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In the Billions and Linear Modeling
Your learners analyze population data to discern if it best fits a linear scenario. The idea of change by equal differences over equal intervals is enforced in this real-life task.
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In the Billions and Exponential Modeling
Modeling population growth gives learners an opportunity to experiment with real data. Comparing the growth rates in this real-life task strengthens learners' understanding that exponential functions change by equal factors over equal...
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Interesting Interest Rates
Your young bankers compare earning interest accumulated yearly and monthly to decide which method most increases their balance. Using an exponential function to model the bank balance affords the learners more practice connecting these...
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Exponential Growth Versus Linear Growth I
Your algebra learners will discover how quickly an exponential function value grows compared to a linear function's value. Making a table of values helps in this comparison, set in the context of making a wage for raking leaves.
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Illegal Fish
Your young fishermen learn about exponential function growth by interpreting the pieces of the given equation within the context of numbers of fish in a lake.
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Linear Functions
Your learners will explore linear functions by analyzing a graph of the linear equations.Then learners analyze through calculating f(x+P) and g(x+p)
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Exponential Functions
Your algebra learners analyze and interpret the general form and the graph of two functions. The increase of the function due to the multiplicative factor is emphasized.
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Exponential Growth versus Polynomial Growth
Your algebra learners explore the values of two types of functions in order to compare growth rates in this short cooperative task. Two types of solutions are given, using a table of values and an abstract argument.
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Exponential Growth versus Linear Growth II
Your algebra learners discover that exponential functions, with a base larger than one, outgrow linear functions when the inputs increase sufficiently. Their analysis includes using a graphing calculator to produce tables.
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A Saturating Exponential
Your learners analyze the familiar model of a cold beverage warming when it is taken out of the refrigerator. The general form of the equation and its graph are presented. Learners learn about the specific pieces of the function by...
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Linear or Exponential?
Your learners analyze various real-life contexts to decide if each is a linear or exponential model. This could be used as an assessment of learners' skills of discerning between a linear and an exponential model.
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Sandia Aerial Tram
Your learners analyze a table of real-life data in order to write an equation that best models the information. Exponential, quadratic, and linear rates of changes are all possibilities in this task.
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Snail Invasion
Exponential growth is modeled by learners as they analyze and interpret the data presented in this real-life scenario centered on the destructive invasion of the Giant African Land Snail. Learners get a touch of history and practice...
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Rumors
Your young gossipers write an exponential function for the number of people who have heard a rumor after a number of days have passed. Learners then answer a series of questions, including whether or not the solutions are realistic by...
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Newton's Law of Cooling
Your Algebra learners analyze and solve an exponential equation in this popular, real-life model of the cooling of a liquid.
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What Functions do Two Graph Points Determine?
Your algebra learners write linear, exponential, and quadratic equations containing the same two graph points in this collaborative task.
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Taxi!
Your young taxi drivers evaluate and articulate the reasoning behind statements in a conceptual task involving linear data. The given data table of distances traveled and the resulting fare in dollars is used by learners to explore...
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US Population 1790-1860
Your young population scientists analyze a table of values, write a model to represent the real life data, finish the table of data and predict future populations in a collaborative, real-life activity.
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US Population 1982-1988
Your algebra learners make predictions using the concepts of a linear model from real-life data given in table form. Learners analyze and discuss solutions without having to write a linear equation.
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Reflections and Equilateral Triangles
Your learners collaboratively find the lines of symmetry in an equilateral triangle using rigid transformations and symmetry. Through congruence proofs they show that they understand congruence in terms of rigid motions as they prove...
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Reflections and Equilateral Triangles II
Given the lines of symmetry in an equilateral triangle, your learners find where the pre-image vertices are mapped onto the new image. They explore the properties of equilateral triangles, the impact of reflections, and the idea that the...
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Why Does ASA Work?
Your geometry learners explore Angle-Side-Angle congruence in this collaborative task. The sum of the interior angles of all triangles being one hundred eighty degrees, is the key learners will discover as they explain their reasoning...
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When Does SSA Work to Determine Triangle Congruence?
Your learners will make good use of the Socratic method in a collaborative task that begins with an assumed solution and ends with deeper understanding of the idea of determining two triangles congruent.
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Symmetries of Rectangles
Learners explore mapping a rectangle onto itself using rigid motion concepts, geometric intuition and experimenting with manipulatives in a collaborative task.
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