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US Households
Learners construct and use inverse functions to model a real-world context. They use the inverse function to interpolate a data point.
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A Valuable Quarter
Your young bankers model an account balance with an exponential function and solve the equation by extracting a root or taking a logarithm. The task involves the context of annual and compounding interest as well as some interesting...
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Skeleton Tower
Your algebra learners build a quadratic function in this task of counting the blocks used to build objects. The arithmetic sequence that shows up brings up a shortcut to the long addition using the Gauss Method. Eventually, learners...
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Model Air Plane Acrobatics
Your young airplane enthusiasts will enjoy this collaborative task of graphing an airplane's distance from the ground as it flies in a perfect circle. They will discover that they have graphed a sinusoidal function that comes from the...
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Latitude
Your young geologists generate a graph given a table of values from the context of latitude and percent of the earth's surface north of that latitude. The questions in the activity then focus the learners to a deeper understanding of the...
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Temperature Conversions
Your young weather buffs use compositions and inverses of functions to convert between Celsius, Fahrenheit, and Kelvin degrees. Then they analyze possible compositions and whether they exist in the real-life context.
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Susita's Account
Your algebra students double their money monthly in this task based on a checking account balance. Learners write an equation to model the situation and then use their model to answer contextual questions.
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Summer Intern
Your young apprentices build a function describing the percent concentration of salt in a brine. The rational function is then related to the parent function, y= 1/x, and graphed. Finally, the apprentices predict the amount of fresh...
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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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Seeing Dots
Your algebra learners interpret algebraic expressions, in order to compare their structures, using a geometric context. They also discern how the two expressions are equivalent and represent a pattern geometrically and algebraically.
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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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Fishing Adventures 3
Your young boaters will enjoy writing and solving inequalities, and representing the solution graphically in this task set in the context of renting a boat.
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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.
Illustrative Mathematics
Do Two Points Always Determine a Linear Function?
Your learners can approach this task algebraically, geometrically, or both. They analyze the building of a linear function given two points and expand the concrete approach to the abstract when they are asked to find the general form of...
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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...