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Rectangulating
Use rectangles to find distances. Given a rectangle and three associated triangles, pupils determine the area of the triangles. Scholars know the three triangles have equal areas along with the perimeter of the rectangle and two other...
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Sine Solution
How many times can eager mathematicians catch the waves? Pupils find the solutions of three different trigonometric equations. They then determine the effect of the slope of a line that intersects a trigonometric function and the number...
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Sharp-Ness of Bends
Define the sharpest in the group. Given a section of a trail map, pupils determine a method to measure the sharpness of each turn in the path. Individuals then determine what modifications to their formulas to make to find the sharpness...
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Same Solution Equations
Group equations by their solutions. Given six different equations, pupils determine which have the same solutions. Scholars explain why some are the same and some are different.
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Petit Fours
Four 4s represent the counting numbers. Pupils attempt to write equivalent expressions to as many counting numbers as possible using only four 4s. Scholars then determine whether the same feat is possible using only three 3s.
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Rule of 72
Find an easier way to double it. Using the price of an item and the Consumer Price Index, learners determine how long it will be for the price to double. Scholars calculate the length of time it would take for the price to double using a...
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Rising Prices
What will that cost in the future? The scenario provides pupils with a growth as a Consumer Price Index. Learners create functions for a given item to determine future prices and graph them. Class members then compare their functions to...
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Quadratic Reflections
Reflect upon the graphs of quadratic functions. Given a quadratic function to graph, pupils determine whether the graph after a horizontal and vertical reflection is still a function. The final two questions ask scholars to describe a...
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Poly II
Create polynomials with specific values. The task consists of writing three polynomial functions that evaluate to specific values for any given number. Scholars first find a polynomial that evaluates to one for a given value, then a...
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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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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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People and Places
Graph growth in the US. Given population and area data for the United States for a period of 200 years, class members create graphs to interpret the growth over time. Graphs include population, area, population density, and population...
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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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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...
Didax
Pi Day #1a – Discovering Pi
Unravel the mystery behind the infamous number pi. Scholars complete a series of activities that explores where pi comes from, its digits and estimation strategies. Pupils should be ready to measure, calculate, and look for patterns to...
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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...