Students learn about material balances, a fundamental concept of chemical engineering. They …
Students learn about material balances, a fundamental concept of chemical engineering. They use stoichiometry to predict the mass of carbon dioxide that escapes after reacting measured quantities of sodium bicarbonate with dilute acetic acid. Students then produce the reactions of the chemicals in a small reactor made from a plastic water bottle and balloon.
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 interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties: translating between percents, decimals, and fractions; representing percent increase and decrease as multiplication; and recognizing the relationship between increases and decreases.
Students are asked to consider the expression that arises in physics as …
Students are asked to consider the expression that arises in physics as the combined resistance of two resistors in parallel. However, the context is not explicitly considered here. The task is good general preparation for problems more specifically aligned to either A-SSE.1 or A-SSE.2.
Students use scaling from real-world data to obtain an idea of the …
Students use scaling from real-world data to obtain an idea of the immense size of Mars in relation to the Earth and the Moon, as well as the distances between them. Students calculate dimensions of the scaled versions of the planets, and then use balloons to represent their relative sizes and locations.
The purpose of this task is to probe students' ability to correlate …
The purpose of this task is to probe students' ability to correlate symbolic statements about a function using function notation with a graph of the function, and to interpret their answers in terms of the quantities between which the function describes a relationship
An interactive applet and associated web page that demonstrate the inscribed angle …
An interactive applet and associated web page that demonstrate the inscribed angle of a circle - the angle subtended at the periphery by two points on the circle. The applet presents a circle with three points on it that can be dragged. The inscribed angle is shown and demonstrates that it is constant as the vertex is dragged. Links to other related topics such as Thales Theorem. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
This task shows how to inscribe a circle in a triangle using …
This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.
This task is primarily for instructive purposes but can be used for …
This task is primarily for instructive purposes but can be used for assessment as well. Parts (a) and (b) are good applications of geometric constructions using a compass and could be used for assessment purposes but the process is a bit long since there are six triangles which need to be constructed.
This problem introduces the circumcenter of a triangle and shows how it …
This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.
This task focuses on a remarkable fact which comes out of the …
This task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.
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 use geometric properties to solve problems. In particular, it will help you identify and help students who have difficulty: decomposing complex shapes into simpler ones in order to solve a problem; bringing together several geometric concepts to solve a problem; and finding the relationship between radii of inscribed and circumscribed circles of right triangles.
These strategies support active student participation in math lessons and allow teachers …
These strategies support active student participation in math lessons and allow teachers to assess the developing proficiency levels of all students in the class by walking around to monitor student responses. These strategies are especially effective during the Mental Math part of an Everyday Mathematics lesson.
This lesson will be the first of six lessons guiding students in …
This lesson will be the first of six lessons guiding students in constructing the abstract concepts necessary to understand adding positive and negative integers. It is designed for adult learners (or middle school or older) who are not fluent with using numbers.
This is the third of six lessons teaching basic concepts related to …
This is the third of six lessons teaching basic concepts related to positive and negative integers. This lesson will review previous knowledge about negative numbers and teach adding integers with the same sign, with connections to “real life” situations such as gains and losses in football yards or bank account overdraws.
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