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Mathematics Weekly Page
This page contains sets sorted by science topic area. The Nationl Academy of Science website includes a complete statement of the national mathematics standards for each grade. These may be found at Unifying Concepts and Processes. Click on the topics below to bring up the NAS page describing the relevant Standards.

Properties of Objects and Materials

Problem 242: Counting Atoms in Molecules Students count the number of atoms in a simple molecule and work out some basic ftactions, percentages and masses. they also complete the chemical formula for the compound. [Grade: 3-6 | Topics: integers; counting similar things; fractions; percentages ]

Problem 269: Parts Per Hundred (pph) Students work with a common unit to describe the number of objects in a population. Other related quantities are the part-per-thousand, part-per-million and part-per-billion. [Grade: 3-5 | Topics: counting, unit conversion]

Problem 230: Galaxy Distances and Mixed Fractions- Students use the relative distances to nearby galaxies expressed in mixed numbers to determine distances between selected galaxies. [Grade: 3-5 | Topics: Basic fraction math.]

Problem 229: Atomic Numbers and Multiplying Fractions- Students use a piece of the Periodic Table of the Elements to figure out the identities of atoms based on numerical clues expressed as mixed numbers. [Grade: 3-5 | Topics: Basic fraction math; mixed numbers.]

Problem 228: Nuclear Arithmetic- Students use the equation N = A - Z to solve for A, Z or N given values for the other two variables. [Grade: 4-6 | Topics: Evaluating a simple equation.]

Problem 180: Planets, Fractions and Scales- Students work with relative planet comparisons to determine the actual sizes of the planets given the diameter of Earth. [Grade: 4-6| Topics: scale models; decimals; fractions]

Problem 325: Kepler Spies Five New Planets Students count squares on a Bizarro Star to study the transit of a planet, and determine the diameter of the planet. This demonstrates the basic principle used by NASA's Kepler satellite to search for Earth-sized planets orbiting distant stars. [Grade: 4-6 | Topics: Counting; graphing; area of a square]

Problem 268: Planetary Conjunctions Students study a simple solar system with three planets and work out how often planets will 'line up'. [Grade: 3-5 | Topics: geometry, time, patterns]

Motions and Forces

Problem 198: Solar Storm Timeline- Students read a narrative about the events involved in a solar storm, creates a chronology for the sequence of events, and answer some simple time-related questions. [Grade: 6-8| Topics: Time calculations.]

Problem 108 A Problem in Satellite Synchrony The THEMIS program uses five satellites in five different orbits to study Earth's magnetic field and its changes during a storm. This problem asks students to use the periods of the five satellites to figure out when all 5 satellites will be lined-up as seen from Earth. They will do this by finding the Greatest Common Multiple of the five orbit periods, first for the case of 2 or 3 satellites, which can be easily diagrammed with concentric circles, then the case for all five satellites together. [Grade: 5-9 | Topics:multiplication; Greatest Common Multiple]

Problem 154: Pan's Highway and Saturn's Rings - Students use an image from the Cassini spacecraft to determine how large the satellite Pan is, and the scale of Saturn's rings using a millimeter ruler. [Grade: 4-6 | Topics:Finding the scale of an image; measurement; unit conversion]

Transfer of Energy

Problem 216: Atomic Fractions- Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder. [Grade: 3-6 | Topics: Basic fraction math]

Problem 215: More Atomic Fractions- Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder. [Grade: 3-6 | Topics: Basic fraction math.]

Problem 214: Atomic Fractions III- Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder. [Grade: 3-6 | Topics: Basic fraction math.]

Problem 199: Solar Storm Energy and Pie Graphs- Students study two Pie graphs describing solar flares and draw conclusions about percentages and their various forms of energy. [Grade: 6-8| Topics: Interpreting Pie Graphs.]

Light

Problem 216: Atomic Fractions- Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder. [Grade: 3-6 | Topics: Basic fraction math]

Problem 215: More Atomic Fractions- Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder. [Grade: 3-6 | Topics: Basic fraction math.]

Problem 214: Atomic Fractions III- Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder. [Grade: 3-6 | Topics: Basic fraction math.]

Problem 156: Spectral Classification of Stars- Students use actual star spectra to classify them into specific spectral types according to a standard ruberic. [Grade: 5-8 | Topics: Working with patterns in data; simple sorting logic

Objects in the Sky

Problem 232: Star Circles- Students use a photograph of star trails around the North Star Polaris to determine the duration of the timed exposure based on star arc lengths. [Grade: 8-9 | Topics: Lengths of arcs of circles; angular measure.]

Problem 231: Star Magnitudes and Decimals- Students work with the stellar magnitude scale to determine the brightness differences between stars. [Grade: 5-8 | Topics: Multiplying decimals.]

Problem 230: Galaxy Distances and Mixed Fractions- Students use the relative distances to nearby galaxies expressed in mixed numbers to determine distances between selected galaxies. [Grade: 3-5 | Topics: Basic fraction math.]

Problem 177: Lunar Cratering: Probability and Odds- Students work with crater counting to estimate the area coveblack by craters and how to convert this into impact probabilities. [Grade: 4-7| Topics: Area; probability]

Problem 173: Groups, Clusters and Individuals- Students determine the number of individual objects given the number of groups and the number of individuals in an average group for clusters of stars and galaxies. [Grade: 3-5 | Topics: multiplication]

Problem 172: The Stellar Magnitude Scale- Students learn about positive and negative numbers using a popular brightness scale used by astronomers. [Grade: 3-6| Topics: number relationships; decimals; negative and positive numbers]

Problem 165: Fractions in Space - Students explore the many ways that simple fractions come up in the study of planetary motion. [Grade: 3-5 | Topics: working with fractions; time calculations]

Problem 161: Earth and Moon to Scale- Students create a scale model of the Earth-Moon system and compare with artistic renditions and actual NASA spacecraft images. [Grade: 4-6| Topics: Decimals; scaling and similarity]

Problem 160: The Relative Sizes of the Sun and Stars- Students work through a series of comparisons of the relative sizes of the sun compablack to other stars, to create a scale model of stellar sizes using simple fractional relationships. ( e.g if Star A is 6 times larger than Star B, and Star C is 1/2 the size of Star B, how big is Star C in terms of Star A?) [Grade: 4-6 | Topics: working with fractions; scale models]

Problem 159: Galaxies to Scale - Students explore the relative sizes of the Milky Way compablack to other galaxies to create a scale model of galaxies, similar to the methods in Problem 161. [Grade: 4-6 | Topics: working with fractions; scale models]

Changes in the Earth and Sky

Problem 151: Time Zone Math - Students learn about time zones and perform simple clock calculations using common United States and European time zones. [Grade: 3-5 | Topics: time units; addition, subtraction]

Problem 29 The Wandering Magnetic North Pole Mapmakers have known for centuries that Earth's magnetic North Pole does not stay put. This activity will have students read a map and calculate the speed of the 'polar wander' from 300 AD to 2000 AD. They will use the map scale and a string to measure the distance traveled by the pole in a set period of time and calculate the wander speed in km/year. They will answer questions about this changing speed. [Grade: 6 - 8 | Topics: Interpreting graphical data; speed = distance/time]

Problem 26 Super-sized Sunspots and the Solar Cycle. Students compare the dates of the largest sunspots since 1900 with the year of the peak sunspot cycle. They check to see if superspots are more common after sunspot maximum or before. They also compare superspot sizes with the area of earth. [Grade: 6 - 8 | Topics: Interpreting tabular data; decimal math]

Problem 23 Solar Flares and Sunspot Sizes Students compare sunspot sizes to the frequency of solar flares and discover that there is no hard and fast rule that relates sunspot size to its ability to produce very large flares. [Grade: 6 - 8 | Topics: Interpreting tabular data; percentages; decimal math ]

Problem 7 Solar Flares, CME's and Aurora Some articles about the Northern Lights imply that solar flares cause them. Students will use data to construct a simple Venn Diagram, and answer an important question about whether solar flares cause CME's and Aurora. [Grade: 5 - 7 | Topics: Venn Diagramming]

Earth in the Solar System

Problem 27 Satellite Failures and the Sunspot Cycle There are over 1500 working satellites orbiting Earth, representing an investment of 160 billion dollars. Every year, between 10 and 30 of these re-enter the atmosphere. In this problem, students compare the sunspot cycle with the record of satellites re-entering the atmosphere and determine if there is a correlation. They also investigate how pervasive satellite technology has become in their daily lives. [Grade: 6 - 8 | Topics: Graphing tabular data; decimal math]

Energy in the Earth System

Problem 9 Aurora Power! Students use data to estimate the power of an aurora, and compare it to common things such as the electrical consumption of a house, a city and a country. [Grade: 5 - 7 | Topics: Interpreting tabular data]

Natural Hazards

Problem 244: Solar Storms - Fractions and Percentages Students create a Venn Diagram to summarize data on a series of solar storms, and determine how often solar flares occur when a solar plasma eruption happens. [Grade: 4-7 | Topics: precentages; Venn Diagramming]

Problem 176: Solar Storms: Sequences and Probabilities I - Students continue their study of a stormy week on the sun by working out the probabilities for joint events. [Grade: 4-7| Topics: probability; numerating possible outcomes]

Problem 175: Solar Storms: Sequences and Probabilities II - Students work out the probabilities for various combinations of solar storms during a given week. [Grade: 4-7| Topics: probability; numerating possible outcomes]

Problem 26 Super-sized Sunspots and the Solar Cycle. Students compare the dates of the largest sunspots since 1900 with the year of the peak sunspot cycle. They check to see if superspots are more common after sunspot maximum or before. They also compare superspot sizes with the area of earth. [Grade: 6 - 8 | Topics: Interpreting tabular data; decimal math]

Problem 23 Solar Flares and Sunspot Sizes Students compare sunspot sizes to the frequency of solar flares and discover that there is no hard and fast rule that relates sunspot size to its ability to produce very large flares. [Grade: 6 - 8 | Topics: Interpreting tabular data; percentages; decimal math ]

Science and Technology in Society

Problem 100 The Sunspot Cycle - endings and beginnings - Students will examine a plot of the sunspot cycle and extract information from the plotted data about the previous sunspot cycle, and make predictions about the next one about to start in 2007. [Grade level: 6-9 | Topics:graph reading; extrapolation; time calculations]

Problem 96 Hinode Satellite Power - Students will study the design of the Hinode solar satellite and calculate how much power it can generate from its solar panels. [Grade level: 9-11 | Topics:area of rectangle,area of cylinder, unit conversion]

Problem 16 Solar Power and Satellite Design Students perform simple surface area calculations to determine how much solar power a satellite can generate, compared to the satellite's needs. [Grade: 6 - 8 | Topics: Area of irregular polygons]

Problem 2 Satellite Surface Area Students calculate the surface area of an octagonal cylinder and calculate the power it would yield from solar cells covering its surface. [Grade: 7 - 9 | Topics: surface areas; hexagone; decimal math]

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