EngageNY
Matrix Addition Is Commutative
Explore properties of addition as they relate to matrices. Using graphical representations of vector matrices, scholars test the commutative and associative properties of addition. They determine if the properties are consistent for...
Curated OER
The Football and Braking Distance: Model Data with Quadratic Functions
Students engage in a lesson that is about the concept of data analysis with the use of quadratics. They use a Precalculus text in order to give guidance for independent practice and to serve as a source for the teacher to use. The data...
EngageNY
Estimating Probability Distributions Empirically 2
Develop probability distributions from simulations. Young mathematicians use simulations to collect data. They use the data to draw graphs of probability distributions for the random variable in question.
EngageNY
Inverses of Logarithmic and Exponential Functions
Revisit the relationship between logarithms and exponentials. Learners review the notion of logarithms as the way to solve exponential equations in the 21st segment in a Pre-calculus series of 23. Pupils use the knowledge to prove that...
EngageNY
The Binomial Theorem
Investigate patterns in the binomial theorem. Pupils begin by reviewing the coefficients from Pascal's triangle. They look at the individual terms, the sums of the coefficients on a row, and the alternating sum of each row. Individuals...
EngageNY
Volume and Cavalieri’s Principle
Take a slice out of life. The ninth section in a series of 23 introduces classmates to Cavalieri's principle using cross sections of a cone and stacks of coins. Class members participate in a discussion using pyramids and how Cavalieri's...
EngageNY
End Behavior of Rational Functions
Connect end behavior to previous learning. Pupils connect finding the end behavior of rational functions to finding end behavior of polynomial functions. The 13th segment in a 23-part unit starts with finding the end behavior or power...
EngageNY
Rational Functions
Make a connection between rational expressions and rational functions. Pupils review simplifying and performing operations on rational expressions and recall what it means for two rational expressions to be equivalent based on their...
EngageNY
Restricting the Domain
But what if the function cannot be inverted? Pupils continue to work with inverses of functions using tables, graphs, and algebraic equations. They restrict the domain of non-invertible functions to make them invertible. Using...
EngageNY
Solving Problems by Function Composition
Stay composed while solving problems. Learners put their knowledge of compositions to solve problems. To connect with the concept, scholars compose equations to answer questions from real-world situations. Finally, pupils practice using...
Curated OER
All Systems Go!
Secret codes are so much fun, and a great way to practice nearly any math skill. Let your class become code breakers as they investigate inverse matrices. They use TI-Nspire technology to solve systems of equations which help them crack...
Curated OER
Exponential Reflections
High Schoolers explore the concept of exponential reflections. They use their Ti-Nspire to reflect the natural logarithm function over the line y=x. Students repeat the process using different exponential functions using a slider.
Curated OER
Going Back to Your Roots
Investigate the Fundamental Theorem of Algebra and explore polynomial equations to determine the number of factors, the number of roots, and investigate multiplicity of roots.
Alabama Learning Exchange
Logarithms: Undo the Exponential
Rumor has it that an exponential can be undone. After playing a rumor game to model exponential growth, pupils learn about undoing exponential functions. They use the definition of the logarithm to convert exponential equations to...
Alabama Learning Exchange
Triangle Area: No Height? Use the Sine
No height? No problem! Learners use their knowledge and a little help from GeoGebra to develop the Law of Sines formula. The Law of Sines helps to determine the height of triangles to calculate the area.
Curated OER
NUMB3RS Activity: Chains and Pyramids
Watch an episode of the TV show, NUMB3RS and then explore the mathematics of chain letters and pyramid schemes, both of which involve geometric progressions and exponential growth. They discuss why both are dangerous and illegal.
Curated OER
Reflections
Learners explore reflection of polygons on a coordinate plane. They examine the relationships that exist between corresponding points and sides.
Curated OER
Rainbows, Bridges & Weather, Oh My!
Explore how real-world applications can be parabolic in nature and how to find quadratic functions that best fit data. A number of different examples of modeling parabolas are explored including a student scavenger hunt, the exploration...
Curated OER
Explore Graphs and Factors
Pupils graph the factors of a quadratic as linear equations and graph the parabolic equation in factored form. Also, they investigate the relationship between the x-intercepts of the lines and the zeros of the parabola.
Curated OER
Finite Differences
Young mathematicians solve problems with polynomials. As they graph and analyze polynomial functions, learners define constant and finite, and determine the relationship between the constant set of differences and the slope of a linear...
Curated OER
Reference Angles
Learn how to measure the reference angles in degrees and radians. High schoolers find reference angles that are coterminal with a given angle.
Curated OER
Complex Roots: A Graphical Solution
Using their Ti-Nspire to determine the solutions of parabolas, students explore the concept of complex roots. Students determine if parabolas have real or complex roots. Students determine the the axis of symmetry and the...
Curated OER
Local Linearity
In order to investigate local linearity, young scholars graph the function on the TI-calculator and zoom to observe the change in slope on the line. They incorporate technology to visualize these problems.
Curated OER
Natural Logarithm
Young mathematicians solve problems of logs and natural logs. They graph functions of natural logs on the TI and relate integrals to natural logarithms.