Learning Links
Astronomy / Polls / Population Studies / Elections / Life Cycles / Lotteries / Economic Trends / Stock Market / Temperature / Banking / Recipes / Sports Statistics / Travel
Related Concepts
Multiple Representations / Mathematical Notation / Number Relations / Equivalent Forms / Number Sense / Estimation / Ratio / Infinity / Number Theory / Limit / Number Systems
Demonstrators should be read from top to bottom, but need not be demonstrated sequentially.
Elementary Demonstrators
• Count forward, count on, count back, and skip count.
• Explore, group, identify, and classify sets of objects without numbers and then with numbers.
• Investigate number systems (zero, grouping, and place value) and operations.
• Construct number meaning and interpret the multiple uses of numbers through real world experiences emphasizing the relative magnitude of numbers.
• Explore estimation strategies and determine when an estimate is appropriate.
• Investigate, model, apply, and communicate multiple representations of whole numbers, fractions, and decimals.
• Recognize integers.
Middle School Demonstrators
• Explain, demonstrate, and model positional value (place value, exponents, number line, scientific notation).
• Model, communicate, and apply multiple representations of rational numbers.
• interpret and use appropriate mathematical notation for numbers (e.g., %, !, /, ).
• Develop and apply number theory concepts (e.g., factors, primes, multiples).
• Use estimation to check the reasonableness of results.
• Investigate models of irrational numbers (e.g., pi, square roots).
• Investigate infinite progressions using number lines and geometric representations.
High School Demonstrators
• Justify and communicate answers and solution processes.
• Determine reasonableness of results by estimation.
• Communicate, model, and apply multiple representations of real numbers.
• Recognize situations which can be represented by complex numbers.
• Investigate and communicate the concept of limit.
Sample Teaching/Assessment Strategies Collaborative Process: Cooperative Learning / Community-Based Instruction: Field Studies, Networking / Graphic Organizers: Mapping/Webbing / Problem Solving: Brainstorming, Inquiry, Questioning, Future Problem Solving, Formulating Models / Technology/Tools: Manipulatives, Games / Writing Process
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 individuals to class whose careers involve working with numbers (e.g., banker, accountant, IRS representative, delivery agency employee, or sports statistician) to discuss the importance of numbers.
• Serve as interns within city hall and help the town clerk with bookkeeping.
• Ask a representative from an agricultural agency in the community to discuss livestock marketing and margins of profit for different animals.
• Participate in a variety of organized mathematics challenges/competitions (e.g., KCTM Math Bowl, Math Reach, MATHCOUNTS).
Core Concept - Number
Sample Elementary Activities
• Make a special book that contains information about numbers (e.g., age, height, phone, strength). P
• Estimate how large a scale model of the United States would have to be if 1" represents 1 mile. Determine the actual distance using a trundle wheel to mark off length. Adapt scale to fit a smaller area. PE, P
• Divide a set (group) of raisins into fractional parts (e.g. , equally divide the group of raisins into three parts). Extend by showing raisins to represent a decimal (from a set of 10 or 100 raisins). PE
• Play the donut factory game. Roll number cubes to collect a number of donuts (Cheerios) and package them into sets of 5 using portion cups. After collecting 5 portion cups, place into a carton (plate). The object is to fill a carton. This may be played in any base. PE
• Show l0 ways to model the number 45 by using manipulatives (e.g., base lO blocks), pictures, and writing. Communicate and compare the representations. OE, P
• Identify the different ways numbers are used in a newspaper. OE
• Determine different ways to estimate the number of beans in a jar. OE
Applications Across the Curriculum
Variations on a theme
Recipes
· Watch someone preparing one of your favorite foods. Write a description to tell someone how to prepare the recipe. PE, P
Science
· Estimate the amount of ingredients necessary to feed your class or school a favorite food. OE
Social Studies
· Find and prepare a recipe written using metric measurements. PE
Arts and Humanities
· Prepare a classroom cookbook of favorite foods. Include drawings or photos, tasting reviews, and recipes. Classify the recipes in a variety of ways. PE, OE, P
Practical Living
· Compare grams of fat, sugar, and nutrients of selected recipes from your cookbook. Graph the results. PE, P
Vocational Education
· Prepare some of your favorite recipes to share with the class. PE, P
Sample Middle School Activities
• Simulate the application of square roots/irrational numbers by constructing line segments (using Pythagorean Theorem) on geoboard or dot paper. P
• Represent integers using colored chips. Represent positive integers with one color and negative integers with another color. PE
• Explain the placement of the decimal point in the product of 2 decimal numbers using decimal squares (base lO blocks). (e.g., .02 x 0.3 = 2/lO X 3/10 = 6/100 = 0.06) OE, P
• Communicate a play-by-play description of a football game using a number line and integers. P
• Build all the possible rectangular arrays using 1 sq. unit, 2 sq. units, and so on. Find a relationship between prime, composite, and square numbers with the arrays. PE, P
• Explain how to solve a mathematical problem using audio or video media. PE, P
• Search periodicals using CD-ROM to locate uses of scientific notation. PE
Applications Across the Curriculum
Language Arts
· Write poems or limericks about math topics or ideas or geometric figures: "There was a math figure named Circle..." P
· Create word problems based on characters, situations, and settings from children's literature . OE
Science
· Estimate and then calculate the number of stairsteps needed to reach from the earth to the moon. P
Social Studies
· Graph relevant statistics of different countries such as population, natural resources, wealth, and standard of living. Draw conclusions. OE, P
Arts and Humanities
· Select one pair of complementary colors. Let warm color represent positive integers and cool represent negative integers. Mix positive and negative in equal parts to create a neutral (grey). Make a painting using only those two complements. (Warm colors advance, cool colors recede and neutrals remain in the middle ground.) PE, OE, P
Practical Living
· Compute personal expenditures for several months and then compute the average per month. PE
· Analyze and compare two different size bottles of aspirin as to number of doses and unit prices. Compute unit price of each dose contained in each container. P
Vocational Education
· Bring in telephone and utility bills. Find cost per minute of long distance calls, and per kilowatt-hour of electricity from utility bills. PE, P
Sample High School Activities
• Graph Y=1/(X2+1 ) exponent on a graphing calculator. Set the range for x from -5 to 5 and the y from -1 to 2. Translate graph from calculator to grid paper. Count the number of the rectangles under the curve to estimate the area under the curve. OE
• Represent complex numbers on polar graph paper and relate them to blips on a radar screen. PE, P
• Develop strategies for estimating large populations (e.g., animals, people, grains of sand). Use sampling techniques. PE, OE, P
• Explain to a classmate the meaning of 30. OE, P
• Find the pattern of the decimal equivalents for all fractions with a denominator of 9. Then extend to include fractions with a denominator of 99. Present findings using computer graphics. OE, P
• Represent, using models, a number as a fraction, decimal, and percent (e.g., 15/1 00 = 3/20, .15, 15%). Identify situations where one representation is more appropriate than another. PE, OE
Applications Across the Curriculum
Language Arts
· Design a poster for recruiting students into higher level mathematics courses. PE, OE
Science
· Use Avogadro's number to determine the depth of a layer of marshmellows spread evenly across the United States. Identify factors which would influence a variation in the depth. PE, OE, P
· Use fractals in the creation of a topographic map. PE, OE, P
Social Studies
· Make predictions about the population, natural resources, wealth, and standard of living of different countries for the year 2025. PE, OE, P
Arts and Humanities
· Create a painting using a limited color scheme that has asymmetrical balance. Write an equation that demonstrates your solution. PE
Practical Living
· Complete a comparative study of the distance runners at the local high school. Do one study in miles, the other in meters. PE, P
· Display information on cardiovascular disease and lifestyle behavior so that it is readily understood. PE, OE, P
Vocational Education
· Estimate and determine the open mesh in a 60xx screen for screen printing. P