Students see that geometric shapes can be found in all sorts of …
Students see that geometric shapes can be found in all sorts of structures as they explore the history of the Roman Empire with a focus on how engineers 2000 years ago laid the groundwork for many structures seen today. Through a short online video, brief lecture material and their own online research directed by worksheet questions, students discover how the Romans invented a structure known today as the Roman arch that enabled them to build architecture never before seen by humankind, including the amazing aqueducts. Students calculate the slope and its total drop and angle over its entire distance for an example aqueduct. Completing this lesson prepares students for the associated activity in which teams build and test model aqueducts that meet specific constraints. This lesson serves as an introduction to many other geometry—and engineering-related lessons—including statics and trusses, scale modeling, and trigonometry.
This course focuses on an in-depth reading of Principia Mathematica Philosophiae Naturalis …
This course focuses on an in-depth reading of Principia Mathematica Philosophiae Naturalis by Isaac Newton, as well as several related commentaries and historical philosophical texts.
Students investigate how old the universe is and when important events took …
Students investigate how old the universe is and when important events took place in the universe and on Earth. They draw the universe timeline from the beginning until today on the scale of a year.
This course covers the same material as Differential Equations (18.03) with more …
This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems.
Students teams determine the size of the caverns necessary to house the …
Students teams determine the size of the caverns necessary to house the population of the state of Alabraska from the impending asteroid impact. They measure their classroom to determine area and volume, determine how many people the space could sleep, and scale this number up to accommodate all Alabraskans. They work through problems on a worksheet and perform math conversions between feet/meters and miles/kilometers.
Students learn about geotechnical engineers and their use of physical properties, such …
Students learn about geotechnical engineers and their use of physical properties, such as soil density, to determine the ability of various soils to offer support to foundations. In an associated activity, students determine the bulk densities of soil samples, and assess their suitability to support foundations.
Students determine the mass and volume of soil samples and calculate the …
Students determine the mass and volume of soil samples and calculate the density of the soils. They use this information to determine the suitability of the soil to support a building foundation.
Students learn that it is incorrect to believe that heavier objects fall …
Students learn that it is incorrect to believe that heavier objects fall faster than lighter objects. By close observation of falling objects, they see that it is the amount of air resistance, not the weight of an object, which determines how quickly an object falls.
This task is designed as an assessment item. It requires students to …
This task is designed as an assessment item. It requires students to use information in a two-way table to calculate a probability and a conditional probability. Although the item is written in multiple choice format, the answer choices could be omitted to create a short-answer task.
While learning about volcanoes, magma and lava flows, students learn about the …
While learning about volcanoes, magma and lava flows, students learn about the properties of liquid movement, coming to understand viscosity and other factors that increase and decrease liquid flow. They also learn about lava composition and its risk to human settlements.
Students practice their multiplication skills using robots with wheels built from LEGO® …
Students practice their multiplication skills using robots with wheels built from LEGO® MINDSTORMS® NXT kits. They brainstorm distance travelled by the robots without physically measuring distance and then apply their math skills to correctly calculate the distance and compare their guesses with physical measurements. Through this activity, students estimate parameters other than by physically measuring them, practice multiplication, develop measuring skills, and use their creativity to come up with successful solutions.
Students measure the permeability of different types of soils, compare results and …
Students measure the permeability of different types of soils, compare results and realize the importance of size, voids and density in permeability response.
In this activity using a balance scale students practice weighing items to …
In this activity using a balance scale students practice weighing items to see how heavy they are. Cubes are used in the balance as units of measure so students may easily count them.
Students work in pairs to measure length by lining up cubes along …
Students work in pairs to measure length by lining up cubes along the longest side of an item. They count and record length by counting the number of cubes.
This task uses student generated data to assess standard 7.SP.7. This task …
This task uses student generated data to assess standard 7.SP.7. This task could also be extended to address Standard 7.SP.1 by adding a small or whole class discussion of whether the class could be considered as a representative sample of all students at your school.
The purpose of this task is for students to apply the concepts …
The purpose of this task is for students to apply the concepts of mass, volume, and density in a real-world context. There are several ways one might approach the problem, e.g., by estimating the volume of a person and dividing by the volume of a cell.
These two fraction division tasks use the same context and ask ŇHow …
These two fraction division tasks use the same context and ask ŇHow much in one group?Ó but require students to divide the fractions in the opposite order. Students struggle to understand which order one should divide in a fraction division context, and these two tasks give them an opportunity to think carefully about the meaning of fraction division.
This task gives children an opportunity to subtract a three-digit number including …
This task gives children an opportunity to subtract a three-digit number including a zero that requires regrouping. The solutions show how students can solve this problem before they have learned the traditional algorithm.
This is a mathematical modeling task aimed at making a reasonable estimate …
This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.
In this problem, the variables a,b,c, and d are introduced to represent …
In this problem, the variables a,b,c, and d are introduced to represent important quantities for this esimate: students should all understand where the formula in the solution for the number of leaves comes from. Estimating the values of these variables is much trickier and the teacher should expect and allow a wide range of variation here.
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