Scratch is a new programming language that makes it easy to create your own interactive stories, animations, games, music, and art -- and share your creations on the web.
Scratch is designed to help young people (ages 8 and up) develop 21st century learning skills. As they create and share Scratch projects, young people learn important mathematical and computational ideas, while also learning to think creatively, reason systematically, and work collaboratively.

Student teams are challenged to evaluate the design of several liquid soaps to answer the question, “Which soap is the best?” Through two simple teacher class demonstrations and the activity investigation, students learn about surface tension and how it is measured, the properties of surfactants (soaps), and how surfactants change the surface properties of liquids. As they evaluate the engineering design of real-world products (different liquid dish washing soap brands), students see the range of design constraints such as cost, reliability, effectiveness and environmental impact. By investigating the critical micelle concentration of various soaps, students determine which requires less volume to be an effective cleaning agent, factors related to both the cost and environmental impact of the surfactant. By investigating the minimum surface tension of the soap, students determine which dissolves dirt and oil most effectively and thus cleans with the least effort. Students evaluate these competing criteria and make their own determination as to which of five liquid soaps make the “best” soap, giving their own evidence and scientific reasoning. They make the connection between gathered data and the real-world experience in using these liquid soaps.

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.

In this undergraduate level seminar series topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.

Seminar for mathematics majors. Students present and discuss the subject matter and write up exercises. Topic for Fall 2002: Classical geometry, beginning with Euclid's Elements and continuing to applications of Galois theory that solve the geometry problems of antiquity. No prior knowledge of Galois theory required. Instruction and practice in oral communication provided.

Over the past 4 years, Hartford Union High School has been working on a curriculum review process to improve secondary mathematics instruction and achievement.  Illustrative Mathematics was selected and adopted for the 2021-2022 school year. Teachers participated in summer IM Teach and Learn training as well as Unit Overviews provided by the Math Institute of Wisconsin.  Teacher's also participated in an IM PLC session, Unit Planning, and a book study.The following modules contain samples and templates of documents that were used to facilitate the adoption including teacher and student surveys, the IM Implementation Rubric, Unit Planning, and book study guides.Hartford Union High School Curriclum Adoption TeamDustin Burg, Hartford Union High School Math Teacher (Algebra 2 Lead Teacher)Kaite Burns, Hartford Union High School Math Teacher (Geometry Lead Teacher)Kelly Lam, Hartford Union High School PrincipalMike McIntyre, Director of Curriculum and InstructionMallory Smith, Instructional CoachBob Sliwinski, Hartford Union High School Math Teacher (Algebra 1 Lead Teacher)

This word problem is based estimating the height of a person over time. Note that there is a significant amount of rounding in the final answer. This is because people almost never report their heights more precisely than the closest half-inch. If we assume that the heights reported in the task stem are rounded to the nearest half-inch, then we should report the heights given in the solution at the same level of precision.

The typical system of equations or inequalities problem gives the system and asks for the graph of the solution. This task turns the problem around. It gives a solution set and asks for the system that corresponds to it. The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations. Students have to focus on what the graph is showing.

This lesson unit is intended to help teachers assess how well students are able to: solve linear equations in one variable with rational number coefficients; collect like terms; expand expressions using the distributive property; and categorize linear equations in one variable as having one, none, or infinitely many solutions. It also aims to encourage discussion on some common misconceptions about algebra.

This lesson unit is intended to help teachers assess how well students are able to formulate and solve problems using algebra and, in particular, to identify and help students who have the following difficulties: solving a problem using two linear equations with two variables; and interpreting the meaning of algebraic expressions.

This lesson unit is intended to help teachers assess how well students are able to: recognize the differences between equations and identities; substitute numbers into algebraic statements in order to test their validity in special cases; resist common errors when manipulating expressions such as 2(x Đ 3) = 2x Đ 3; (x + 3)_ = x_ + 3_; and carry out correct algebraic manipulations. It also aims to encourage discussion on some common misconceptions about algebra.

Learning Targets
* I can make connections between different algebraic representations: graphs, equations, verbal rules, and tables
* I understand how the equation determines the shape of the graph
* I can develop a convincing argument using a variety of algebraic concepts
* I am able to move from specific solutions to thinking about generalizations

Success Criteria
* Students will be able to accurately link various representations of functions and form a cohesive argument for their thinking.

Introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory and optimization techniques. Emphasis on basic ideas and on applications in mechanical engineering. Selection will change every year. This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

In this video segment from Cyberchase, Hacker and the CyberSquad race to reach the Good Vibration on staircases that grow at different rates and have steps of varying sizes.

In this Illuminations lesson, students apply their knowledge of addition equations to investigate the equivalence of two numeric expressions using the "Pan Balance-Numbers" applet (cataloged separately). An instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given for the lesson as well as links to the applet and a student activity sheet(word format).

This Lesson Plan goes over how to find the Mean, Median, Mode, IQR, and Mean Absolute Deviation of a data set. We will go over some generic examples in the lesson and then do some practical application, as we find each of these from the samples taken to ensure consistent weight of the paper from BPM.

This lesson unit is intended to help teachers assess how well students are able to: form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.

This problem provides students with an opportunity to discover algebraic structure in a geometric context. More specifically, the student will need to divide up the given polygons into triangles and then use the fact that the sum of the angles in each triangle is 180_.

Parts (d) and (e) of this task constitute a very advanced application of the skill of making use of structure: in (d) students are being asked to use the defining property of even and odd functions to manipulate expressions involving function notation. In (e) they are asked to see the structure in the system of two equations involving functions.