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EngageNY
The Mean as a Balance Point
It's a balancing act! Pupils balance pennies on a ruler to create a physical representation of a dot plot. The scholars then find the distances of the data points from the balance point, the mean.
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Relationships Between Two Numerical Variables
Is there another way to view whether the data is linear or not? Class members work alone and in pairs to create scatter plots in order to determine whether there is a linear pattern or not. The exit ticket provides a quick way to...
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Summarizing Bivariate Categorical Data with Relative Frequencies
It is hard to determine whether there is a relationship with the categorical data, because the numbers are so different. Working with a familiar two-way table on super powers, the class determines relative frequencies for each...
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Analyzing Data Collected on Two Variables
Assign an interactive poster activity to assess your class's knowledge and skill concerning data analysis. The teacher reference provides solid questions to ask individuals or groups as they complete their posters.
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The Special Role of Zero in Factoring
Use everything you know about quadratic equations to solve polynomial equations! Learners apply the Zero Product Property to factor and solve polynomial equations. They make a direct connection to methods they have used with quadratic...
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Word Problems Leading to Rational Equations
Show learners how to apply rational equations to the real world. Learners solve problems such as those involving averages and dilution. They write equations to model the situation and then solve them to answer the question —...
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A Focus on Square Roots
Pupils learn to solve square root equations and rationalize denominators. Problems include those with extraneous solutions.
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Linear Systems in Three Variables
Put all that algebra learning to use! Using algebraic strategies, learners solve three-variable systems. They then use the three-variable systems to write a quadratic equation given three points on the parabola.
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Overcoming a Third Obstacle to Factoring— What If There Are No Real Number Solutions?
Time for pupils to use their imagination! Learners examine the relationship between a system with no real solution and its graph. They then verify their discoveries with algebra.
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Graphing the Sine and Cosine Functions
Doing is more effective than watching. Learners use spaghetti to discover the relationship between the unit circle and the graph of the sine and cosine functions. As they measure lengths on the unit circle and transfer them to a...
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Calculating Conditional Probabilities and Evaluating Independence Using Two-Way Tables (part 1)
Being a statistician means never having to say you're certain! Learners develop two-way frequency tables and calculate conditional and independent probabilities. They understand probability as a method of making a prediction.
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Calculating Conditional Probabilities and Evaluating Independence Using Two-Way Tables (part 2)
Without data, all you are is another person with an opinion. Show learners the power of statistics and probability in making conclusions and predictions. Using two-way frequency tables, learners determine independence by analyzing...
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Sampling Variability in the Sample Proportion (part 1)
Increase your sample and increase your accuracy! Scholars complete an activity that compares sample size to variability in results. Learners realize that the greater the sample size, the smaller the range in the distribution of sample...
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Sampling Variability in the Sample Mean (part 2)
Reduce variability for more accurate statistics. Through simulation, learners examine sample data and calculate a sample mean. They understand that increasing the number of samples creates results that are more representative of the...
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Ruling Out Chance (part 3)
Pupils analyze group data to identify significant differences. They use simulation to create their own random assignment data for comparison.
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Solving Logarithmic Equations
Of course you're going to be solving an equation—it's algebra class after all. The 14th installment of a 35-part module first has pupils converting logarithmic equations into equivalent exponential equations. The conversion allows for...
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Rational and Irrational Numbers
Back to the basics: learning how to add numbers. The 17th installment of a 35-part module first reviews addition techniques for rational numbers, such as graphical methods (number line) and numerical methods (standard algorithm). It goes...
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The Mathematics Behind a Structured Savings Plan
Make your money work for you. Future economists learn how to apply sigma notation and how to calculate the sum of a finite geometric series. The skill is essential in determining the future value of a structured savings plan with...
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Buying a Car
Future car owners use geometric sums to calculate payments for a car loan in the 31st installment of a 35-part module. These same concepts provide the basis for calculating annuity payments.
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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...
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Directed Line Segments and Vectors
Investigate the components of vectors and vector addition through geometric representations. Pupils learn the parallelogram rule for adding vectors and demonstrate their understanding graphically. They utilize the correct notation and...
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The Graph of a Function
Mathematics set notation can be represented through a computer program loop. Making the connection to a computer program loop helps pupils see the process that set notation describes. The activity allows for different types domain and...
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Making Fair Decisions
Life's not fair, but decisions can be. The 17th installment of a 21-part module teaches learners about fair decisions. They use simulations to develop strategies to make fair decisions.
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Fair Games
What constitutes a fair game? Scholars learn about fair games and analyze some to see if they are fair. They extend this idea to warranties and other contexts.