Math Investigations and Mini-lessons

Use the student-facing STEM math investigations listed below for your project based learning (PBL) classroom or as a homeschooling resource. Mini-lessons are primarily Desmos classroom activities created by David Zelenka.

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Type	All Investigation Mini-lesson
Theme	All Architecture Art Calculus Chemistry Coding Combinations and Permutations Discrete Engineering Equality Expressions Fractions Functions General Geometry Graphing Historical Inequalities Life Skills Linear Equations Measurement Modeling Music Nature Numbers Physics Puzzles and Games Ratios Sequences Sets Spreadsheets Statistics Trigonometry Word Problems
Grades	All 3 4 5 6 7 8 9 10 11 12

	Type	Theme	Learning Target
Display # 5 10 15 20 25 30 50 100 all Total: 58
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Three-Cubed Cube Puzzle Grades: 7, 8, 9, 10, 11, 12 Investigation	Investigation	Puzzles and Games	Students will build a puzzle from 27 wood cubes focusing on how to create a challenging puzzle.		View
Joules of the River Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Physics	Students will study the kinetic energy of streamflow of a nearby river and compare it to the amount of energy in one gallon of gasoline.		View
Earthquake Heat Map Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Statistics	Students will analyze USGS seismology data using spreadsheets and produce a heat map graph to look for seismic patterns at a latitude and longitude top view.		View
Right on Time with Flight Vectors Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Physics	Students will study vectors through the analysis of wind barbs on weather maps, as they develop a flight plan from Renton to Spokane, Washington.		View
Famous Mathematician Pointillism Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Coding	Students will create pointillism artwork of a famous mathematician using a coordinate plane.		View
Finding Solar Noon Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Modeling	Students will use precision and accuracy while creatively developing a method to determine the exact time of solar noon at school on a particular day.		View
Common Error Puzzle Poster Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Physics	Students will create an error analysis poster for a topic within their area of math study and find the error in four other student's work.		View
Build a PVC Flute Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Music	Student will learn how to build and tune a PVC Flute.		View
Animal Vision Grades: 5, 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Nature	Student will construct and measure binocular and monocular vision angles for one species of animal, while constructing a model for apparent vision.		View
Euler's Circuit Riders Grades: 7, 8, 9, 10, 11, 12 Investigation	Investigation	Discrete	Students will create a unique Euler's circuit and code it using Turtle with Code.org.		View
Catch the Wave Grades: 7, 8, 9, 10, 11, 12 Investigation	Investigation	Physics	Students will measure wavelength of ocean waves from a satellite view and research period, frequency, and origin of their wave forms.		View
Matchbox Car Collision Grades: 7, 8, 9, 10, 11, 12 Investigation	Investigation	Physics	Students will calculate marble acceleration on a ramp through a regression while determining the parent graph for impact data.		View
Temp Trends Infographic Grades: 7, 8, 9, 10, 11, 12 Investigation	Investigation	Statistics	Students will investigate a atmospheric temperature dataset to plot temps since the 1970s to produce an infographic, showing trends in two different levels of the troposphere at a select region of the globe.		View
Modeling a Bouncing Ball Grades: 7, 8, 9, 10, 11, 12 Investigation	Investigation	Modeling	Students will model the functions behind a bouncing ball by plotting time versus height and regressing the data.		View
Where is Tidal Range the Greatest? Grades: 7, 8, 9, 10, 11, 12 Investigation	Investigation	Nature	Students will look for relationships between the moon, sun, geography, and tides.		View
Deep Sea Mapping in Context Grades: 5, 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Ratios	Students will compose a scale model of an oceanic geographic feature and compare it to a similar land feature.		View
Carving Pumpkins with OpenSCAD Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Coding	Students will use boolean functions in OpenSCAD to add and subtract shapes to carve a digital 3D pumpkin.		View
The Big One? Grades: 7, 8, 9, 10, 11, 12 Investigation	Investigation	Modeling	Students will plot a frequency chart of 2.0-9.0 magnitude earthquakes in Seattle and determine the likelihood of a very large earthquake of occurring (6, 7, 8, 9) and compare that to news article predictions.		View
Chlorophyll Chromatography Grades: 5, 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Ratios	Students will analyze the Rf values for two species of plant material and analyze those values in a classroom spreadsheet.		View
Fractals in Nature Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Geometry	Students will learn how patterns in nature and mathematics repeat, while producing their own fractal artwork.		View
Bird Migration Dot Art Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Nature	Students will learn about migration as they create migratory bird art using conic equations.		View
Artemis I: To the Moon and Beyond Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Engineering	Students will build a decision tree for analyzing errors in flight while comparing and contrasting Earth and Martian resources.		View
Should I? Grades: 5, 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Inequalities	Students will create a weighted balance diagram (infographic) and write an inequality to help make an informed decision while communicating that decision to others.		View
Poetry and Math Grades: 4, 5, 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Art	Students will interpret and visualize the rhythm, meter, and content of a poem using math.		View
Slo-Mo Glaciers Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Modeling	Students will calculate physical characteristics and flow rate of one glacier and determine its hydrological downstream impacts.		View
Battery Concept Design Grades: 6, 7, 8, 9, 10 Investigation	Investigation	Architecture	Students will use math or OpenSCAD coding to create a concept design for an electrochemical battery.		View
Flight Statistics Grades: 4, 5, 6, 7, 8, 9, 10 Investigation	Investigation	Statistics	Students will analyze flight and wing data for paper airplane test flights using distributions and scatterplots.		View
Get Set Jet Set Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Combinations and Permutations	Students will use discrete mathematics to determine the best possible route between four major world-wide cities.		View
Christmas Lights Quadratics Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Functions	Students will use the vertex form of the quadratic equation to build Christmas tree lights.		View
Color Theory Logo Design Grades: 5, 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Art	Students will design a logo (using 3 RGB colors) describing the colors and structure mathematically.		View
Center of a-Tension Grades: 5, 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Physics	Students will measure the change in mass with various pulley systems and analyze classroom data.		View
International Dot Day Grades: 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Art	Students will adjust circle equation values and points on a coordinate plane to create circle and dot art of their favorite fruit.		View
The Rain in Spain Falls Mainly... Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Statistics	Students will learn how to graph multiple sets of related data on one graph and use the data to justify a decision.		View
Personal Finance Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Life Skills	Students will learn how to develop a monthly budget using a spreadsheet.		View
Baking Beautifully Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Life Skills	Students will learn about algorithms and create artistic mathematical patterns by baking, cooking, or arranging food.		View
Interactive Infographic Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	General	Students will learn develop an interactive infographic to teach a math concept.		View
Famous Mathematician Investigation Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	General	Students will construct an infographic and mini-biography on a famous mathematician using the Desmos calculator.		View
Three Sheet Tower Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Engineering	Students will learn about the engineering design process while building a tower out of paper.		View
Bridge Design Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Engineering	Students will learn about three major bridge types while working with ratios and percentages and learning about three common functions.		View
Calculating Pi Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Engineering	Students will use a physical model to determine the value of pi algebraically.		View
Architecture Using SCAD Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Engineering	Students will use boolean functions in OpenSCAD to add and subtract shapes to design an architectural structure.		View
If Leonardo Had CAD! Grades: 5, 6, 7, 8, 9, 10, 11, 12 Investigation	Investigation	Engineering	Students will use boolean functions in OpenSCAD to add and subtract shapes to design a structure.		View
My Math Band Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Music	Students will collaborate together on a music project, focusing on the pentatonic scale.		View
Build a Musical Instrument Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Music	Student will learn how to build and tune a musical instrument to the pentatonic scale.		View
Music in the Waves Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Music	Students will learn about the physics of waves and music theory while tuning a standing waves to a musical note on either end of an octave.		View
Earth's Place in the Solar System Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Nature	Students will compare orbital and rotational differences between the Sun, Earth, and Moon.		View
Mammal Comparison Investigation Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Nature	Students will learn the basics of spreadsheet coding and graphing by analyzing mammal data.		View
Modeling Ocean Processes Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Nature	Students will learn how to model ocean processes using periodic functions, illustrations, or research.		View
Snowflake Modeling Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Nature	Students will model snowflake formation using multiple media types.		View
Illuminated Letter Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Art	Students will develop a sense geometric pattens through the construction of Illuminated Letters with Celtic Knots.		View
Celtic Knot Overview Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Art	Students will develop a sense geometric pattens through the construction of Celtic Knots.		View
Chess Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Puzzles and Games	Students will recognize that games contain rules and structure, which are very much like the rules and structure found in mathematics.		View
Fibonacci Art Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Art	Students can recognize recursive sequences and creatively apply Fibonacci squares or the Golden Mean in an art project.		View
Origami Mobile Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Art	Students will learn to attend to precision and develop perseverance for solving complex algorithms.		View
Ancient Math Systems Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Historical	Students will learn how to calculate using Egyptian, Roman, or Mayan mathematics and switching bases. Students will develop their own number system and justify/provide rationale for its use.		View
Analyzing Birth Data Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Spreadsheets	Students will analyze United States birth data and discover social trends. Students will learn how to generate a pivot table in Excel and visualize data in different ways.		View
Let's Look Inside the Earth Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Nature	Students will analyze USGS seismology data in the classroom using spreadsheets and scatter plots to look for patterns and structure in the Earth’s crust.		View
Overwhelmed by Cats Grades: 5, 6, 7, 8, 9, 10 Investigation	Investigation	Nature	Students will develop a method for estimating cat populations using spreadsheets, online graphs, or paper.		View