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: 76
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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
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
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
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
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
Cancel Me! Grades: 6, 7, 8 Mini-lesson	Mini-lesson	Expressions	Students will learn how to use of identity property of multiplication.		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
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
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
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
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
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
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
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
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
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
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
Tanagram - PowerPoint Grades: 5, 6, 7, 8, 9, 10 Mini-lesson	Mini-lesson	Architecture	Students will persevere solving graphical tanagram puzzles.		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
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
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
Fuel Efficiency Data Grades: 9, 10 Mini-lesson	Mini-lesson	Modeling	Students will learn how to fit a logistics model to automobile fuel efficiency data.		View
Guess My Number Grades: 5, 6 Mini-lesson	Mini-lesson	Expressions	Students will use mathematical language to talk about numbers.		View
Completing the Square Grades: 9, 10 Mini-lesson	Mini-lesson	Functions	Students will learn how to solve quadratic equations by completing the square graphically and algebraically.		View
Estimating Pi with Triangles Grades: 9, 10 Mini-lesson	Mini-lesson	Trigonometry	Students will learn how to estimate the value for the number pi using trigonometry.		View
Deciphering Math Vocabulary Grades: 5, 6 Mini-lesson	Mini-lesson	Word Problems	Students will compare math vocabulary and learn to convert word problems to expressions and equations.		View
Polygraph: Proportional and Non-Proportional Relationships Grades: 7, 8 Mini-lesson	Mini-lesson	Ratios	Students will engage in vocabulary-rich conversations about proportional and non-proportional relationships.		View
Polygraph: Expression and Equations Grades: 5, 6 Mini-lesson	Mini-lesson	Expressions	Students will engage in vocabulary-rich conversations about expressions and equations.		View
Using Functions in OpenSCAD Grades: 9, 10 Mini-lesson	Mini-lesson	Engineering	Students will incorporate functions into OpenSCAD engineering code.		View
Solving Quadratic Equations Using the Area Model Grades: 9, 10 Mini-lesson	Mini-lesson	Functions	Students will solve quadratic equations using the area model and plot solutions and equation on a graphing calculator.		View
Constructing and Calculating Volumes Grades: 5, 6 Mini-lesson	Mini-lesson	Coding	Students will construct complex rectangular prisms in OpenSCAD, then calculate their volumes.		View
Constructing Proportional Rectangular Prisms Grades: 7, 8 Mini-lesson	Mini-lesson	Coding	Students will construct proportional rectangular prisms in OpenSCAD and have other student calculate the scaling factor.		View
Elephant Mass Modeling Grades: 9, 10 Mini-lesson	Mini-lesson	Statistics	Students will learn about scatterplots, modeling nature through functions, and least-squares regression.		View
Best Kiwi Prices Around! Grades: 7, 8 Mini-lesson	Mini-lesson	Ratios	Students will compare prices by converting to unit rates.		View
Trigonometry Overview Grades: 9, 10 Mini-lesson	Mini-lesson	Trigonometry	Students will understand how right triangle ratios and the Pythagorean Theorem forms the basis for trigonometry and the unit circle.		View
Surface Area of Prisms Grades: 5, 6 https://www.math-aids.com Mini-lesson	Mini-lesson	Geometry	Students will practice finding surface area of various prisms.		View
Fraction Fluency Grades: 5, 6 Mini-lesson	Mini-lesson	Fractions	Students will work together on a whiteboard to demonstrate fraction equivalency.		View
Flexing with Linear Equations Grades: 9, 10 Mini-lesson	Mini-lesson	Linear Equations	Students will gain greater flexibility for finding solutions for two linear equations.		View
Algebra Transformers Grades: 7, 8 Mini-lesson	Mini-lesson	Equality	Students will learn to fluidly transform and manipulate algebraic equations.		View
Area of a Triangle Grades: 4, 5, 6 Mini-lesson	Mini-lesson	Geometry	Students will find area of right triangles and other triangles.		View
Area and Perimeter of Polygons (Pythagorean theorem) Grades: 7, 8 Mini-lesson	Mini-lesson	Geometry	Students will find area and perimeter of various polygons using the Pythagorean theorem.		View
Area and Perimeter of Polygons Grades: 5, 6 Mini-lesson	Mini-lesson	Geometry	Students will find area and perimeter of various polygons.		View
Calculating Area and Perimeter of Circle from a Triangle Grades: 7, 8 Mini-lesson	Mini-lesson	Geometry	Students will find area and perimeter of a circle using the Pythagorean Theorem.		View
Animating Using Variables Grades: 5, 6, 7, 8 Mini-lesson	Mini-lesson	Graphing	Students will learn how to add variables to ordered pairs to animate objects on the coordinate plane.		View
Exponents: Integer and Rational Grades: 9, 10 Mini-lesson	Mini-lesson	General	Students will review the properties of radical and integer exponents.		View
Expression Review for 7th and 8th Grades Grades: 7, 8 Mini-lesson	Mini-lesson	General	Students will understand how to simplify algebraic expressions.		View
Expression Review for 5th and 6th Grades Grades: 5, 6 Mini-lesson	Mini-lesson	General	Students will understand how to simplify basic expressions.		View
Create Simple Topological Puzzles (Mazes) Grades: 5, 6 Mini-lesson	Mini-lesson	Puzzles and Games	Students will learn how to collaborate with mathematics .		View