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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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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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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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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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Bacteria Populations
Your young microbiologists will interpret and solve exponential equations in this real-world context task set in a hospital research scenario. Learners think in terms of the functions as well as their rates of change.
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Yam in the Oven
Your vegetable eaters will practice function notation statement interpretation in this short task. These few exercises will bring out misconceptions students may have about function notation as well.
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Cell Phones
Your texters will enjoy assessing their knowledge of function notation in this simple set of exercises. They will also interpret function notation in terms of the given context.
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Algae Blooms
Your microbiologists explore a changing algae population and build an exponential function modeling algae concentration from the description given of the relationship between concentrations in cells/ml and days of rapid growth.
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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 high schoolers 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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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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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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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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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...
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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...
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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, 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,...
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Carbon 14 Dating
Evaluating and analyzing exponential functions will help your archaeologists find the amount of Carbon 14 remaining in a plant in this real-life task centered on carbon dating. Learners will also be introduced to the concept of half-life.