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Mathematics Weekly Page
This page contains sets sorted by mathematics topic area. The National Council of Teachers of Mathematics website includes a complete statement of the national mathematics standards for each grade. These may be found at Principles and Standards for School mathematics. Click on the topics below to bring up the NCTM page describing the relevant Standards.

Numbers and Operations

Integers

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 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]

Problem 243: ISS - Orbit Altitude Changes Students read an essay describing the increases and decreases in the International Space Station orbit, and calculate the final orbit altitude after all the changes are applied. [Grade: 3-5 | Topics: combining positive and negative mixed numbers; fractions]

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 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 20 A Space Science Crossword Puzzle Students work with positive and negative numbers to solve a crossword puzzle. The theme is 'Scientists use math to explore Nature'. Good exercise for pre-algebra review of adding and subtracting positive and negative numbers. [Grade: 4 - 6 | Topics: Integer arithmetic; associative and distributive laws]

Fractions and Mixed Numbers

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

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 217: Fractions and Chemistry- Students study simple chemical equations by using simple proportions and mixed numbers. [Grade: 3-6 | Topics: Basic fraction math; ratios.]

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 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 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]

Decimals

Problem 166: The Dollars and Cents of Research - Students work with dollar amounts, hourly salary rates, percentages to explore various models of the cost of scientific research as seen by the individual scientist. [Grade: 4-6 | Topics: percentages, decimal math, simple rates (e.g dollars/hour)]

Time

Problem 174: A Matter of Timing - Students study satellites of Saturn to work out graphically how often they will line up. [Grade: 3-6| Topics: scale model; time calculation; fractions; working with rulers and compasses]

Problem 163: Time Intervals - Students calculate time intervals between a number of astronomical events, from milliseconds to years. [Grade: 3-5 | Topics: Time calculations; unit conversions; decimal math]

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 37 Time Zone Mathematics. Students will learn about the time zones around the world, and why it is important to keep track of where you are when you see an astronomical phenomenon. A series of simple time calculations teaches students about converting from one time zone to another. [Grade: 5 - 7 | Topics: Time zone math]

Problem 10 The Life Cycle of an Aurora Students examine two eye-witness descriptions of an aurora and identify the common elements so that they can extract a common pattern of changes. [Grade: 4 - 6 | Topics: Creating a timeline from narrative; ordering events by date and time]

Positive and Negative Numbers

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 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 62 Star light...Star bright - A question of magnitude! - Since the time of the ancient Greek astronomer Hipparchus, astronomers have measured and cataloged the brightness of stars according to the 'apparent magnitude scale'. This activity lets students experience this peculiar numbering system where bright stars have small numbers (even negative: our sun is a -26 magnitude!) and faint stars have large numbers (faintest stars are +29 magnitudes). Students will calculate the brightness differences between stars using multiplication and division. Working with the number line will be a big help and math review! [Grade level: 4-6 | Topics: Positive and negative numbers; decimal math]

Algebra

Problem 222: Kelvin Temperatures and Very Cold Things- Students convert from Centigrade to Fahrenheit and to Kelvin using three linear equations. [Grade: 5-8 | Topics: Evaluating simple linear equations for given values..]

Problem 221: Pulsars and Simple Equations- Students work with linear equations describing the rotation period of a pulsar, and evaluate the equations for various conditions. Students use the equations to pblackict intersection points in time. [Grade: 6-8 | Topics: Evaluating simple one-variable equations]

Problem 219: Variables and Expressions from Around the Cosmos- Students evaluate linear equations describing a variety of astronomical situations. [Grade: 6-8 | Topics: Evaluating simple one-variable equations.]

Problem 153: Number Sentence Puzzles - Students are presented with three number sentences such as 145 + N = 375, and asked to select which 'spacy' word problem they belong to. [Grade: 3-4 | Topics: Number Topics and problem solving]

Problem 149: Equations with One Variable - Students solve formulas of the form 2001 = 1858 + 11x to find 'X'. [Grade: 3-5 | Topics: addition, subtraction, multiplication, division; solving simple equations]

Problem 24 Reading Between the Lines Students solve simple equations for x, (like 2x + 3 = 5) to discover which words complete an essay on the causes of aurora, and answer questions after reading the completed essay. [Grade: 5 - 7 | Topics: solving for X; distributive law; associative law]

Geometry, Areas, Volumes

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 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 225: Areas Under Curves; An astronomical perspective- Students work with a bar graph of the number of planet discoveries since 1995 to evaluate the total discoveries, as areas under the graph, for various combinations of time periods. [Grade: 6-8 | Topics: Adding areas in bar graphs.]

Problem 60 When is a planet not a planet? - In 2003, Dr. Michael Brown and his colleagues at CalTech discovered an object nearly 30% larger than Pluto, which is designated as 2003UB313. It is also known unofficially as Xenia, after the famous Tv Warrior Princess! Is 2003UB313 really a planet? In this activity, students will examine this topic by surveying various internet resources that attempt to define the astronomical term 'planet'. How do astronomers actually assign names to astronomical objects? Does 2003UB313 deserve to be called a planet, or should it be classified as something else? What would the new classification mean for asteroids such as Ceres, or objects such as Sedna, Quaoar and Varuna? [Grade level: 6-8 | Topics: Non-mathematical essay; reading to be informed]

Problem 59 Getting A Round in the Solar System! - How big does a body have to be before it becomes round? In this activity, students examine images of asteroids and planetary moons to determine the critical size for an object to become round under the action of its own gravitational field. Thanks to many Internet image archives this activity can be expanded to include dozens of small bodies in the solar system to enlarge the research data for this problem. Only a few example images are provided, but these are enough for the student to get a rough answer! [Grade level: 6-8 | Topics: Data analysis; decimals; ratios; graphing]

Problem 51 Sunspots Close-up and Personal - Students will analyze a picture of a sunspot to learn more about its size, and examine the sizes of various other features on the surface of the sun that astronomers study. [Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; decimal math]

Problem 38 Solar Eclipses and Satellite Power From the ground we see total solar eclipses where the New Moon passes directly between Earth and Sun. Satellites use solar cells to generate electricity, but this is only possible when the Earth is not 'eclipsing' the sun. Students will create a scaled drawing of the orbits of three satellites around Earth, and calculate how long each satellite will be in the shadow of Earth. They will be asked to figure out how to keep the satellites operating even without sunlight to power their solar panels. [Grade: 5 - 8 | Topics: Geometry; decimal math]

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: 5 - 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]

Problem 11 How high is an aurora Students use the properties of a triangle to determine how high up aurora are. They also learn about the parallax method for finding distances to remote objects. [Grade: 5 - 8 | Topics: Geometery; angle measure]

Measurement

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 161: Earth and Moon to Scale- Students create a scale model of trhe 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]

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]

Problem 143 So..How big is it? - Asteroid Eros surface Students calculate the scale of an image of the surface of the asteroid Eros from the NEAR mission, and determine how big rocks and boulders are on its surface. [Grade: 4 - 7 | Topics: Scaling; multiplication, division; metric measure]

Problem 139 How Big Is It? - Mars Students use an image of a crater wall on mars to investigate ancient water gullies discovered in 2008 by the Mars Orbiter. [Grade: 4 - 7 | Topics:image scales; metric measurement; division and multiplication; decimals]

Problem 135 How Big is It? - Io and Jupiter. Students work with an image taken by the Cassini spacecraft of Jupiter and its satellite Io. They determine the image scale, and calculate the sizes of various features in the image. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 133 How Big is It? - The Mars Rover. Students work with an image taken by the Mars Orbiter satellite of the Spirit landing site. They determine the image scale, and calculate the sizes of various surface features from the image. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 131 How Big is It? - Las Vegas up close. Students work with an image taken by the QuickBird imaging satellite of downtown Las Vegas, Nevada. They determine the image scale, and calculate the sizes of streets, cars and buildings from the image. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 129 How Big is It? - The Moon up close. Students work with an image taken by the Lunar Orbiter III spacecraft to determine image scale, and search for the smallest things seen in a photograph. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 127 How Big is It? - The Moon up close. Students work with an image taken by the Lunar Orbiter IV spacecraft to determine image scale, and search for the smallest things seen in a photograph. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 126 How Big is It? - A Martian Avalanche! Students work with a Mars reconnissance Orbiter image to determine image scale, and search for the smallest things seen in a photograph.This avalanche was caught as it occurred on February 19, 2008! [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 125 How Big is It? - Washington DC up close. Students work with an image taken by ISS astronauts to determine image scale, and search for the smallest things seen in a photograph. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 97 Hinode - Closeup of a Sunspot - Students will determine the sizes of sunspots and solar granulation cells from a recent image taken by the Hinode solar observatory. [Grade level: 6-8 | Topics:image scales, metric units, unit conversion]

Problem 52 Measuring the size of a Star Cluster - Astronomers often use a photograph to determine the size of astronomical objects. The Pleiades is a famous cluster of hundreds of bright stars. In this activity, students will determine the photographic scale, and use this to estimate the projected (2-D) distances between the stars in this cluster. They will also use internet and library resources to learn more about this cluster. [Grade level: 4-6 | Topics: Online research; Finding the scale of an image; metric measurement; decimal math]

Problem 22 The Auroral Oval Students learn that the aurora are observed as two 'halos' of light encircling the North and South Poles. Students use measurements made from two satellite images of the 'auroral ovals' to determine the diameter of the rings, and their approximate geographic centers - which are not at the geographic poles! [Grade: 5 - 7 | Topics: Finding the scale of an image; measurement; decimal math]

Data Analysis and Probability

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 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.]

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 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 162: Areas and Probabilities- Students explore how area and probability are related in working out meteor impact and 'stormy day' problems. [Grade: 4-6 | Topics: Working out all possible outcomes for a set of events; fractions and percentages]

Problem 150: Cosmic Bar Graphs - Students interpret simple bar graphs taken from astronomical data. [Grade: 3-5 | Topics: finding maxima and minima; fractions; extrapolating data]

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 36 The Space Station Orbit Decay and Space Weather Students will learn about the continued decay of the orbit of the International Space Station by studying a graph of the Station's altitude versus time. They will calculate the orbit decay rates, and investigate why this might be happening. [Grade: 5 - 8 | Topics: Interpreting graphical data; decimal math]

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: 5 - 8 | Topics: Area of irregular polygons]

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]

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]

Problem Solving

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

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]

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