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Michael Conte, Jr.
Children, ages 10-16, in the middle schools are going through dramatic and dynamic changes in their physical and psychological development. The various and obvious physical changes give us an opportunity to illustrate many mathematical concepts. There is a great variation in the onset and rate of physical development that children are curious about and need to know about. The areas that I chose, offer non-sensitive but essential parts of the body that are easily shown and readily available to the children. A major objective is for teachers to explore the skeleton as a basis to teach problem solving, graphing, ratios, proportions, percents, etc. The material to know is included. This unit is a resource guide and catalyst to ďget you goingĒ in presenting other aspects using your teaching expertise.
The objectives of this unit include the child being able to:
The objectives described above will be accomplished using scientific information, names and explanations, through integration into the mathematical curriculum area. The skills that I plan to teach using this unit include: scale, growth charting, tangrams (hand, teeth), graphing, ratios, proportions, percentages, geometric designs. circumference, diameter, radius, metric conversions (length, weight, mass), problem solving, addition, subtraction and measuring using body parts as a standard.
- 1. name and give examples of the 4 types of bones
- ____-long, short, irregular, flat
- 2. describe the 4 types of bones
- ____-long (femur, humerus), short (wrist, ankle), flat (cranium, scapula), irregular (vertebrae)
- 3. define axial and appendicular skeletons
- 4. describe how bones grow using the femur as an illustration
- 5. show age differences in skeletons
- 6. show sex differences in skeletons
- 7. list the functions of bones
- ____-support, protection, movement, hemopoiesis, reservoir for elements
- 8. list the parts of a long bone
- ____-diaphysis, epiphyses, articular cartilage, periosteum, medullary cavity, endosteum
- 9. label the major parts of the hand
- ____-carpus, metacarpus, phalanges
- 10. Label parts of the tooth
- ____-crown, neck, root, enamel, gum, dentine, pulp, bone
- 11. list the teeth found in humans
- ____-incisors, canines, bicuspids, molars
In the pages that follow, I will collect and put forth all the material needed to teach this unit. I would like each section introduced using filmstrips and teacher prepared diagrams and graphs as a visual tool permanently on display while the unit is being taught.
Although the number of bones are the same for both sexes, there are some obvious differences. Generally speaking, the size and weight of bones of female skeletons are smaller and lighter than the male and the pelvic area has anatomical differences. There are also growth and development changes in the skeletal system between infancy and adulthood. For example: the head becomes proportionately smaller (1/8 of its body height instead of 1/4 in an infant), the shape of the thorax changes, the pelvis becomes larger, 2 curves develop in the vertebral column, the legs become proportionately longer, the cranial capacity changes, the facial bones change and the epiphyses of the long bones become ossified except for the articular cartilage. (Anthony p. 116)
The skeletal elements, especially the long bones in the human embryo, are cartilaginous models of bones. Through the process of osteogenesis (ossification) special cells called osteoblasts form bone matrix, a mixture of protein (collagen) and mucopolysacharides. (see table below)
Bone Structure (figure acquired from Body on File 05.003)
In the human body there are 4 types of bones: long bones (femur, tibia, humerus), short bones (carpals and tarsals), flat bones (cranium and scapula) and irregular bones (vertebrae, sacrum, coccyx). The internal as well as external architecture of these bones vary and express the function each is meant to contribute to the skeleton. Aside from supporting the entire body much like that of a frame for a house, the skeleton also protects the important soft tissue and organs of the body (brain, heart, lungs) while aiding body movements through a complex system of levers made possible by muscle attachments to the bone. Two other functions of the skeletal system as a reservoir for a range of chemical elements needed for metabolism and hemopodesis, the location (medullary cavity) for the formation of blood cells, are little known to the general public. All of the activities of bones as organs and as tissue are necessary for the proper functioning of the entire body.
Several math activities that may be used when teaching this section might be: measurement of the classbody length, weight and height, put it on a graph or chart using metric or standard units; determine the percent of bone (weight) that each child has as determined by their body weight, measure the circumference of the head (around the eyes) in relation to body height (1/8); make scale drawings based on information gathered on the children in class; use growth charts (CHCP) to graph class, determine percentiles of growth and make predictions of where the average will be in 2months, 6months time.
Bone: structure (figure acquired from Body on File 0.5.003)
Thigh and leg (figure acquired from Body on File 05.021)
Sample math activities for skill and concept development would include (using chicken, turkey or human bones): measuring length and weight in metric and standard units; determining circumference, radius and diameter; measuring the angles of trochanters; determine the mass of the bones; weigh 2 different types of long bones and detail the differences in weight, length, mass, circumference, diameter and radius; enlarge the chart ratio and percent of ossification by taking the measurements off the chart.
The hand contains a total of 27 bones divided into 3 groups: the carpals, metacarpals and phalanges. (see figure below) The carpals consist of 8 irregular bones in two rows (4 each) called the proximal and distal rows. The distal row acts as anchors for the metacarpals, 5 long bones articulating with the distal row at its base, while joining with the three sets of phalanges-proximal, middle,distal(l2 bones), The thumb has only 2 phalanges.
Hands (figure acquired from Body on File 05.019)
Ossification in each bone of the phalanges begins in the shaft, except for the distal set where it commences at the distal end. The approximate timetable for the onset in each set is:
Sample math activities that the teacher might use would be: measure the circumferences of the wrist and ankle and make a comparison ratio: make charts of the fingers of the children in the class, length, hand spans: make a chart describing the different periods of time that the bones in the hand ossify; produce ratios of the hand parts in regards to length and age; make ratios about finger parts-metacarpals to phalanges; make a tangram of the hand and have the children assemble it.
- distal 7th to 9th week (post natal), proximal, 9th week and middle 12th week. The epiphyseal centers join at puberty. In the thumb, the last phalange shows the first ossifying nucleus in the hand.
Teeth: 2 (figure acquired from Body on File 05.012)
The teeth in the adult are: the incisors, wedge shaped teeth that are use for cutting; the canines, tearing teeth; bicuspids, double canines; and molars, that are used to grind food. The dental formula for adults is lower 2-1-2-3/upper 2-1-2-3. (see figure below) In man the teeth are small relative to weight and size. Over the millions of years of primate development the proportions of the face have changed radically, probably in response to functional needs. Manís teeth are small since we now use implements (tools) for activities which we may in the past have used teeth.
Teeth: 1 (figure acquired from Body on File 05.011)
The cells of the pulp cavity, below the dentine, exchange material with the bloodstream to keep the tooth viable. Below the gumline the dentine in the tooth root is surrounded by cementum, the mineralized tissue that holds the tooth in place. (Ligaments attach from cementum into the jaw bones.) Above the gum line enamel covers the tooth and protects it. Enamel, is what one sees and where we brush, has no cells and cannot be repaired or regenerated if it decays.. It is this reason why there is a need for preventive measures. A sound enamel produced through good nutrition during the growth period (through the age of 20) is aided by the addition of fluoride. This fluoride, which can only be absorbed by growing teeth, is beneficial when supplied at 1 part per million as in our local water supply.
Activities that can enhance your mathematics skill and concept work might be: compare the ratio of mineralized tissue in teeth to that in bone; plot on a graph, years of age vs growth of teeth; measure teeth, length, weight in metric and standard, make a tangram of the mouth and have the children assemble the teeth in their correct order, make comparisons between the different teeth (ratio).
- 1. If bones weigh 20% of our total body weight, what is the weight of bones in a person weighing 80 pounds?
- 2. Harry weighs 150 pounds and loses 3O pounds on a crash diet. What percent of his new weight is bone material?
- 3. The femur is a long bone in the body that has a hollow cavity which holds marrow. If a bone weighs 10 pounds and is 25% lighter because it is hollow, how much would it weigh if it were solid?
- 4. An infant has a ratio of 1-4 skull size (height) to the rest of his body. If a baby is 40 inches long, what is the length of its head?
- 5. A sample of human bone is about 1/3 organic material. If the total weight of bones equal 30 pounds, what is the weight of inorganic material?
Objective The child will be able to construct ratios using the hand as data.
Materials paper, pencil. ruler. tape measure (metric, standard)
- 1. Teach the section of the unit on the hand to the children detailing and explaining the parts of the hand and showing diagrams of how they look.
- 2. Discuss what ratios are and how they are formed. (use the textbook)
- 3. Review how to measure objects using a tape measure in metric and standard 1/2, 1/4, 1/8, cm, mm.
- 4. Have the children measure their fingers and put the appropriate measurements in the table.
- 5. Have the children make ratios using the information gathered to develop problems for their classmates.
Index Middle Ring Pinky
- Middle Distal
(Index) middle middle (Middle) Leave out the value distal. = distal of the distal middle
Objective The child will be able to (using examples of cortical and trabecular bone found in the long bones) measure circumference, diameter, length, and weight of long bones.
Materials long bones (chicken, turkey), paper, pencils, ruler, tape measure
- 1. Teach overview and femur sections of the unit. Note: cortical and trabecular bone charts and diagrams in the unit.
- 2. Discuss concepts and skills relating to circumference. (use the textbook)
- 3. Review measuring procedures for weight, length, diameter, circumference.
- 4. Cut a few long bones so that children can look at trabecular and cortical bone.
- 5. Have the children measure the bones (length, etc.) and put them on a graph.
- 6. Have the children draw diagrams of the bones and label the parts they may want to draw cross sections.
Objective The child will be able to fill in a growth chart (CHCP) and perform mathematical computations using this data.
Materials paper, pencils, scales, growth charts, yardsticks
- 1. Teach the overview sections to the class.
- 2. Review measuring techniques for weight and height.
- 3. Teach the class how to plot the growth chart and use this information to perform computations.
- 4. Have the class measure each other and themselves.
Computations to perform:
- 1. If bones weigh 20% of our total body weight, what is the weight of bones in my body?
- 2. Human bone is 1/3 organic material. What is the total weight of inorganic material in my bones? (use answer from above)
- 3. If my femur weighs 10 lbs. and is hollow and weighs 25% lighter than solid bone: what would it weigh if it were solid?
- 4. Our body height is in a 1-8 ratio with the circumference of our head at adulthood. What is your growth ratio?
Filmstrips Filmstrips can be found in the New Haven Public School System through the Audio-Visual Department
Eye Gate Media Incorporated
1. The Teeth B 556-D Filmstrip-cas.
2. The Skeleton B 556-E Filmstrip-cas.
National Geographic Society
Diagrams (For display in the classroom. These can be found in the books listed in the bibliography and made into charts.)
- 1. The Human Body II: Support and Movement of Bones and Muscles 04277 Filmstrip-cas.
1. Skeleton Body on File 05.001
2. Ossification-Long bone Francis Human Anatomy p.30
3. Bone/Cartilage Body on File 05.003
4. Growth Charts CHCP
1. Long Pane Parts Anthony Anatomy and Physiology p. 83
2. Femur-diagram Anthony Anatomy and Physiology p.112
3. Femur-diagram Francis Human Anatomy p.67-8
4. Thigh Body on File 05.022
5. Bone:Structure Body on File 05.002
1. Hand Parts Body on File 05.019
2. Hand Parts diagram Anthony Anatomy and Physiology p.107
3. Hand Parts-diagram Frazer Human Skeleton p.89
1. Deciduous Teeth Body on File 05.012
2. Permanent Teeth Body on File O5.O11
3. Tooth Structure Asimov The Human Body p.82
An easy book for children to read. Particularly useful are pages 28 and 40 where head size is measured and discussed in charts.
Goldsmith, Ilse. Anatomy for Children. New York: Sterling Publishing Company, 1978.
A very good book for children to get brief basic facts about the human body, illustrations are adequate.
Klein, Aaron. You and Your Body: A Book of Experiments to Perform on Yourself, Garden City, New York: Doubleday and Company, Inc., 1977.
This book gives very short summaries of the parts of the body with simple experiments children can perform.
Tully, Marianne and Mary Alice. Facts About the Human Body. New York: Franklin Watts, 1977.
An excellent book for children. It is a series of questions and answers about the body:
Wilson, Hon. How the Body Works. New York: Larousse and Co. Inc., 1978.
A good book for children to use with bright illustrations and language appropriate for grades 5-7.
Zim, Herbert. Bones. New York: William Morrow and Co., 1969.
A childrenís book with very simple pictures and vocabulary. a good first book to use.
A very Simple to read teacher resource, explanations are clear and the illustrations are good.
Asimov, lsaac. The Human Body Its Structure and Operation. Houghton Mifflin Company, 1963.
A resource book to aid in gaining knowledge and a reference for teeth.
Crescimbeni, Joseph. Treasury of Classroom Artihmetic Activities. West Nyack, New York: Parker Publishing Company, Inc., 1969.
A book on activities in mathematics.
Breathnach, A. S., editor. Frazerís Anatomy of The Human Skeleton. Boston: Little, Brown and Company, 1965.
Very technical resource with pictures that are hard to decipher, only for advanced readers with a science background.
Lasker, Gabriel Ward. The Evolution of Man. New York: Holt, Rinehart and Winston Inc., 1962.
A very technical book. Chapter 19 gives fairly good examples on Growth Patterns in the Individual.
Lenihan, John. Human Engineering. New York: George Braziller, 1975.
This book talks about the human body from a mechanical engineerís viewpoint. Very interesting reading.
Loomis, Andrew, Figure Drawing for All Its Worth. Viking Press, 1973.
A good art book to show children parts of the body.
Schider, Fritz. An Atlas of Anatomy for Artists. Dover Publishing Company, 1957.
An art book depicting the parts of the body.
Swan, Ruth, editor. The Human Body on File. New York: Facts on File, Inc., 1-98-3:
This is the resource to use for diagrams. A must!! The illustrations are clear and labeled well.
Walker, Warren. Vertebrate Dissection. W.B. Saunders Company, 1975.
A teacherís reference book that can be used to find information relating to different vertebrate creatures.
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