EngageNY
How Do 3D Printers Work?
If we stack up all the cross sections of a figure, does it create the figure? Pupils make the connection between the complete set of cross sections and the solid. They then view videos in order to see how 3D printers use Cavalerie's...
EngageNY
Comparing Methods—Long Division, Again?
Remember long division from fifth grade? Use the same algorithm to divide polynomials. Learners develop a strategy for dividing polynomials using what they remember from dividing whole numbers.
EngageNY
Construct an Equilateral Triangle (part 1)
Drawing circles isn't the only thing compasses are good for. In this first installment of a 36-part series, high schoolers learn how to draw equilateral triangles by investigating real-world situations, such as finding the location of a...
EngageNY
Graphs of Exponential Functions and Logarithmic Functions
Graphing by hand does have its advantages. The 19th installment of a 35-part module prompts pupils to use skills from previous lessons to graph exponential and logarithmic functions. They reflect each function type over a diagonal line...
EngageNY
The Graph of the Natural Logarithm Function
If two is company and three's a crowd, then what's e? Scholars observe how changes in the base affect the graph of a logarithmic function. They then graph the natural logarithm function and learn that all logarithmic functions can be...
Inside Mathematics
Hopewell Geometry
The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...
Inside Mathematics
Graphs (2007)
Challenge the class to utilize their knowledge of linear and quadratic functions to determine the intersection of the parent quadratic graph and linear proportional graphs. Using the pattern for the solutions, individuals develop a...
EngageNY
An Application of Linear Equations
Just how far will the Facebook post go? Lead a discussion on how to manipulate the sum of a geometric series to figure out a formula to find the sum at any step. The plan contains an alternative to the discussion with more accessible...
EngageNY
Law of Cosines
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
EngageNY
First Consequences of FTS
Challenge the young mathematicians to find the exact coordinates of a dilated point. The fifth segment in a 16-part series introduces the class to the converse of the Fundamental Theorem of Similarity. Scholars use the theorem to find...
EngageNY
More About Similar Triangles
Determine whether two triangles are similar. The lesson presents opportunities for pupils to find the criterion needed to show that two triangles are similar. Scholars use the definition of similarity to find any missing side...
EngageNY
Numbers in Exponential Form Raised to a Power
Develop an understanding of the properties of exponents through this series of activities. This third lesson of 15 explores the patterns associated with the power property. Scholars expand the powers before applying the property.
EngageNY
The Computation of the Slope of a Non-Vertical Line
Determine the slope when the unit rate is difficult to see. The 17th part of a 33-part series presents a situation that calls for a method to calculate the slope for any two points. It provides examples when the slope is hard to...
EngageNY
Using Sample Data to Compare the Means of Two or More Populations II
The 23rd segment in a series of 25 presents random samples from two populations to determine whether there is a difference. Groups determine whether they believe there is a difference between the two populations and later use an...
EngageNY
Why Worry About Sampling Variability?
Are the means the same or not? Groups create samples from a bag of numbers and calculate the sample means. Using the sample means as an estimate for the population mean, scholars try to determine whether the difference is real or not.
EngageNY
Solving Problems by Finding Equivalent Ratios II
Changing ratios make for interesting problems. Pupils solve problems that involve ratios between two quantities that change. Groups use tape diagrams to represent and solve classroom exercises and share their solutions.
EngageNY
Solving Percent Problems III
What happens when combining percentage discounts? The last lesson in a series of 29 introduces the idea of combining discounts one after another. Pupils wrestle with the claim that to find the total discount, they need to only add the...
Baylor College
Post-Assessment: Global Atmospheric Change
Find out how much your earth scientists learned about the atmosphere in the unit on global atmospheric change with this assessment. After writing a letter to persuade others to make changes to protect our atmosphere, pupils take the same...
EngageNY
What Are Similarity Transformations, and Why Do We Need Them?
It's time for your young artists to shine! Learners examine images to determine possible similarity transformations. They then provide a sequence of transformations that map one image to the next, or give an explanation why it is not...
EngageNY
Using Trigonometry to Find Side Lengths of an Acute Triangle
Not all triangles are right! Pupils learn to tackle non-right triangles using the Law of Sines and Law of Cosines. After using the two laws, they then apply them to word problems.
EngageNY
The Distance from a Point to a Line
What is the fastest way to get from point A to line l? A straight perpendicular line! Learners use what they have learned in the previous lessons in this series and develop a formula for finding the shortest distance from a point to a...
EngageNY
Thales’ Theorem
Isn't paper pushing supposed to be boring? Learners attempt a paper-pushing puzzle to develop ideas about angles inscribed on a diameter of a circle. Learners then formalize Thales' theorem and use geometric properties to develop a proof...
EngageNY
Unknown Length and Area Problems
What is an annulus? Pupils first learn about how to create an annulus, then consider how to find the area of such shapes. They then complete a problem set on arc length and areas of sectors.
EngageNY
Adding and Subtracting Rational Expressions
There's a fine line between a numerator and a denominator! Learners find common denominators in order to add and subtract rational expressions. Examples include addition, subtraction, and complex fractions.