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c information killian elaine acting out translated figures mathematical concept translation grade levels 7th 8th nctm standards and principles of school mathematics understand relationships among the angles side lengths perimeters areas and volumes of similar objects create and critique inductive and deductive arguments concerning geometric ideas and relationships such as congruence similarity and the pythagorean relationship use geometric models to represent and explain numerical and algebraic relationships recognize and apply geometric ideas and relationships in areas outside the mathematics classroom such as art science and everyday life materials masking taped grid on the floor of the class yarn different pre cut figures written down in x y notation copies of translation worksheet detailed description the following activity will describe translation of figures by completion of this lesson students should understand that a translated image is an image that slides in a given direction the original object and its translation have the same shape size and face in the same direction students will act out a figure in the exercise given below students will participate by being the original figure and a translated figure procedure 1 before class the teacher will create an x and y axis grid on the floor using masking tape 2 divide the class into small working groups 3 students will come up to the table groups and choose a figure to represent 4 the figure will be written down in x y ordered notation form 5 each student will represent a point on the polygon the polygon will be completed using yarn to connect the points students 6 the next group will come up and perform the given translation 7 each group should get a chance to be the original figure and the translated figure 8 to follow up student comprehension students will be given the attached translation worksheet for homework attachment worksheet activity student page translation handout leave a comment filed under geometry activity file july 26 2010 6 55 am rotation bibliographic information harrington carla alexander county public schools teacher mathematical concept rotation grade levels 7th 8th nctm standards and principles of school mathematics understand relationships among the angles side lengths perimeters areas and volumes of similar objects create and critique inductive and deductive arguments concerning geometric ideas and relationships such as congruence similarity and the pythagorean relationship use geometric models to represent and explain numerical and algebraic relationships recognize and apply geometric ideas and relationships in areas outside the mathematics classroom such as art science and everyday life materials pencils computer with access to smartboard copies of rotational symmetry in the alphabet and rotational symmetry in road signs handouts rotation of shapes handout detailed description these activities are designed to introduce students to rotational symmetry upon completion of these activities students will know that an image is said to have rotational symmetry if it looks exactly the same when rotated to illustrate examples of rotational symmetry i will be using the smartboards application for rotation sent to me by mrs carla harrington using this interactive tool an image may be selected after covering with virtual tracing paper the image is outlined then you may click on rotate to see how the traced image would appear if the original was rotated at 90 180 270 and 360 it can be found at the following website http www teacherled com 2008 01 28 rotational symmetry activity procedure 1 give out the sheets titled rotational symmetry in the alphabet and rotational symmetry in road signs 2 have students tell below each letter sign if it has rotational symmetry 3 if a letter sign does have rotational symmetry have the students to mark the centre of rotation 4 once students have completed the sheets discuss the results with the class 5 assign rotation of shapes handout for homework attachment worksheet activity student page rotation handout leave a comment filed under geometry activity file july 25 2010 2 51 pm reflection practice using mira s bibliographic information woodward ernest and hamel thomas geometric constructions and investigations with a mira maine j weston walch 1992 mathematical concept reflection and using mira s grade levels 6th 8th nctm standards and principles of school mathematics understand relationships among the angles side lengths perimeters areas and volumes of similar objects create and critique inductive and deductive arguments concerning geometric ideas and relationships such as congruence similarity and the pythagorean relationship use geometric models to represent and explain numerical and algebraic relationships recognize and apply geometric ideas and relationships in areas outside the mathematics classroom such as art science and everyday life materials graphing paper colored pencils sharp writing pencils mira s copies of pages 3 and 5 from geometric constructions and investigations detailed description completion of the following activities will allow students to learn the language associated with reflections and draw a reflected image of a figure over a line of reflection students will also be able to perform two dimensional reflections while using a mira as well as recognize when a figure is not symmetrical by the end of this lesson students should realize that if the reflective figure looks reversed from its original it is not symmetrical procedure 1 activity one a hand out graphing paper to each student b have the students divide a piece of graph paper into four quadrants by drawing the axis lines c in any one quadrant create a pattern of polygons from the lines on the paper and diagonals d have students to copy the patterns into the other three quadrants by reflecting the pattern over the axis lines 2 activity two a divide the class into working partners b hand each student a piece of graphing paper c divide the graph paper into four quadrants by drawing the axis lines d have each student draw a pattern in any one of the quadrants e each student should pass their graph paper to their partner f the partner is to reflect the pattern over the axis lines 3 activity three a pass out copies of page 3 from geometric constructions and investigations b pass out a mira to each student direct students to find the beveled edge the edge that seems to cut inward and that this beleved edge should be placed down c allow students to practice using the mira as they complete page 3 from geometric constructions and investigations d students should use the mira to find the line of reflection which puts the boy on the swing e have students to trace the line of reflection f finally students will trace the boy on the other side of the mira while looking through it as the teacher monitors the activity and gives assistance as necessary 4 activity four a pass out copies of page 5 from geometric constructions and investigations b instruct students to complete this activity the same way as activity 3 was completed they are to follow the handouts instructions to place the hats on the woman s head c remind students to trace the line of reflection onto the handout attachment worksheet activity student page geometric constructions and investigations page 3 geometric constructions and investigations page 5 leave a comment filed under geometry activity file july 23 2010 4 01 am symmetry polygons and lines of symmetry bibliographic information muschla judith a and gary r muschla polygons and lines of symmetry geometry teachers s activities kit ready to use lessons worksheets for grades 6 12 west nyack new york 2000 pages 130 isbn 0 13 016777 0 mathematical concept symmetry grade levels 6th 7th nc standard course of study competency 3 the learner will understand and use properties and relationships of geometric figures in geometry 3 01 using three dimensional figures identify describe and draw from various views top side front corner build from various views describe cross sectional views 3 02 identify define and describe similar and congruent polygons with respect to angle measures length of sides and proportionality of sides 3 03 use scaling and proportional reasoning to solve problems related to similar and congruent polygons materials pencils rulers protractors unlined paper optional handout detailed description students will draw polygons that have a specific number of lines of symmetry students should work individually to complete this activity because the sides and angles of many kinds of polygons are congruent they can be used to illustrate symmetry in this activity as students draw polygons they will also consider their lines of symmetry procedure 1 introduce this activity by explaining that symmetry is a relationship in which opposite sides of an object or figure are mirror images of each other 2 ask students if they can name examples of symmetry in the world nature human beings have 2 eyes 2 ears 2 arms 2 legs most animals are symmetrical many flowers buildings butterflies 3 handout copies of the worksheet titled polygons and lines of symmetry 4 review the instructions with the students 5 students are to complete the activity independently 6 once all students are finished with the assignment the class will go over the answers extension assignment as an extension to this assignment the class may be assigned to form a poster of symmetrical images found in magazines students should cut out the figure glue it onto poster board and draw its line of symmetry attachment worksheet activity student page symmetry polygons and lines of symmetry handout leave a comment filed under geometry activity file july 23 2010 3 46 am networks from point to polyhedron bibliographic information thomas christine d and carmelita santiago 2002 building mathematically powerful students through connections mathematics teaching in the middle school may 2002 vol 7 iss 9 p 484 488 mathematical concept exploring networks with polyhedron grade levels 6th 8th nctm principles and standards for school mathematics precisely describe classify and understand relationships among types of two and three dimensional objects using their defining properties understand relationships among the angles side lengths perimeters areas and volumes of similar objects create and critique inductive and deductive arguments concerning geometric ideas and relationships such as congruence similarity and the pythagorean relationship materials 75 colored non bendable straws yarn twine dental floss or string scissors rulers protractors bamboo skewers sharp knife instruction sheet student materials notebook portfolio for research calculator colored pencils markers detailed description this activity is based on parts from the building mathematically powerful students through connections article prior to completing this unit the instructor is encouraged to design each of the straw polyhedron and display them around the room the models will be used to investigate concepts such as point line line segment rays angles and networks while engaged in this project students will view themselves as mathematicians and researchers as models are developed by the students they will explore two dimensional figures through investigations of polygons and their properties finally the teams will delve into three dimensional polyhedrons students will examine their string of triangles in terms of network which is a figure made up of points vertices connected by non intersecting edges arcs procedure 1 organize students into research teams of 2 4 students a each student s mission will be to contribute to the team s development of the model acquire an understanding of geometry concepts and relationships among the concepts extend the team s thinking about mathematics through research and share and discuss insights with the team i through investigations students should be able to find congruent angles alternate interior angles alternate exterior angles corresponding angles and supplementary angles b the students will maintain a research portfolio in which they will keep i a log of daily investigations facts and findings ii charts diagrams and classroom notes to support investigations facts and findings iii make inferences or speculations based on conclusions from the investigations iv a vocabulary list of new terms v written reflections for each day s activities 2 students will be assigned to find potential connections to real life situations through research exploration and mathematical discoveries a each team will have a person to work on the following tasks or the teacher may divide each group of 4 as one specific team i e group 1 will be the research team etc i the research team will investigate how the structures changes from adding new straws and or vertices analyze the properties of triangles parallelograms and trapezoids and include the study of parallel lines ii the measurement team will find the following measurements the length of the straw angle measures and the area formulas for the triangle trapezoid and parallelogram iii the algebraic team will create a chart and look for patterns to determine the number of straws required for a string of equilateral triangles of any length as well as determine a formula for finding the number of straws to create a string of n triangles 2n 1 iv the discrete mathematics team will use the horizontal string of triangles to define and investigate networks this group will also conduct internet research on mathematician leonhard euler specifically looking for information on his work in graph theory 3 network after gaining some background knowledge of the study of networks the students will examine their string of triangles in terms of networks i students will examine the number of edges leading into each vertex and number each vertex accordingly ii discussion should ensue about finding an euler path traversing all edges without using any edge twice iii students should discover that they must begin at a certain vertex to completely travel the network and pass through every edge once and only once iv euler s theorem if a network has 2 or fewer odd vertices then it has at least 1 euler path v students should conclude that because the string of connected triangles was a network with 2 odd vertices they must begin and end at an odd vertex to trace an euler path 4 pass out the instruction sheet titled straw polyhedra other nets 5 pass out copies of polyhedra outlines as accessed on let s face it from pbs org mathline for students to use as visual guides while constructing the polyhedron networks students can use these handouts as guides for what the polyhedra should look like when it is lying flat attachment worksheet activity student page instructions as taken from the following website http www math nmsu edu breakingaway lessons straw straw html instructions leave a comment filed un...