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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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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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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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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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Look High and Low
From the highest high to the lowest low here's a resource that won't fall flat. Given data on the area and the highest and lowest elevations of each of the 50 states, learners decide which states are the least flat and the most flat. Of...
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"Equal" Equations
Different equations, same solution. Scholars first find a system with equations y1 and y2 that have a given solution. They then find a different system with equations y3 and y4 that have the same solution. The ultimate goal is to...
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Isosceles Triangle Spaces
How many different types of triangles can your class name? A discovery lesson guides learners through an exploration of the different triangle types and the relationships between their angles and sides. Using coordinate geometry,...
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Intersections I
One, two, or zero solutions—quadratic systems have a variety of solution possibilities. Using the parent function and the standard form of the function, learners describe the values of a, b, and c that produce each solution type. They...
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Flying High
Some planes are just more efficient than others. Young mathematicians use data on the number of seats, airborne speed, flight length, fuel consumption, and operating cost for airplanes to analyze their efficiency. They select and use...
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Divisions
Divide and conquer the geometry problem. Young scholars consider how to subdivide triangles into smaller ones that have equal areas. They must apply their knowledge of medians to help accomplish the task.
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Last Digit Arithmetic
Mathematics involves a study of patterns. The exploratory lesson has learners consider the addition pattern in different sets of numbers. Each set has a different pattern that pupils describe mathematically. The patterns involve both...
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Intersections II
How many intersections can two absolute value functions have? Young scholars consider the question and then develop a set of rules that describe the number of solutions a given system will have. Using the parent function and the standard...
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Integer Solutions
Experiment with integer relationships. Young scholars consider integers that have a sum of 10. They begin with two integers, then three, four, and more. As they consider each situation, they discover patterns in the possible solutions.
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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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Center of Population
Let the resource take center stage in a lesson on population density. Scholars use provided historical data on the center of the US population to see how it shifted over time. They plot the data on a spreadsheet to look the speed of its...
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Sum and Product
From linear to quadratic with a simple operation. An exploratory lesson challenges learners to find two linear functions that, when multiplied, produce a given parabola. The task includes the graph of the sum of the functions as well as...
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Heights and Weights
Height is dependent on weight—or is it the other way around? Given data from a physicians handbook, individuals compare the height and weight of males and females at different areas. They calculate differences and ratios to assist with...
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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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Function Project
What if a coordinate plane becomes a slope-intercept plane? What does the graph of a linear function look like? Learners explore these questions by graphing the y-intercept of a linear equation as a function of its slope. The result is a...
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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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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 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 that...