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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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 Grades: 5, 6 Mini-lesson	Mini-lesson	Geometry	Students will find area and perimeter of various polygons.		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
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
Exponents: Integer and Rational Grades: 9, 10 Mini-lesson	Mini-lesson	General	Students will review the properties of radical and integer exponents.		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
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