Teach Engineering
Can You Take the Pressure?
Do not let the pressure get to you. The first lesson in a unit of 22 introduces the concept of air pressure. Using background knowledge, the resource gives teachers the information they need to discuss how people measure air pressure and...
Teach Engineering
Future Flights: Imagine Your Own Flying Machines!
What will flying look like in the future? The 21st lesson in a 22-part unit on aviation reviews the major aspects of the lesson. Pupils brainstorm ideas of a future flying machine.
Teach Engineering
Properties of Mixtures vs. Solutions: Mix It Up!
Now it becomes crystal clear why the unit is called Mixtures and Solutions. The fifth installment of a six-part unit explores mixtures and solutions. After viewing a demonstration on mixing pebbles with water, salt with water, and...
EngageNY
Making Scale Drawings Using the Ratio Method
Is that drawn to scale? Capture the artistry of geometry using the ratio method to create dilations. Mathematicians use a center and ratio to create a scaled drawing. They then use a ruler and protractor to verify measurements.
EngageNY
How Do Dilations Map Lines, Rays, and Circles?
Applying a learned technique to a new type of problem is an important skill in mathematics. The lesson asks scholars to apply their understanding to analyze dilations of different figures. They make conjectures and conclusions to...
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...
EngageNY
Similarity
Learn similarity through a transformations lens! Individuals examine the effects of transformations and analyze the properties of similarity, and conclude that any image that can be created through transformations is similar. The...
EngageNY
The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
Playing with mathematics can invoke curiosity and excitement. As pupils construct triangles with given criteria, they determine the necessary requirements to support similarity. After determining the criteria, they practice...
EngageNY
Multiplying and Dividing Expressions with Radicals
That's radical! Simplifying radicals may not be exciting, but it is an important skill. A math lesson provides explanations of properties used throughout the material. Scholars practice skills needed to multiply and divide...
EngageNY
Adding and Subtracting Expressions with Radicals
I can multiply, so why can't I add these radicals? Mathematicians use the distributive property to explain addition of radical expressions. As they learn how to add radicals, they then apply that concept to find the perimeter of...
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
Definition and Properties of Volume
Lead a discussion on the similarities between the properties of area and the properties of volume. Using upper and lower approximations, pupils arrive at the formula for the volume of a general cylinder.
EngageNY
The Volume Formula of a Sphere
What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a...
EngageNY
Lines That Pass Through Regions
Good things happen when algebra and geometry get together! Continue the exploration of coordinate geometry in the third lesson in the series. Pupils explore linear equations and describe the points of intersection with a given polygon as...
EngageNY
Analytic Proofs of Theorems Previously Proved by Synthetic Means
Prove theorems through an analysis. Learners find the midpoint of each side of a triangle, draw the medians, and find the centroid. They then examine the location of the centroid on each median discovering there is a 1:2 relationship....
EngageNY
Overcoming Obstacles in Factoring
What do you do when factoring doesn't work? Learners complete the square when faced with quadratic expression that don't factor traditionally. They then use factoring by grouping to solve polynomial equations.
EngageNY
Structure in Graphs of Polynomial Functions
Don't allow those polynomial functions to misbehave! Understand the end behavior of a polynomial function based on the degree and leading coefficient. Learners examine the patterns of even and odd degree polynomials and apply them to...
EngageNY
A Focus on Square Roots
Pupils learn to solve square root equations and rationalize denominators. Problems include those with extraneous solutions.
EngageNY
Are All Parabolas Congruent?
Augment a unit on parabolas with an instructive math activity. Pupils graph parabolas by examining the relationship between the focus and directrix.
EngageNY
Complex Numbers as Solutions to Equations
Quadratic solutions come in all shapes and sizes, so help your classes find the right one! Learners use the quadratic formula to find solutions for quadratic equations. Solutions vary from one, two, and complex.
EngageNY
Secant and the Co-Functions
Turn your class upside down as they explore the reciprocal functions. Scholars use the unit circle to develop the definition of the secant and cosecant functions. They analyze the domain, range, and end behavior of each function.
EngageNY
Awkward! Who Chose the Number 360, Anyway?
Don't give your classes the third degree. Use radians instead! While working with degrees, learners find that they are not efficient and explore radians as an alternative. They convert between the two measures and use radians with the...
EngageNY
Transforming the Graph of the Sine Function
Build a solid understanding of trigonometric transformations through exploration. Learners work in teams to analyze the effects of different algebraic components on the graph of a sine function.
EngageNY
Calculating Probabilities of Events Using Two-Way Tables
Tables are useful for more than just eating. Learners use tables to organize data and calculate probabilities and conditional probabilities.