This activity introduces students to radar bills (currency that has serial numbers that read the same forward and backward) and challenges them to estimate how frequently radar bills occur. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how symmetry and repeating patterns are important to mathematicians, scientists, and artists. The Hint tells students that our currency has eight-digit serial numbers, and the solution provides
Author(s): National Council of Teachers of Mathematics (NCTM)

At least two people in school have the same initials? : no way!
This activity challenges students to determine how many students would need to be in a school for two of them to have the same first and last initials. The activity is part of the Figure This! collection of challenges emphasizing real-world math. It introduces the pigeonhole principle and explains that it is used when people organize files and pack shipping crates. The Hint suggests that students approach the problem by finding out how many people would have to be present for at least two of the
Author(s): National Council of Teachers of Mathematics (NCTM)

Do women live longer than men?
This activity opens with a graph that depicts the life expectancies of men and women born in the United States. Students are asked to estimate the greatest difference between genders in the years between 1920 and 1996. The activity, part of the Figure This! collection of 80 real-world math challenges, introduces trend analysis and explains its utility to market research, radio stations, and manufacturers. The Hint tells students how they should read the graph to determine the life expectancy for
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
In this activity, students are given the mileage and gasoline tank capacity of three models of automobiles and asked to determine which car will go the farthest on a single tank of gas. The activity, part of the Figure This! collection of 80 real-world math challenges, explains that rates are important in the work of demographers, financiers, and economists. Using miles per gallon as an example of a rate, students are encouraged to begin the problem by calculating how far each car could go in th
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
Given that a square table sits one person per side, this activity challenges students to figure out how many tables would need to be pushed together to seat a party of nineteen. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how arranging geometric shapes is important to architects, landscapers, and quilters. Students are encouraged to model the problem using squares of paper to represent tables. Related questions ask students
Author(s): National Council of Teachers of Mathematics (NCTM)

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
Author(s): National Council of Teachers of Mathematics (NCTM)

Census : how many people live in the United States?
This activity opens with a bar graph depicting low, middle, and high estimates of United States population growth between 2000 and 2100. Students are given two statements about population growth and asked to decide if the data support those statements. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how graphic representations of population growth are used by politicians and city planners. The Hint suggests that students approa
Author(s): National Council of Teachers of Mathematics (NCTM)

Bar codes : can you decode a barcode?
In this activity, students are shown a key to the post office conversion code and given a bar coded zip code to decipher. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, introduces the bar-coding system and explains how the system enables businesses and banks to run more efficiently. The Hint suggests that students group the long and short bars into sets of five and then refer to the key to see what number is being represented. Related
Author(s): National Council of Teachers of Mathematics (NCTM)

Animal ages : do dogs age faster than people?
This activity challenges students to calculate the age of a large dog in equivalent human years. The activity, part of the Figure This! collection of 80 real world math challenges, explains the importance of conversion formulas to statisticians, scientists, and engineers. The Hint points out that the dog's growth rate changes after the first year. Related questions ask students to develop formulas that show the relationships between human years and the ages of small dogs and cats. The Did You Kn
Author(s): National Council of Teachers of Mathematics (NCTM)

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
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity challenges students to interpret a bar graph to determine the average number of hours teenagers work per week. The activity, part of the Figure This! collection of 80 real world math challenges, explains how averages are used to describe data on academic performance, athletics, and wages. The Hint suggests that students assume that 100 students participated in the survey. Related questions ask students to calculate averages for additional data sets. The Did You Know feature offers
Author(s): National Council of Teachers of Mathematics (NCTM)

VCR : do you always get 6 hours of recording on a 6-hour tape?
This activity challenges students to use proportions to estimate how many 30-minute television shows can be recorded on a VCR tape using the SP (standard play) and the EP (extended play) modes. It is part of the Figure This! collection of 80 math challenges emphasizing math in the real world. The activity begins with the observation that fractions, ratios, and proportions are used in comparison shopping, making scale models, and describing population densities. The Hint suggests that students be
Author(s): National Council of Teachers of Mathematics (NCTM)

Three squares : when do two squares make a new square?
This activity opens with a diagram of two unequal squares and challenges students to find a way to construct a third square from them. It is part of the Figure This! collection of 80 math challenges emphasizing math in the real world. The activity introduces the Pythagorean theorem and explains its importance in construction and engineering professions. Students are encouraged to model the problem using squares of paper. Related questions introduce Pythagorean triples, and the Did You Know page
Author(s): National Council of Teachers of Mathematics (NCTM)

Gone fishing : my, my little fish, how you've grown!
Opening with a cartoon showing the weights of three combinations of fish, this activity challenges students to determine the weight of each fish. This activity is part of the Figure This! collection of challenges emphasizing real-world uses of mathematics. The introduction discusses algebraic reasoning and notes its importance to scientists, engineers, and psychologists. Students are encouraged to begin by adding the weights on all three scales. The answer page describes three strategies for sol
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity challenges students to fold a sheet of paper to create a business-size envelope in a way that wastes as little paper as possible. The activity, part of the Figure This! collection of 80 challenges emphasizing real-world uses of mathematics, introduces tessellations and explains how they are used to manufacture containers efficiently. Students are encouraged to begin the challenge by examining the pattern of an unfolded business envelope. Related questions ask students to consider t
Author(s): National Council of Teachers of Mathematics (NCTM)

Two points! : who wins the game?
This activity challenges students to determine the probability of a basketball player scoring two points on a free throw if she is likely to make a basket three-fourths of the time. The activity, part of the Figure This! collection of 80 real world math challenges, introduces probability and explains its importance in the insurance industry, medical testing, and genetics. The Hint suggests that students model the problem by tossing a pair of coins. Related questions ask students to calculate the
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity challenges students to calculate, given the rate and hours per day in flight, how many days an arctic tern would require to fly the 9,000-mile roundtrip from the Arctic Circle to Antarctica. The activity, part of the Figure This! collection of 80 real world math challenges, explains the importance of calculating distances for railroad companies, trucking firms, and airlines. The Hint suggests that students begin by calculating how many miles the tern flies in one day. Related quest
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity opens with a scenario in which a rack of clothing, originally on sale for thirty percent off the original price, has been discounted by an additional fifty percent. Students are challenged to determine if the new price is actually eighty percent of the original price. The activity, part of the Figure This! collection of 80 real world math challenges, demonstrates that understanding percentages is important for making decisions based upon survey results, interest rates, and medical
Author(s): National Action Council for Minorities in Engineer

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
Author(s): National Council of Teachers of Mathematics (NCTM)

Fire hydrant : what shape is at the very top of a fire hydrant?
This activity begins an exploration of geometric shapes by asking students why the five-sided (pentagonal) water control valve of a fire hydrant cannot be opened by a common household wrench. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how geometric shape contributes to the usefulness of many objects. A hint on the page calls students' attention to the shape of a normal household wrench, which has two parallel sides. Relate
Author(s): National Council of Teachers of Mathematics (NCTM)