The famous story of Archimedes running through the streets of Syracuse (in Sicily during the third century bc) shouting ''Eureka!!!'' (I have found it) reportedly occurred after he solved this problem. The problem combines the ideas of ratio and proportion within the context of density of matter.

This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.

Create your own shapes using colorful blocks and explore the relationship between perimeter and area. Compare the area and perimeter of two shapes side-by-side. Challenge yourself in the game screen to build shapes or find the area of funky figures. Try to collect lots of stars!

Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams.
Find the value of the question marks in the diagrams. All of the shapes are rectangles but are not drawn to scale.

Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the game screen to test your multiplication and factoring skills!

This is a lesson for learning about area and perimeter of rectangles.

This corresponds to "College and Career Ready" standard (3.MD.7a) -- Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
(I was not able to find that standard here.)

This is a hands-on guided lesson for relating area to factors. Students will model area of rectangles using Cheez-Its and define factors as the dimensions of the rectangles.

Overview: Math in Real Life (MiRL) supports the expansion of regional networks to create an environment of innovation in math teaching and learning.  The focus on applied mathematics supports the natural interconnectedness of math to other disciplines while infusing relevance for students.  MiRL supports a limited number of networked math learning communities that focus on developing and testing applied problems in mathematics.  The networks help math teachers refine innovative teaching strategies with the guidance of regional partners and the Oregon Department of Education.

The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

Remember your multiplication tables? ... me neither. Brush up on your multiplication, division, and factoring skills with this exciting game. No calculators allowed! The students will be given mutiplication and division problems which they must answer. They also have the option of being given a number then stating the factors of how that number was attained using either multiplication or division.

The resource leads to an interactive website where students can learn and practice arithmetic essentials. Currently these are Mean and Median, Exponents, Square Roots and Arithmetic Sequences. I hope to be expanding the website as time allows.

This arithmetic lesson demonstrates more long division problems with remainders.[Arithmetic playlist: Lesson 26 of 38]

Brush up on your multiplication, division, and factoring skills with this interactive multiplication chart. Three levels and timed or untimed options are available.

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

The Assessment of Authentic Learning Rubric focuses on the areas of agency and authenticity, concepts derived from the Student as Producer and Social Pedagogies frameworks. The rubric consists of five areas: learning tasks, learning process, social core, learning assessments, and lifelong learning. Each of the five areas contains statements that course designers can use to evaluate their course/s. Instructors may elect to use the rubric as a self-evaluation tool or might elect to work through it with support from an instructional designer. The rubric can be used for course taught in a variety of modalities including online, hybrid, and face-to-face.

Educators and parents can use the Washington Starting Smarter site to better understand the scores and reports for the Smarter Balanced tests, see sample items, and access additional resources.All resources on the site are copyright The Regents of the University of California.  Though the connected resources are free for viewing online, please note that your permitted use of the materials for other uses will vary. Image by StartupStockPhotos from Pixabay  

Students design and develop a useful assistive device for people challenged by fine motor skill development who cannot grasp and control objects. In the process of designing prototype devices, they learn about the engineering design process and how to use it to solve problems. After an introduction about the effects of disabilities and the importance of hand and finger dexterity, student pairs research, brainstorm, plan, budget, compare, select, prototype, test, evaluate and modify their design ideas to create devices that enable a student to hold and use a small paintbrush or crayon. The design challenge includes clearly identified criteria and constraints, to which teams rate their competing design solutions. Prototype testing includes independent evaluations by three classmates, after which students redesign to make improvements. To conclude, teams make one-slide presentations to the class to recap their design projects. This activity incorporates a 3D modeling and 3D printing component as students generate prototypes of their designs. However, if no 3D printer is available, the project can be modified to use traditional and/or simpler fabrication processes and basic materials.

This is a challenge based activity in which students use augmented reality and trial and error in order to determine how changes to a quadratic equation affect the shape of a parabola. Students use the Geogebra AR app to manipulate equations and change the parabola to fit around a physical object.