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...
EngageNY
Choosing a Model
There's a function for that! Scholars examine real-world situations to determine which type of function would best model the data in the 23rd installment of a 35-part module. It involves considering the nature of the data in addition to...
EngageNY
Bean Counting
Why do I have to do bean counting if I'm not going to become an accountant? The 24th installment of a 35-part module has the class conducting experiments using beans to collect data. Learners use exponential functions to model this...
EngageNY
Modeling with Exponential Functions
These aren't models made of clay. Young mathematicians model given population data using exponential functions. They consider different models and choose the best one.
EngageNY
Newton’s Law of Cooling, Revisited
Does Newton's Law of Cooling have anything to do with apples? Scholars apply Newton's Law of Cooling to solve problems in the 29th installment of a 35-part module. Now that they have knowledge of logarithms, they can determine the decay...
EngageNY
Exploiting the Connection to Trigonometry 1
Class members use the powers of multiplication in the 19th installment of the 32-part unit has individuals to utilize what they know about the multiplication of complex numbers to calculate the integral powers of a complex number. Groups...
EngageNY
Exploiting the Connection to Trigonometry 2
The class checks to see if the formula for finding powers of a complex number works to find the roots too. Pupils review the previous day's work and graph on the polar grid. The discussion leads the class to think about how to reverse...
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
Graphing Cubic, Square Root, and Cube Root Functions
Is there a relationship between powers and roots? Here is a lesson that asks individuals to examine the graphical relationship. Pupils create a table of values and then graph a square root and quadratic equation. They repeat the process...
EngageNY
Representing, Naming, and Evaluating Functions (Part 2)
Notation in mathematics can be intimidating. Use this activity to expose pupils to the various ways of representing a function and the accompanying notation. The material also addresses the importance of including a domain if necessary....
University of Nottingham
Modeling Conditional Probabilities: 2
Bring the concept of conditional probability alive by allowing your classes to explore different probability scenarios. Many tasks have multiple solutions that encourage students to continue exploring their problems even after a solution...
EngageNY
Special Triangles and the Unit Circle
Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value of...
EngageNY
Formal Definition of a Function
Formalize the notion of a function. Scholars continue their exploration of functions in the second lesson plan of the module. They consider functions as input-output machines and develop function rules for selected functions.
EngageNY
Waves, Sinusoids, and Identities
What is the net effect when two waves interfere with each other? The lesson plan answers this question by helping the class visualize waves through graphing. Pupils graph individual waves and determine the effect of the interference...
EngageNY
Exponential Notation
Exponentially increase your pupils' understanding of exponents with an activity that asks them to explore the meaning of exponential notation. Scholars learn how to use exponential notation and understand its necessity. They use negative...
EngageNY
Magnitude
Build an understanding of the powers of 10. Pupils investigate the results of raising 10 to positive and negative powers. They relate this understanding to the magnitude these powers represent in this seventh lesson of 15.
EngageNY
Operations with Numbers in Scientific Notation
Demonstrate the use of scientific notation within word problems. The lesson presents problems with large numbers best represented with scientific notation. Pupils use these numbers to solve the problems in the 11th installment in a...
EngageNY
Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology
Examine numbers in scientific notation as a comparison of size. The 14th lesson in the series asks learners to rewrite numbers as the same power of 10 in scientific notation to make comparisons. Pupils also learn how to use a calculator...
EngageNY
Solving a Linear Equation
Solving an equation is the art of creating simpler equivalent equations using properties of equality. Here, classes see that solving an equation is not always as easy as guessing. The lesson plan presents linear equations that scholars...
EngageNY
Using Linear Models in a Data Context
Practice using linear models to answer a question of interest. The 12th installment of a 16-part module combines many of the skills from previous lessons. It has scholars draw scatter plots and trend lines, develop linear models, and...
EngageNY
The Pythagorean Theorem
Class members explore the estimation of irrational numbers in association with the Pythagorean Theorem. The first instructional activity of this module challenges pupils to use the Pythagorean Theorem to find unknown side lengths. When...
Mathematics Assessment Project
Modeling Motion: Rolling Cups
Connect the size of a rolling cup to the size of circle it makes. Pupils view videos of cups of different sizes rolling in a circle. Using the videos and additional data, they attempt to determine a relationship between cup measurements...
Illustrative Mathematics
Latitude
The greater the latitude, the less of the Earth is north. Scholars graph the relationship between the latitude and the percentage of the Earth that is north of the latitude. Using the graph and the table, class members interpret values...
Illustrative Mathematics
Households
Use an inverse linear function to interpolate a point. Presented with the number of households over a period of year, pupils find a linear function that will be a model. Class members determine the inverse of the linear function and use...