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
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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
Road Building on Mathlantis Grades: 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Combinations and Permutations	Students will develop a sense of discrete mathematics and combinations.		View
Faults and Plate Boundaries Grades: 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Modeling	Students will learn the difference between faults and plate boundaries by building them using various tools.		View
Jumpline Grades: 8, 9, 10 Mini-lesson	Mini-lesson	Functions	Students will use functions and limit the domain to create functions for a Desmos Marbleslide.		View
Tanagram - PowerPoint Grades: 5, 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Architecture	Students will persevere solving graphical tanagram puzzles.		View
Yeti Ice Cream Grades: 5, 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Discrete	Students will determine the best location for their ice cream stores. Be prepared to use the Pythagorean Theorem.		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
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
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
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
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
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
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
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
Transforming Giraffes Grades: 6, 7, 8 Mini-lesson	Mini-lesson	Geometry	Students will learn about eight types of coordinate transformations.		View
Semi-Truck Division Grades: 4, 5 Mini-lesson	Mini-lesson	Numbers	Students will learn how to divide fractions by filling an adjustable semi-truck.		View
Optics - Refraction and Lenses Grades: 7, 8, 9, 10 Mini-lesson	Mini-lesson	Physics	Students will ray trace light through lenses and learn about refraction, focal length, divergent and convergent lenses.		View
Animal Vision Grades: 5, 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Geometry	Students will use a protractor to estimate angles for binocular and monocular vision while hypothesizing why vision scope differs among species.		View
Nautical Knots Grades: 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Historical	Students will learn how to convert between knots and miles per hour and understand how nautical miles are calculated.		View
Polyominoes Grades: 5, 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Sequences	Students are asked to think in squares by building and quantifying their results through developing custom combination equations.		View
Hydraulic Advantage Grades: 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Geometry	Students will calculate the mechanical advantage of a hydraulic lift system using area, volume, and the pressure equation.		View
Rhythm Experiment Grades: 5, 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Music	Students will use counting patterns to create a repeating 25-second percussion rhythm.		View
Unions, Intersections, and Compliments Grades: 5, 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Sets	Students will explore various sets and their relationships.		View
Music: Frequency vs. Wavelength Grades: 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Music	Students will learn about inverse relationship between frequency and wavelength while learning how to construct a pan flute.		View
Dragon Fruit Delivery Grades: 5, 6, 7, 8 Mini-lesson	Mini-lesson	Ratios	Students will determine unit rates for dragon fruit options at a market and convert at least one unit.		View
Traversing Verse with Math Grades: 4, 5, 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Numbers	Students will generate ideas for a math poem, learn the common meter forms, and write a poem using math terms.		View
Reservoir Levels in Western Washington Grades: 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Modeling	Students will model reservoir levels, convert values, and measure using GIS tools.		View
Glacier Rates Grades: 7, 8, 9 Mini-lesson	Mini-lesson	Ratios	Students will learn how to find rates with different base times.		View
Math of Climate Change Grades: 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Statistics	Students will analyze various datasets that relate to climate science.		View
How Old is Our Baikal Friend? Grades: 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Functions	Students will learn about using exponential functions and their inverses.		View
Energy Return on Investment Grades: 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Statistics	Students will analyze various data sets, work with charts, graphs and ratios to learn about energy sources and energy return on investment.		View
Atoms and Ions (Adding and Subtracting Integers) Grades: 4, 5, 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Chemistry	Students will practice integer addition and subtraction using atoms and ions.		View
Tic-Tac-Toe Products Grades: 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Numbers	Students will develop strategies for creating products from numbers.		View
Bernoulli's Principle Grades: 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Ratios	Students will explore density (dots per inch) and apply it to mass/volume.		View
Christmas Tree Extrusion Grades: 5, 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Engineering	Students will use coordinate pairs to create an extrusion Christmas tree in OpenSCAD.		View
Fraction Operations on a Number Line Grades: 4, 5 Mini-lesson	Mini-lesson	Numbers	Students will learn to add, subtract, and plot fractions on a number line.		View
Color Preference Analysis Grades: 6, 7, 8, 9, 10, 11, 12 Mini-lesson	Mini-lesson	Statistics	Students will produce color preference data and create a method to analyze multidimensional data.		View
Counting with the Maya Grades: 5, 6, 7, 8, 9 Mini-lesson	Mini-lesson	Numbers	Students will explore working with base 20, place values, and exponents.		View
Expression Builder Grades: 5, 6, 7, 8, 9 Mini-lesson	Mini-lesson	Expressions	Students will look for patterns and build expressions that describe the quantity of dots shown.		View
Planet X Grades: 9, 10, 11, 12 Mini-lesson	Mini-lesson	Functions	Students will create a function for astronomical data to determine how many years it takes for the mystery Planet X to orbit around the sun.		View
Summation Square Grades: 5, 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Numbers	Students will construct rational fractions using a visual model.		View
Tessellations Grades: 5, 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Geometry	Students will tesselate regular polygons into interesting patterns.		View
Solving A Geometry Word Problem by Using Quadratic Equations Grades: 9, 10 Mini-lesson	Mini-lesson	Word Problems	Students will understand how to solve geometry word problems using quadratic equations.		View
Derivative of a Function Grades: 9, 10 Mini-lesson	Mini-lesson	Calculus	Students will learn how to solve for a derivative of a function using the derivative definition.		View
QWERTY Coins Grades: 5, 6 Mini-lesson	Mini-lesson	Ratios	Students will develop number sense while creating conversion ratios for various mystery coin currency.		View
Histogram of Recent Earthquakes Grades: 5, 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Statistics	Students will summarize and describe earthquake magnitude distributions in a histogram.		View
Bowling for Stars Grades: 9, 10 Mini-lesson	Mini-lesson	Functions	Students will use their knowledge of various functions to create pathways on a coordinate plane.		View
Visualizing Cross-sections in Primitive 3D Shapes Grades: 5, 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Geometry	Students will describe the two-dimensional figures that result from slicing three-dimensional figures.		View
Roller Coaster Boxplots Grades: 5, 6, 7, 8 Mini-lesson	Mini-lesson	Statistics	Students will construct boxplots and dotplots using roller coaster data.		View
Riemann Roller Coaster Grades: 7, 8, 9, 10 Mini-lesson	Mini-lesson	Calculus	Students will use Riemann sums to estimate board length of a roller coaster.		View
Polygraph: Inequalities on a Number Line Grades: 5, 6 Mini-lesson	Mini-lesson	Inequalities	Students will learn how to recognize inequalities on a number line and compare to domain inequalities. Use the following academic language: greater than, less than, equal to, integer, negative, positive. See how few questions can be asked per session.		View
Rad Angles Grades: 9, 10 Mini-lesson	Mini-lesson	Trigonometry	Students will compare radians, degrees, and angles. Academic language used: greater or less than, radians, degrees, angles.		View
Comparing Values in the Metric System Grades: 5, 6 Mini-lesson	Mini-lesson	Measurement	Students will compare length, mass, and liquid volume.		View
Functions in Nature Grades: 9, 10 Mini-lesson	Mini-lesson	Functions	Students will find function relationships in natural systems.		View
Woodcutter's Paradise Grades: 7, 8 Mini-lesson	Mini-lesson	Geometry	Students will use volume of cylinders to help support their firewood selling business.		View
Boxing the Cubes Grades: 7, 8 Mini-lesson	Mini-lesson	General	Students will develop volume equations and solve for unknown variables, while helping their boss get the job done.		View
Samara's Garden Grades: 7, 8, 9, 10 Mini-lesson	Mini-lesson	Geometry	Students will use circumference and knowledge of circles to calculate perimeter and area of complex shapes.		View