Learning Links
Anatomy / Programming / Cause-and-Effect / Outline / Research / Mayan/Incan/Aztec/Egyptian Cultures / DNA / Binary System / Political Systems / Cryptology / Government
Related Concepts
Logic / Systems of Equations / Discrete Structures / Number Systems / Order Relations / Inequalities / Patterns / Matrices / Axiomatic Systems / Properties (Fields)
Demonstrators should be read from bottom to top, but need not be demonstrated sequentially.
Elementary Demonstrators
• Sort objects and compare attributes.
• Explore the properties of relations, including order (i.e., <, >, familial relationships, longer than).
• Explore logical thinking (i.e., analogies and syllogisms).
• Compare and contrast the structural characteristics of varying numeration systems (e.g., other bases, Roman numerals, cuneiform).
Middle School Demonstrators
• Use order of operations with rational numbers.
• Apply field properties to solve problems and equations (e.g., pencil/paper and mentally).
• Communicate (by modeling, verbal/ written explanation, and graphing on a number line) an understanding of order relations and inequalities.
• Use and compare various number systems.
High School Demonstrators
• Investigate and solve optimization problems.
• Analyze the structural characteristics of the real number system and various subsystems.
• Communicate the logic of algebraic procedures.
• Analyze similarities in various mathematical systems.
• Use deduction in an axiomatic system.
Sample Teaching/Assessment Strategies
Graphic Organizers: Compare/Contrast Structures, Mapping, Matrix / Problem Solving: Heuristics, Inquiry, Debate, Oral History / Technology/Tools: Calculators, Computers, Games, Manipulatives
These sample strategies offer ideas and are not meant to limit teacher resourcefulness. More strategies are found in the resource section.
Ideas for Incorporating Community Resources
• Invite a variety of ethnic representatives in the community to bring the class samples of their number systems.
• Examine, with a local architect, buildings in the community that illustrate the "Golden Rectangle."
• Interview police, attorneys, and physicians on the effect of using DNA for identification in criminal cases.
Core Concept - Mathematical Structure
Sample Elementary Activities
• Study the culture of Egypt; describe and compare the use of Egyptian and Hindu-Arabic (ours) numerals. P
• Solve and create analogies:
a. inch: yard: centimeter: METER;
b. ball: circle: BOX: rectangle P
• Examine the Fibonacci numbers and find examples in nature (petals on a flower, birthrate of rabbits, spirals on a pine cone). OE, P
• Prepare a graphic organizer (web) of your family. In a cooperative group, each student assumes the role of a specified family member. Each student explains his/her relationship to other members of the group. OE, P
• Stand in hula hoops (Venn diagram) according to assigned attributes, (e.g., red shirts in one hula hoop, blue tennis shoes in another hoop). PE
• Discuss when you might need to sort into given classes or subclasses. OE
Applications Across the Curriculum
Language Arts
• Write directions to enter a mathematical expression into a calculator. PE, P
Science
• Determine the surface area of different leaf specimens by using grids or geoboards, Sequence the leaves based on the surface areas; graph the results. PE, OE, P
Social Studies
• Develop a chart showing the relationship between the population of states and the number of votes in the electoral college. The chart should arrange states from largest to smallest in terms of population. OE
Arts and Humanities
• Photograph classmates to determine components of interesting pictures. OE, P
Practical Living
• Make a chart showing positions and responsibilities of players on a flag football team. OE
Vocational Education
• Conduct a food drive; sort collected food into food groups. Organize into nutritious meals. PE, OE
Sample Middle School Activities
• Use models to compare the relative sizes of fractions and decimals (fraction bars, decimal factory, and/or decimal squares). OE
• Analyze problems to see how the field properties can simplify computations and practice using mental math strategies (e.g., 12(1/2 + 1/3) = 12x1/2 + 12x 1/3 or 16+(84+59) = (16+84) + 59). OE
• Invent, develop, and explain a monetary system and put it into operation in the classroom. PE, PO
• Create a number puzzle that chains a starting number and ending number together using all four operations. OE, PE, P
• Illustrate a recent homework problem using a flowchart. PE
Applications Across the Curriculum
Language Arts
• Write a story to describe an algebraic equation. Use names of class members and familiar situations. OE, P
Science
• Compare the surface area available for photosynthesis on a variety of leaves and needles and make correlations with the total number leaves on the tree. PE, OE, P
• Determine the gene frequency of a trait in your classroom population. P
Social Studies
• Chart the passage of a bill through Congress. PE, OE, P
Arts and Humanities
• Use a formal structure to notate "Jingle Bells." PE, OE, P
Practical Living
• Use a computer program to chart the individual intake of minerals and vitamins for one day. Relate to the RDA (required daily allowance). OE, P
Vocational Education
• Compute the time it will take an accident victim to rebuild a given blood loss. OE, P
Sample High School Activities
• Explain the error in an incorrect algebraic procedure (e.g., (4x+2)/6 = (2x+2)/3 ). OE, P
• Test the set of integers under the operation of addition and multiplication for the field postulates. P
• Use models to show the relationship between perimeter, area, and volume. Make a written record of your observations. P
• Investigate and design a plan for transporting 200 students from hotel to convention center if there are these constraints: There is only one limousine and one van; the limo costs $7.0O per trip, and it can make the one-way trip in five minutes and holds 6 people; the van cost 25 cents per person, makes the one-way trip in 20 minutes, and holds 10 people. OE, P
• Make tables for modular arithmetic or electric circuitry. Test each system for field properties. P
Applications Across the Curriculum
Variations on a theme: Genetics
Language Arts
• Produce a
Science
fiction video of a simulated DNA experiment. PE, OE, P
Science
• Manipulate permutations of gene placement and predict the results using a computer simulation program. PE, OE, P
Social Studies
• Prepare a HyperCard stack of Science fiction movies with a "genetics" theme. PE, OE, P
Arts and Humanities
• Review selected "genetics related"
Science
fiction movies and create a flowchart showing their use of selected technology(s). OE, P
Practical Living
• Invite a geneticist to class to discuss computer applications in genetics research and counseling. OE
Vocational Education
• Document the genealogy chart of selected characteristics in animal breeding. P