This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
Students learn how to use wind energy to combat gravity and create …
Students learn how to use wind energy to combat gravity and create lift by creating their own tetrahedral kites capable of flying. They explore different tetrahedron kite designs, learning that the geometry of the tetrahedron shape lends itself well to kites and wings because of its advantageous strength-to-weight ratio. Then they design their own kites using drinking straws, string, lightweight paper/plastic and glue/tape. Student teams experience the full engineering design cycle as if they are aeronautical engineers—they determine the project constraints, research the problem, brainstorm ideas, select a promising design and build a prototype; then they test and redesign to achieve a successful flying kite. Pre/post quizzes and a worksheet are provided.
This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to: Select appropriate mathematical methods to use for an unstructured problem; interpret a problem situation, identifying constraints and variables, and specify assumptions; work with 2- and 3-dimensional shapes to solve a problem involving capacity and surface area; and communicate their reasoning clearly.
This is a math-science integrated unit about spectrographs. Learners will find and …
This is a math-science integrated unit about spectrographs. Learners will find and calculate the angle that light is transmitted through a holographic diffraction grating using trigonometry. After finding this angle, the students will build their own spectrographs in groups and research and design a ground or space-based mission using their creation. After the project is complete, student groups will present to the class on their trials, tribulations, and findings during this process. The activity is part of Project Spectra, a science and engineering program for middle-high school students, focusing on how light is used to explore the Solar System.
This course covers the design, construction, and testing of field robotic systems, …
This course covers the design, construction, and testing of field robotic systems, through team projects with each student responsible for a specific subsystem. Projects focus on electronics, instrumentation, and machine elements. Design for operation in uncertain conditions is a focus point, with ocean waves and marine structures as a central theme. Topics include basic statistics, linear systems, Fourier transforms, random processes, spectra, ethics in engineering practice, and extreme events with applications in design.
Students divide a parking lot into evenly spaced sections based on various …
Students divide a parking lot into evenly spaced sections based on various widths of the dividers. Students will generalize the experience to write equations to help evenly space any size parking lot with any size dividers and any number of dividers.
This interactive web tool and lesson helps students count large numbers of …
This interactive web tool and lesson helps students count large numbers of things by using the mathematical structures of area and proportionality. Students use a ratio table to keep track of their work as they count the number of tiles required to cover a floor, and the time required to put those tiles in place.
The activity is a two-part activity. The first part is a short …
The activity is a two-part activity. The first part is a short 2 minute video that goes through the four different types of slopes: positive, negative, undefined, and zero. The video discusses all four types and gives an example of a line.
The second part has students using this knowledge to identify different types of slopes of each letter of the alphabet.
The purpose of this task is to develop spatial structuring by showing …
The purpose of this task is to develop spatial structuring by showing the student that a rectangle can be partitioned into unit squares. I used it in addition to the "Partitioning a Rectangle into Unit Squares"https://www.illustrativemathematics.org/content-standards/tasks/2063, for those students who were not able to complete the first activity of drawing a grid on the rectangle by connecting each mark. On the rectangle worksheets you may need to scaffold through the rectangles, starting with placing unit tiles or squares on the rectangle. Then proceed through the rectangles scaffolding as needed.
In 2001, Budding Blooms Greenhouse was created and initiated for fourth-grade students …
In 2001, Budding Blooms Greenhouse was created and initiated for fourth-grade students between two elementary school teachers at Tower Rock Elementary School in Prairie du Sac. The purpose was to create hands-on activities that promote an understanding and respect for Wisconsin’s agriculture. The vision for ls project was three-fold: to-naturally integrate real-world learning in every part of the curriculum, to utilize the program as a mentorship opportunity, and to obtain district-wide involvement.
This lesson unit is intended to help you assess whether students recognize …
This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who: use inappropriate additive strategies in scaling problems, which have a multiplicative structure; rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems; and see multiplication as making numbers bigger, and division as making numbers smaller.
Students practice data collection by gathering data within the classroom on common …
Students practice data collection by gathering data within the classroom on common causes of allergies. They examine and interpret data charts on national trends in allergies.
This task supports students in correctly writing numbers. Because students have to …
This task supports students in correctly writing numbers. Because students have to trace the number, instead of coloring in a bubble with the number in it or circling the correct number, they gain handwriting practice as well as counting and addition practice.
This is the first semester of a two-semester sequence on Differential Analysis. …
This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods.
In this course, we study elliptic Partial Differential Equations (PDEs) with variable …
In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation. Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the Calderon-Zygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the non-linear Schrodinger equation. All through the course, we work on the craft of proving estimates.
This course is an introduction to differential geometry. The course itself is …
This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.
Spreadsheets Across the Curriculum module. Students analyze a given data set to …
Spreadsheets Across the Curriculum module. Students analyze a given data set to understand the "Digital Divide" by means of percentages and the Subtotal tool in Excel.
This task gives students the opportunity to verify that a dilation takes …
This task gives students the opportunity to verify that a dilation takes a line that does not pass through the center to a line parallel to the original line, and to verify that a dilation of a line segment (whether it passes through the center or not) is longer or shorter by the scale factor.
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