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Math Investigations and Mini-lessons

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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.
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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.
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Glacier Rates
Grades: 7, 8, 9
Mini-lesson
Mini-lesson Ratios Students will learn how to find rates with different base times.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Interactive Infographic
Grades: 5, 6, 7, 8, 9, 10
Investigation
Investigation General Students will learn develop an interactive infographic to teach a math concept.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Snowflake Modeling
Grades: 5, 6, 7, 8, 9, 10
Investigation
Investigation Nature Students will model snowflake formation using multiple media types.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Transforming Giraffes
Grades: 6, 7, 8
Mini-lesson
Mini-lesson Geometry Students will learn about eight types of coordinate transformations.
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Semi-Truck Division
Grades: 4, 5
Mini-lesson
Mini-lesson Numbers Students will learn how to divide fractions by filling an adjustable semi-truck.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Summation Square
Grades: 5, 6, 7, 8, 9, 10
Mini-lesson
Mini-lesson Numbers Students will construct rational fractions using a visual model.
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Tessellations
Grades: 5, 6, 7, 8, 9, 10
Mini-lesson
Mini-lesson Geometry Students will tesselate regular polygons into interesting patterns.
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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.
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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.
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QWERTY Coins
Grades: 5, 6
Mini-lesson
Mini-lesson Ratios Students will develop number sense while creating conversion ratios for various mystery coin currency.
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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.
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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.
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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.
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Roller Coaster Boxplots
Grades: 5, 6, 7, 8
Mini-lesson
Mini-lesson Statistics Students will construct boxplots and dotplots using roller coaster data.
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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.
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Tanagram - PowerPoint
Grades: 5, 6, 7, 8, 9, 10
Mini-lesson
Mini-lesson Architecture Students will persevere solving graphical tanagram puzzles.
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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.
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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.
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Comparing Values in the Metric System
Grades: 5, 6
Mini-lesson
Mini-lesson Measurement Students will compare length, mass, and liquid volume.
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Functions in Nature
Grades: 9, 10
Mini-lesson
Mini-lesson Functions Students will find function relationships in natural systems.
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Woodcutter's Paradise
Grades: 7, 8
Mini-lesson
Mini-lesson Geometry Students will use volume of cylinders to help support their firewood selling business.
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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.
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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.
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