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 visualize two-dimensional cross-sections of representations of three-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing two-dimensional cross-sections at different points along a plane of a representation of a three-dimensional object.

This Demonstration illustrates the concept of rotating a 2D polygon. The rotation ...

This Demonstration illustrates the concept of rotating a 2D polygon. The rotation matrix is displayed for the current angle. The default polygon is a square that you can modify.

An interactive applet and associated web page that shows how triangles that ...

An interactive applet and associated web page that shows how triangles that have two angles and a non-included side the same must be congruent. The applet shows two triangles, one of which can be reshaped by dragging any vertex. The other changes to remain congruent to it and the two angles and non-included side are outlined in bold to show they are the same measure and are the elements being used to prove congruence. The web page describes all this and has links to other related pages. 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 examines the ways in which the plane can be covered ...

This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

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: work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles; Identify and understand the significance of a counter-example; Prove, and evaluate proofs in a geometric context.

In this activity, learners use a hand-made protractor to measure angles they ...

In this activity, learners use a hand-made protractor to measure angles they find in playground equipment. Learners will observe that angle measurements do not change with distance, because they are distance invariant, or constant. Note: The "Pocket Protractor" activity should be done ahead as a separate activity (see related resource), but a standard protractor can be used as a substitute.

We use the derivative to determine the maximum and minimum values of ...

We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).Differentiation is also used in analysis of finance and economics.

This lesson unit is intended to help you assess how well students ...

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.

This learning video deals with a question of geometrical probability. A key ...

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.

This task asks students to use similarity to solve a problem in ...

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.

This activity explores the main algorithms that are used as the basis ...

This activity explores the main algorithms that are used as the basis for searching on computers, using different variations on the game of battleships. This activity demonstrates three search methods for finding information in data: linear searching, binary searching and hashing. It also includes an optional introductory activity as well as a video showing a fun demonstration related to the same content.

This task was developed by high school and postsecondary mathematics and design/pre-construction ...

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This task was developed by high school and postsecondary mathematics and design/pre-construction ...

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This task was developed by high school and postsecondary mathematics and design/pre-construction ...

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This task was developed by high school and postsecondary mathematics and health ...

This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This lesson unit is intended to help teahcers assess how well students ...

This lesson unit is intended to help teahcers assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties; computing measurements using formulas; decomposing compound shapes into simpler ones; using right triangles and their properties to solve real-world problems.

Students' first experience with transformations is likely to be with specific shapes ...

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

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.

Ana Donevska Todorova Humboldt Universitﾊt zu Berlin Mathematisch-Naturwissenschaftliche Fakultﾊt II Institut fﾟr ...

Ana Donevska Todorova Humboldt Universitﾊt zu Berlin Mathematisch-Naturwissenschaftliche Fakultﾊt II Institut fﾟr Mathematik, Didaktik der Mathematik ??? ?????????? ?????? ???????? ?? ???????????? ????? ? ????

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.

This lesson unit is intended to help assess how well students are ...

This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.

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 the Pythagorean theorem to derive the equation of a circle; and translate between the geometric features of circles and their equations.

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: translate between the equations of circles and their geometric features; and sketch a circle from its equation.

This lesson unit is intended to help you assess how well students ...

This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.

This lesson unit is intended to help you assess how well students ...

This lesson unit is intended to help you assess how well students are able to: Model a situation; make sensible, realistic assumptions and estimates; and use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

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 solve problems involving area and volume, and in particular, to help you identify and assist students who have difficulties with the following: computing perimeters, areas and volumes using formulas; and finding the relationships between perimeters, areas, and volumes of shapes after scaling.

This lesson unit is intended to help teachers assess how well students ...

This lesson unit is intended to help teachers assess how well students can: Understand the concepts of length and area; use the concept of area in proving why two areas are or are not equal; and construct their own examples and counterexamples to help justify or refute conjectures.

This is a comprehensive math textbook for Grade 11. It can be ...

This is a comprehensive math textbook for Grade 11. It can be downloaded, read on-line on a mobile phone, computer or iPad. Every chapter has links to on-line video lessons and explanations. Summary presentations at the end of each chapter offer an overview of the content covered, with key points highlighted for easy revision. Topics covered are: language of mathematics, exponents, surds, error margins, quadratic sequences, finance, quadratic equations, quadratic inequalities, simultaneous equations, mathematical models, quadratic functions and graphs, hyperbolic functions and graphs, exponential functions and graphs, gradient at point, linear programming, geometry, trigonometry, statistics, independent variables, dependent events. This book is based upon the original Free High School Science Text series.

In this activity, learners use pattern blocks and mirrors to explore symmetry. ...

In this activity, learners use pattern blocks and mirrors to explore symmetry. Learners work in pairs and build mirror images of each other's designs. In doing so, learners will examine principles of symmetry and reflection.

In this activity, learners design unique tiles and make repeating patterns to ...

In this activity, learners design unique tiles and make repeating patterns to create tessellations. This activity combines the creativity of an art project with the challenge of solving a puzzle. This lesson features three investigations, in which learners make tessellations by translating, rotating, and reflecting the patterns.

This learning video introduces students to the world of Fractal Geometry through ...

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of different equations.

This learning video introduces students to the world of Fractal Geometry through ...

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of different equations.

This web site offers families, teachers, and tutors 80 mathematical challenges helpful ...

This web site offers families, teachers, and tutors 80 mathematical challenges helpful for encouraging problem solving with students in grades 6 to 8. The math challenges focus on concepts and objects found in everyday life, such as how fast your heart beats, what shape container holds the most popcorn, and how much of me shows in a mirror. Each challenge contains an initial problem with a solution hint, a complete explanation of the answer, and additional problems related to the same challenge. Resources for further investigations are suggested as well. From the Printing the Challenges link on the homepage, PDF files are available for all 80 challenges in English, the first 15 challenges in Spanish, and the family resource materials in English and Spanish.

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in ...

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

The purpose of this task is for students to translate between measurements ...

The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing.

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