EngageNY
Solution Sets to Equations with Two Variables
Can an equation have an infinite number of solutions? Allow your class to discover the relationship between the input and output variables in a two-variable equation. Class members explore the concept through tables and graphs and...
EngageNY
Solution Sets to Inequalities with Two Variables
What better way to learn graphing inequalities than through discovering your own method! Class members use a discovery approach to finding solutions to inequalities by following steps that lead them through the process and even include...
EngageNY
Solution Sets to Simultaneous Equations (part 1)
How are systems related? Build on your pupils' previous knowledge of solving systems of equations by introducing systems of inequalities. Learners explore similarities between systems of equations and inequalities to make a strong...
Mathematics Vision Project
Module 4: Rational Functions
Time to study the most sensible function — rational functions! The seven-lesson unit develops the concept of a rational function through a connection to rational numbers and fractions. Scholars graph functions, solve equations, and...
Mathematics Vision Project
Module 7: Modeling with Functions
The sky's the limit of what you create when combining functions! The module begins with a review of transformations of parent functions and then moves to combining different function types using addition, subtraction, and multiplication....
Teach Engineering
Coordinates and the Cartesian Plane
The plot thickens to get a functional understanding. After a short review of plotting points on the coordinate plane, class members learn the difference between functions and relations in the second lesson in a series of nine. They show...
Teach Engineering
Forms of Linear Equations
Linear equations are all about form. The fifth part in a unit of nine works with the different equivalent forms of linear equations. Class members become familiar with each form by identifying key aspects, graphing, and converting from...
EngageNY
Equations Involving a Variable Expression in the Denominator
0/0 doesn't equal 0! Begin this instructional activity by allowing the class to explore the concept of dividing by zero. The introduction allows for discovery and provides meaningful examples of dividing by zero. This understanding leads...
EngageNY
Newton’s Law of Cooling
As part of an investigation of transformations of exponential functions, class members use Newton's Law of Cooling as an exponential model to determine temperature based on varying aspects. The resource makes comparisons between models...
EngageNY
Creating and Solving Quadratic Equations in One Variable
Give your classes practice at modeling using quadratic models with a resource that uses area and integer problems to allow individuals to create second degree polynomials. Young mathematicians solve equations using factoring and then...
EngageNY
Coordinates of Points in Space
Combine vectors and matrices to describe transformations in space. Class members create visual representations of the addition of ordered pairs to discover the resulting parallelogram. They also examine the graphical representation of...
EngageNY
Linear Transformations as Matrices
Don't stop with two-dimensional learning, go to the next dimension! Learners verify that 3x3 matrices represent linear transformations in the third dimension. Additionally, they verify the algebraic properties that extend to vector...
EngageNY
Composition of Linear Transformations 1
Learners discover that multiplying transformation matrices produces a composition of transformations. Using software, they map the transformations and relate their findings to the matrices.
EngageNY
Projecting a 3-D Object onto a 2-D Plane
Teach how graphic designers can use mathematics to represent three-dimensional movement on a two-dimensional television surface. Pupils use matrices, vectors, and transformations to model rotational movement. Their exploration involves...
EngageNY
Vectors and Translation Maps
Discover the connection between vectors and translations. Through the lesson, learners see the strong relationship between vectors, matrices, and translations. Their inquiries begin in the two-dimensional plane and then progress to the...
EngageNY
Vectors and Stone Bridges
What does it take to build a stable arch? Pupils apply vectors and physics as they examine arched bridges and their structural integrity. They use vectors to represent the forces acting on the stone sections and make conclusions based on...
EngageNY
Mid-Module Assessment Task: Pre-Calculus Module 2
Assess your classes' knowledge using questions that require high-level thinking and explanation. Learners use matrices to answer application questions. They also demonstrate their understanding of matrix operations.
Inside Mathematics
Aaron's Designs
Working with transformations allows the class to take a turn for the better. The short assessment has class members perform transformations on the coordinate plane. The translations, reflections, and rotations create pattern designs on...
EngageNY
End-of-Module Assessment Task - Geometry (module 1)
Have you hit a wall when trying to create performance task questions? Several open-ended response questions require a deep level of thinking. Topics include triangle congruence, quadrilaterals, special segments, constructions, and...
Federal Reserve Bank
Creating a Budget
Learning to create and maintain a budget is an important life skill. Guide individuals in the discovery of their spending habits and how to track them. They then use what they learned to create a budget and make decisions on where they...
Curriculum Corner
Guest Teacher Plans: Grade 6
Taking a day off of school can feel like a lot more work than going because of the time and effort that goes into making sub plans. Make your life easier with a daily plan for a guest teacher designed to meet the needs of sixth graders...
EngageNY
Completing the Square (part 1)
Avoid the trap of memorizing steps when completing the square with a resources that provides a conceptual approach to completing the square. Learners that are able to recognize a perfect square trinomial are ready to complete the square.
EngageNY
Deriving the Quadratic Formula
Where did that formula come from? Lead pupils on a journey through completing the square to discover the creation of the quadratic formula. Individuals use the quadratic formula to solve quadratic equations and compare the method to...
EngageNY
Congruence Criteria for Triangles—SAS
Looking for a different approach to triangle congruence criteria? Employ transformations to determine congruent triangles. Learners list the transformations required to map one triangle to the next. They learn to identify congruence if...
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