasks.

2 – Students needed regular maintenance to stay on task and required outside assistance to complete tasks.

1 – Students lacked focus and ability to function cooperatively during most of the activity

0 – Students demonstrated no ability to function cooperatively

Accommodations/Adaptations:

· ESL: ESL students should be paired with a higher functioning student who speaks their native language. Provision of handouts in their native language.

· Special Ed.: Pair students with a higher functioning peer with whom they feel comfortable. Provide students with handouts that have fewer directions at one time. More individual attention from teacher.

· Enrichment: As a follow-up activity, students will work individually or as a group to complete research on how this information is applied in real life. This project will be in lieu of the previously explained follow-up activities. Students may make a poster, give an oral report or write a one page paper.

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