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The Canoe Trip, Variation 2
The behavior of a rational function near a vertical asymptote is the focus around this trip up a river. Specifically, numerical and graphical understanding is studied. The canoe context pushes the variables as numbers, rather than as...
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The Canoe Trip, Variation 1
Your river sportsmen will explore an example of paddling upstream as they build functions modeling speed and time in terms of the speed of the current. They then use their algebraic models to interpret features of the function related to...
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Compounding with a 5% Interest Rate
The balance in an account continuously compounding interest is the context of this engaging task. Your young accountants will investigate the ending balance in an account as they compound the interest more and more. Learners write the...
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Triangle Series
Your algebra learners emphasize the"geometric" in geometric series as they use a common ratio between algebraic terms and find that it corresponds to a repeated similarity transformation.
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Sum of Even and Odd
Your algebra learners will make use of structure and manipulate expressions involving function notation using the definition of odd and even functions. They then advance even further to analyze the structure in a system of two equations.
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Quadrupling Leads of Halving
Your statisticians will see that an expression is made up of one or more parts that can be seen as a single entity. Learners give an explanation, in terms of the structure. of the expression and, why it halves in value when n is quadrupled.
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Profit of a Company
Your business executives choose which of three equivalent forms of a quadratic equation is the most useful for finding various pieces of information in this task centered on a company's profits.
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Throwing Horseshoes
Collaborative learners interpret a quadratic expression written in different forms in this task centered on throwing horseshoes.
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Doubling Your Money
Your young financial geniuses explore the Rule of 70 as they analyze the exponential function that models the doubling time of investments.
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Two Points Determine an Exponential Function II
Your algebra learners will build an exponential equation given a graph with two specific points labeled.
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Do Two Points Always Determine an Exponential Function?
Algebra learners explore, analyze and build an exponential equation given its form and a specific point that exists on the function in this task. The last question asks learners to apply their ideas to an exponential equation given two...
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Two Points Determine an Exponential Function I
Learners construct an exponential function from a graph, and two given points on the graph, as they analyze what makes up an exponential function.
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Comparing Exponentials
Growing money exponentially is the context of this scenario that asks learners to compare investments in two certificate of deposit accounts. Your young investment analysts will learn about the exponential characteristics of money...
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Basketball Rebounds
Your young basketball players will build a table and develop a general formula for a decaying exponential scenario involving the rebound distance of a bouncing ball. Using a CBR and graphing calculator can make this even more hands-on...
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Building a General Quadratic Function
Learners rewrite a general quadratic function by completing the square to see a new form of the function that more easily identifies the x-coordinate of the vertex and the two roots of the function.
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Taxes and Sales
Collaborative discussions around this retail store problem will be taxing. Calculating discount and tax and the order of the operations are used to motivate an opportunity for learners to make a convincing argument using algebraic...
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Building a Quadratic Function Form
Comparing the movement of graphs geometrically when small changes are made to the parent function motivates this collaborative discussion on the transformations of functions to their various forms. Vertical and horizontal shifts due to...
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Forms of Exponential Expressions
Your young physicists analyze the forms of four equivalent exponential expressions representing an amount of a radioactive material in a substance. They show how each expression is equivalent to the others and what aspects of the decay...
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Mixing Fertilizer
Your young landscapers do concentration calculations in this problem dealing with mixing fertilizer. Learners use and analyze rational expressions within this context.
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Equal Differences Over Equal Intervals 2
Your algebra learners explore linear functions concretely using tables of values in a collaborative task. The idea that linear function values change by equal differences over equal intervals, is emphasized. The slope and y-intercept...
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Equal Differences Over Equal Intervals 1
Learners explore linear functions concretely using tables of values in a cooperative task. The concept of the values of linear functions changing by equal differences over equal intervals of one is emphasized. Learners will discover the...
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Equal Factors Over Equal Intervals
Exponential functions and their growth rates are explored concretely using tables in a collaborative task. Then the successive quotient is explored algebraically.
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Carbon 14 Dating in Practice II
Your archaeologists combine proportional reasoning with exponential functions in a real-life task centered on Carbon 14 dating.
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Carbon 14 Dating, Variation 2
Your archaeologists begin this task with a table of values to estimate the time passed based on the half-life of Carbon 14 remaining in a plant. They then move on to find when a specific amount of Carbon 14 is present in the same plant,...