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Parameters and Clusters I
Chase the traveling solution. Pupils analyze the solutions to a system of linear equations as the parameter in one equation changes. Scholars then use graphs to illustrate their analyses.
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Painted Stage
Find the area as it slides. Pupils derive an equation to find the painted area of a section of a trapezoidal-shaped stage The section depends upon the sliding distance the edge of the painted section is from a vertex of the trapezoid....
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Outward Bound
Just how far can I see? The short assessment question uses the Pythagorean Theorem to find the distance to the horizon from a given altitude. Scholars use the relationship of a tangent segment and the radius of a circle to find the...
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Poly I
Root for young mathematicians learning about functions. A set of two problems assesses understanding of polynomial functions and their roots. Scholars select values for a, b, and c, and then create two functions that meet given...
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Full of Beans
Scholars have an opportunity to use their geometric modeling skills. Pupils determine a reasonable estimate of the number of string beans that would fill the average human body.
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Fermi Weight
Wait, there is an estimate for how much that weighs. The resource contains three questions about weight. Using dimensional analysis and benchmarks, pupils determine a reasonable weight for trash, food, and a grain of salt.
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Fermi Volume
It is about this big. An assessment provides three questions on the estimations of volume. Pupils determine the quantities needed and use dimensional analysis to arrive at estimations involving dollar bills, paint, and gasoline.
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Fermi Time
It's all just a matter of time. The resource provides four Fermi questions in reference to time. The questions are open-ended and require classmates to make use of estimation and dimensional analysis.
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Orthogonal Circles
Here's some very interesting circles for your very interested pupils. A performance task requires scholars to sketch a pair of orthogonal circles so the centers are the endpoints of one side of a triangle. They draw an additional circle...
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Looking through a Window
Here's a window into graphing calculators. Scholars use a graphing calculator to plot a quadratic function. They then adjust the window to make the graph look like that of a linear function and must recreate given graphs.
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Keeping Pace
What came first, pedestrian one or pedestrian two? Scholars consider a problem scenario in which two people walk at different rates at different times. They must decide who reaches a checkpoint first. Their answers are likely to surprise...
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Leap Years and Calendars
How many birthdays do leap year babies have in a lifetime? Learners explore the question among others in a lesson focused on different calendar systems. Given explanations of the Julian, Gregorian, and Martian calendars, individuals use...
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It's In the Mail
It's time to check the mail! The task is to determine the most cost-effective way to mail a packet of information. Young scholars write an equation that models the amount of postage as a function of the number of sheets mailed and...
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Other Road
Take the road to a greater knowledge of functions. Young mathematicians graph an absolute value function representing a road connecting several towns. Given a description, they identify the locations of the towns on the graph.
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On the Road to Zirbet
The road to a greater knowledge of functions lies in the informative resource. Young mathematicians first graph a square root function in a short performance task. They then use given descriptions of towns and the key features of the...
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Not So Identities
Don't compromise the identity. Given pairs of equations, scholars determine whether the equations are true for the same set of values. They explain their reasoning, considering whether it's possible to combine the equations into an...
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Mystery Dice
Dice aren't typically mysterious devices, but these dice are anything but typical. Scholars try to come up with dice that match given information on the relative frequency when they roll them a certain number of times. They must then...
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More or Less
How long can the cable get? A short performance task provides learners with information on the length of cables and the margin of error for each. They must determine the longest and shortest cable possible by splicing these cables.
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Mirror, Mirror I
How do you see yourself? Young mathematicians consider whether it's possible to view their whole bodies in a mirror with a length that is half their height. They write a letter to a friend explaining their positions mathematically.
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Metric Volume
Master metric measurements. Given the fact that the volume of one milliliter of water is one cubic centimeter, scholars figure out the volume of one liter of water. They must determine the correct unit of length for a unit cube that...
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Measuring the Unit Circle
Here's the right task to investigate right triangles in the unit circle. A short performance task has learners determine the product of two side lengths in a unit circle. They must apply similarity concepts and trigonometric ratios to...
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Maximum Volumes
It's great to have a large swimming pool. An interesting performance task asks learners to optimize the volume of pools for a given surface area. They consider four different shapes for pools and find the maximum volume for each pool.
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Maintain Your Composition
Compose yourself! Learners first use given graphs of functions f and g to graph the composition function f(g(x)) and identify its value for a specific input. They then consider functions for which f(g(x)) = g(f(x)).
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Losing Track
Don't lose the chance to use the task. Given three diagrams of curved pieces of wires, young mathematicians must explain whether it's possible to conclusively match the wires as representing cubic, exponential, or quadratic functions....