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Calculator Numbers
Know thy calculator. Young mathematicians use their calculators to answer a set of questions. They consider how the number of digits the calculator displays affects the answers to calculations. They then find examples of computations...
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Catching Up
Class members have some catching up to do. Given a linear equation describing the distance of a runner, young mathematicians interpret the equation in terms of the context. They consider a general equation of the same form and describe...
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Bicycle Chain
Model a bicycle chain with circles and tangent lines. Given the dimensions of the sprocket wheels, young scholars calculate the length of the chain that surrounds them. A second task has learners write a function for the length of a...
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Boards I
Learners create patterns in a table to mimic the function of an electronic spreadsheet. The result is a table that creates an addition table for decimals in intervals of one-tenth. While creating the pattern, pupils must thoroughly...
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Broken Spreadsheet I
There is power in spreadsheet formulas and learners use this power to model quadratic data. Given a scatterplot of a parabola, pupils create formulas in a spreadsheet to populate the data. The formulas they use lead to an understanding...
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Spinning an Old Record
Take a trip back in time to examine angular velocity. Using the revolutions per minute, learners calculate the speed of a point on a 33 record. They compare the speed of a point on the edge of the record to the speed of a point closer to...
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Gravity
Weight is a function of the distance from sea level. Learners explore the many implications of this fact in an inquiry-based task. Given the function, pupils answer questions before manipulating the function to rewrite the distance...
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Bill the Ball Bearing Man
Just how durable could a hollow ball bearing be? Learners model the strength of the walls of a ball bearing as a function of the radius of its cavity. They use their models to make reasonable conclusions about the probability of failure...
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Boards II
Build spreadsheet skills while investigating decimal multiplication. An open-ended task asks learners to edit a spreadsheet to create a multiplication table for decimals. Provided with a specific interval, pupils create formulas...
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Boards III
Learn to visualize mathematical patterns as a folded pattern. Beginning with a visual display, the task encourages pupils to view sequences as a folded table. The pattern of the table then becomes a formula in a spreadsheet that...
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Boards IV
Build a connection between algebraic sequences and spreadsheets. Learners examine a specific folding pattern and convert the pattern into a spreadsheet. The goal of the spreadsheet is to produce a sequence of a specific pattern modeled...
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Broken Spreadsheet II
Work in reverse with the product becoming the given. Using a spreadsheet image of the graph of a trigonometric function, young scholars investigate methods of creating spreadsheet data that results in the given graph. The catch? The data...
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Circling Trains
And round and round the park we go! Given a description of an amusement park with the locations of three attractions connected by walkways, learners consider what happens when additional attractions join the mix by doubling the length of...
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Going Up
Going on up—and up and up! An open-ended task asks learners to model the movement of an amusement ride with parametric equations. They then analyze their equations to determine how the shadow of the ride's car moves as it rises at a...
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Graphical Depictions
Parent functions and their combinations create unique graphical designs. Learners explore these relationships with a progressive approach. Beginning with linear equations and inequalities and progressing to more complex functions,...
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Graphing Elements
How do you graph a sentence? Scholars do just that as they represent relationships between independent and dependent variables with a graphical representation. Given a sentence, they determine the pertinent relationship and create a...
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Here Comes the Sun
Many phenomena in life are periodic in nature. A task-based lesson asks scholars to explore one of these phenomena. They collect data showing the sunrise time of a specific location over the period of a year. Using the data, they create...
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Square-Ness
Are there some rectangles that are more square than others? A thought-provoking task asks individuals to create a formula that objectifies the square-ness of a set of rectangles. They then use their formulas to rank a set of...
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Gestation and Longevity
Is the gestation length of an animal a predictor of the average life expectancy of that animal? Learners analyze similar data for more than 50 different animals. They choose a data display and draw conclusions from their graphs.
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Functions by the Slice
Piece by piece ... dismantling a function can highlight interesting patterns. The task asks learners to slice functions in sections with the same vertical change. They then recreate the graph with these slices positioned horizontally....
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The Line and the Ellipse
What do a line and an ellipse have in common? Maybe zero, one, or two points! Learners consider the equation of an ellipse and a line to determine if their graphs have any shared points. They then write a system of equations, including...
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Systematic Solution II
Up the difficulty level by solving a system of equations with variable coefficients. Young scholars devise a plan to solve for x and y in terms of a and b. They represent their solutions as expressions and explain their...
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Systematic Solution I
Writing a general rule to model a specific pattern is a high-level skill. Your classes practice the important skill as they write rules describing the solutions to a system of equations with variable coefficients. As an added challenge,...
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Symbolic Similarity
How many things does one transformation tell you? Learners compare and contrast the graphs of different parent functions with the same transformation. Using a rational and absolute value function, pupils identify key features of their...
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