A Logo-based Task for Arithmetical Activity

Young children attend to answer-getting readings of arithmetical notation. This is evidenced by many childrens exclusive acceptance of a + b = c syntaxes that lend themselves to computational readings (e.g. Behr et al., 1976; Carpenter & Levi, 2000; Knuth, Stephens, McNeil & Alibali 2006). Even those children who do accept a wider variety of syntaxes, such as a + b = b + a and c = a + b , adhere to a computational view involving getting answers to both sides of the equals sign and checking the

Introduction to Economic Analysis

This book presents introductory economics ("principles") material using standard mathematical tools, including calculus. It is designed for a relatively sophisticated undergraduate who has not taken a basic university course in economics. It also contains the standard intermediate microeconomics material. 328 page pdf.

Energy Balance Climate Model

Students explore a Global Energy Balance Climate Model Using Stella II. This Stella model focuses on global energy balance and creating a useful climate model. Students can explore how the model planetary surface and atmospheric temperatures respond to variations in solar input, atmospheric and surface albedo, atmospheric water vapor and carbon dioxide, volcanic eruptions, and mixed layer ocean depth. Climate feedbacks such as water vapor or ice-albedo can be turned on or off. The activity provi

Daisy World Model

The Daisy World model is intended to illustrate a mechanism through which biota might optimize their environment by means of negative feedback. The model offers a very simplified approach to a feedback system and can provide an introductory lesson in how models work. The aim of the model is to implement and test a mathematical model describing possible influence of biota on an abiotic (climatic) system using GAWK and GNUPLOT. The model tests the hypothesis that biota can influence the planetary

Crossroads in Mathematics: Standards for introductory college mathematics before calculus.

Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus has two major goals: to improve mathematics education at two-year colleges and at the lower division of four-year colleges and universities and to encourage more students to study mathematics. The document presents standards that are intended to revitalize the mathematics curriculum preceding calculus and to stimulate changes in instructional methods so that students will be engaged as active learners in wo

Can you draw a picture of the stars on an American flag?

This online activity offers students a chance to analyze possible patterns for the 50 stars on the US flag. Students determine the possible patterns using the clue that each row contains either one more or one less star than the row next to it. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activity features a solution hint and a solution that suggests two ways to think about the problem and shows

Middle School Portal: Math and Science Pathways (MSP2)

This online challenge activity introduces a gift-counting problem that requires students to organize information in a table and then to draw conclusions. The importance of organizing information for decision making is noted for census takers, librarians, and demographers. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The solution hint suggests how to organize a useful table. Related questions ask stud

Morphing : can you turn a frown into a smile?

This online challenge activity offers students a look into the world of computer animation. It features a simplified explanation of how one image can be transformed into another image using digitization and explains the mathematics concept of the average. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. Related questions ask students to consider other situations that require the use of percentages to mea

Bowl 'em over : does he have a chance?

The initial question for this online activity asks students to determine the probability of winning a bowling tournament, given scores for the first five games. Students determine what the score in a sixth game must be in order to win the tournament. They also calculate the probability of bowling that score. Two solutions to this problem are included. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. In r

Middle School Portal: Math and Science Pathways (MSP2)

This online activity offers students a chance to compare soda prices from two stores using data displayed on a scatter plot graph. Students are shown how the line y = x can be used to analyze the data and draw a conclusion. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activity contains a solution hint, two different ways to find the solution, questions related to analyzing similar data from other

Middle School Portal: Math and Science Pathways (MSP2)

With this online activity, students explore the classic mathematics map-coloring question known as the four-color problem. Students must determine the minimum number of colors needed to color a map so that entities sharing a border have different colors. Initially, students investigate the minimum number of colors necessary to color a map of states west of the Mississippi River. The activity's Getting Started section suggests coloring the states in a specific order. The Solution page uses odd an

Middle School Portal: Math and Science Pathways (MSP2)

This online activity offers students a chance to apply the concept of symmetry to a real archaeology question. The activity calls for a hands-on solution to the initial challenge of determining the size of a plate from only a fragment or shard. Related math questions offer the opportunity to think about lines of symmetry for a variety of shapes. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activi

Profit or loss?

This online activity challenges students to think about money and profit as they consider buying and selling a Beanie Baby. The activity is one of 80 mathematical challenges featured on the Figure This! web site emphasizing real-world uses of mathematics. After determining the profit for two transactions involving a Beanie Baby, students are asked to determine the number of attendees necessary to make a profit for a dance and to find the profit from buying and selling stock. Information about th

Middle School Portal: Math and Science Pathways (MSP2)

In this activity, students are asked to decide which would melt faster: a large block of ice or the same block cut into three cubes. The activity is one of 80 mathematical challenges featured on the FigureThis! web site. The animated introduction to this activity notes that surface area and volume are important to the work of architects, interior designers, and chemists. Students are encouraged to compare the surface area of the ice cubes to the larger block. The complete solution demonstrates h

Middle School Portal: Math and Science Pathways (MSP2)

This activity opens with a cartoon in which two characters present students with directions for arriving at a special number. Students then correlate their special number with a letter of the alphabet and choose a color that begins with that letter. The characters bet that the color is yellow, and students are challenged to discover why the bet would be correct. The activity is one of 80 mathematical challenges featured on the Figure This! web site. It introduces algebraic procedures and notes t

Tan, don't burn : how long before you burn?

This online activity offers students the opportunity to reason with numbers as they examine the practical implications of sun protection factor (SPF) numbers on sunblock. The activity is part of the Figure This! collection of 80 online mathematical challenges emphasizing real-world uses of mathematics. In this activity, the Hint and Getting Started sections illustrate how to apply mathematical reasoning. They demonstrate how to think through the answer to the initial question about how a person

Sand pictures : what's missing?

This activity opens with pictures of traditional African sand paintings called sonas. A sona is comprised of dots and loops. One design is missing, and students are asked to study the patterns and determine the appearance of the missing design. The activity, part of the Figure This! collection of 80 math challenges emphasizing real world math, explains the importance of mathematical patterns in archaeology and cultural anthropology. The Hint suggests that students examine the number and arrangem

Middle School Portal: Math and Science Pathways (MSP2)

In this activity, students explore what percentage means when looking at election results. The activity is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. The activity features questions designed to help students think carefully about how percentages are used mathematically to determine outcomes. The answer to the first question provides a detailed examination of election results. The importance of understanding the meaning of

Combination locks : I forgot the combination! How many combinations will I have to try?

This activity asks the student to find the number of possible combinations for a lock showing the numbers 0 to 39. It is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. The solution to the combination question applies the technique of using a smaller number of possible arrangements to study a problem. Students learn to use a tree diagram to model possible outcomes and explore the mathematical meaning of the term combination. Th

Middle School Portal: Math and Science Pathways (MSP2)

In this activity, students learn about the body mass index (BMI) formula and how it can be used to determine health risk. The activity is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. The activity web page contains links to a solution hint, the solution, and to other math questions, such as how the BMI formula can be written to show weight in kilograms and height in centimeters. Students and their families are challenged to u