The purpose of this task is to provide students with a multi-step problem involving volume and to give them a chance to discuss the difference between exact calculations and their meaning in a context.
The purpose of this task is to provide students with a concrete situation they can model by dividing a whole number by a unit fraction.
This real world task requires students to answer questions about equations for calculating compound interest.
This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.
The purpose of this task is to help students understand what is meant by a base and its corresponding height in a triangle and to be able to correctly identify all three base-height pairs.
This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.
This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course would. It should be possible to use these notes for a beginning of a more advanced course, but further material should be added.
This short video and interactive assessment activity is designed to teach third graders an overview of lines, curves, vertices, and sides of 2d shapes.
This short video and interactive assessment activity is designed to teach second graders an overview of lines, curves, vertices, and sides of 2d shapes.
This short video and interactive assessment activity is designed to teach second graders an overview of simple figure patterns.
This short video and interactive assessment activity is designed to teach third graders an overview of simple figure patterns.
This short video and interactive assessment activity is designed to give fourth graders an overview of simple figure patterns.
This short video and interactive assessment activity is designed to give fifth graders an overview of simple figure patterns.
This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.
This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.
Beginning kindergarteners are introduced to science and engineering concepts through questions such as “What is a Scientist?” and “What is an Engineer?”, and go on to compare and contrast the two. They are introduced to five steps of the engineering design process and explore these steps using the “I do, we do, you do” set of guided instruction. At the end of the project, students produce a set of purple popsicles that they design using various materials and by following a set of criteria.
This short video and interactive assessment activity is designed to teach third graders about before and after problems.
Real Numbers
This course covers a range of algebraic topics: Setting up and solving linear equations, graphing, finding linear relations, solving systems of equations, working with polynomials, factoring, working with rational and radical expressions, solving rational and radical equations, solving quadratic equations, and working with functions. More importantly, this course is intended to provide you with a solid foundation for the rest of your math courses. As such, emphasis will be placed on mathematical reasoning, not just memorizing procedures and formulas. There is enough content in this course to cover both beginning and intermediate college-level algebra.
This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.