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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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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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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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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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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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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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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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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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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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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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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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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.
Describing Egypt
Sennedjem - (19th Dynasty)
Who was Sennedjem and how does he relate to ancient Egypt? The resource describes the artisan's life as well as the village in which he lived, called Set Ma'at. Learners view where the people who built the tombs for powerful Egyptians...
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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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Proportional Representation
Sometimes the solution is all a matter of perspective. The short assessment task presents a problem to pupils that requires them to make sense of a diagram. Once learners see two similar triangles, the rest of the solution is solving a...
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Perfect Ten
How many ways can you make 10? Class members tackle three problems to find all possible ways three numbers add to be 10. The first is with positive integers, secondly with non-negative integers, and finally with real numbers. Pupils also...
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Parameters and Clusters II
Let's give parameters a second try. Scholars take a second look at a system of linear equations that involve a parameter. Using their knowledge of solutions of systems of linear equations, learners describe the solution to the system as...
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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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Rational and Not So Rational Functions
Do not cross the line while graphing. Provided with several coordinate axes along with asymptotes, pupils determine two functions that will fit the given restrictions. Scholars then determine other geometrical relationships of asymptotes...
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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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