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Unit 7 Grade 5 Geometry Lesson 1 7-a: Lines and Line Segments Start a chart in your notes! Description Examples Symbol Read A point is No symbol Point P the an exact location. Descriptio Examples Symbol Read n A line is a line ST straight path or that goes on line TS forever in both directions. It has no endpoints. Descriptio Examples Symbol Read n A line Line segment is segment a part of a MN or line line. It has segment two NM endpoints. Descriptio Examples Symbol Read n A ray is a part ray CD of a line that begins at one endpoint and goes on forever in the other direction. Descriptio Examples Symbol Read n An angle is angle KIM formed by two rays that have a common angle MIK endpoint. The endpoint angle I is called the vertex. Descriptio Examples Symbol Read n A plane is No symbol Plane ABC a flat surface that goes on forever in all directions. Description Examples Symbol Read Parallel lines Line MN is are lines in a MN OP parallel to plane that are line OP always equal distance apart, never intersect, and have no common points. Description Examples Symbol Read Intersecting No symbol Line WZ lines are intersects lines that Line YX at cross or Point A touch at exactly one point. Description Examples Symbol Read Intersecting No symbol Line WZ lines are intersects lines that Line YX at cross at Point A exactly one point. Description Examples Symbol Read Perpendicular Line TU is lines are lines TU AB perpendicular that intersect at to line AB a 90 degree (right) angle. Description Examples Symbol Read Skew lines are No line ?? and not parallel and symbol line ?? are do not skew intersect. Skew lines are in different planes. http://mathworld.wolfram.com/SkewLines.html Classwork Look around the room. Find 3 examples of the following terms. Angle Ray Line Line segment Parallel Lines Intersecting Lines Perpendicular Lines Skew Lines BE VERY SPECIFIC Example: Skew: The top line of the chalkboard to the bottom line of the wall with the whiteboard. Closure Where can we see geometric figures in real life? Homework H54 Lesson 6.1 (1) and Lesson 6.2 (1-7) Lesson 2 7-b: Angles and Their Measures What geometric ideas do you see in the face of a clock? Circles are divided into 360 degrees. We can use these degrees to help measure angles. Complementary Angles Two angles are complementary if the sum of their measures is 90 degrees. Supplementary Angles Two angles whose measures add up to 180 degrees. Vertical Angles: When two lines intersect, the angles opposite each other are called vertical angles. Vertical angles have equal measures. Adjacent Angles: When two lines intersect, the angles next to each other are adjacent. They are supplementary angles. Central Angles Reflex Central Angle: measure greater than 180 degrees but less than 360 degrees QuickTime™ an d a decompressor are need ed to see this picture . Quic kTime™ and a decom pres sor are needed to s ee this picture. Chapter 10 Animations Playing Golf with Angles Quic kTime™ and a decom pres sor are needed to s ee this picture. And Angles http://www.classzone.com/cz/books/msmath_2_n a/get_chapter_group.htm?cin=4&rg=ani_math&at =animations&var=animations Classwork New Purple 511-515 and 516-520 Biggest Problem of Miners worksheet Closure What angles do you see around the room? Homework Pages 186-187 Problems (1-20) Lesson 3 7-c : Angles with Transversals What do you think the measure of each angle might be? What type of angles are they? QuickTime™ and a decompressor are neede d to see this picture. Measuring angles Protractor: tool to measure angles QuickTime™ and a decompressor are neede d to see this picture. QuickTime™ an d a decompressor are need ed to see this p icture . What’s My Measure? QuickTime™ an d a decompressor are need ed to see this p icture . Transversal is a line that intersects two parallel lines. QuickTime™ and a decompressor are neede d to see this picture. What are the relationships? QuickTime™ and a decompressor are need ed to see this picture. Classwork Old Purple page 360-361 Problems (1-9) Pouring Oil Into a Car worksheet Closure If you have a transversal but the two lines are not parallel, will you have any of the same relationships? Homework Brontosaurus Band-Aids and Judge Rotten Milk Worksheets Lesson 4 7-d: Identify and Classify Angles (measure them) What’s My Measure?????? How to Use Protractors http://www.amblesideprimary.com/amblewe b/mentalmaths/protractor.html Ninja Angles http://www.bbc.co.uk/keyskills/flash/kfa/kfa. shtml Copy this link down to find cool stuff! http://jmathpage.com/JIMSGeometrypage.h tml Really cool geometry games online! Take a peek! Classwork Books Never Written worksheet Draw and measure angles if there is extra time Closure Why do protractors have two sets of numbers going in different directions. Homework What Happens When Cupid Shoots an Arrow? Worksheet Lesson 5 7-e: Identify Polygons 7-f: Identify Polygons in a composite figure Name each of the shapes Polygons: A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. The following are examples of polygons: The figure below is not a polygon, since it is not a closed figure: The figure below is not a polygon, since it is not made of line segments: The figure below is not a polygon, since its sides do not intersect in exactly two places each: Types of Polygons 3:Triangle 4: Quadrilateral 5: Pentagon 6: Hexagon 7: Heptagon 8: Octagon 9: Nonagon 10: Decagon 11: Undecagon 12: Dodecagon Quadrilaterals: a plane figure formed by 4 segments called sides. Each side intersects exactly two sides, one at each endpoint, and no two sides are part of the same line. All angles add up to be 360 degrees. Parallelogram Opposite sides of a parallelogram are parallel and equal in length. Opposite angles are equal in size. Rectangle Opposite sides of a rectangle are parallel and equal in length. All angles are equal to 90°. Rhombus (Diamond) All sides of a rhombus are equal in length Opposite sides are parallel. Opposite angles of a rhombus are equal. The diagonals of a rhombus bisect each other at right angles. Square Opposite sides of a square are parallel and all sides are equal in length. All angles are equal to 90°. Trapezoid A trapezoid has one pair of opposite sides parallel. A regular trapezoid has non-parallel sides equal and its base angles are equal, as shown in the diagram Another name for it is trapezium Concave and Convex Concave Polygons have at least one interior angle that is greater than 180 QuickTime™ and a decompressor are needed to see this picture. degrees. Quic kTime™ and a QuickT ime™ and a decom pressor dec ompress or are needed to see this pict ure. are needed to see this pic ture. Convex Polygons have all interior angles less than 180 degrees. QuickTime™ and a decompressor are needed to see this picture. Quic kTim e™ and a decompress or Qu i ckTi m e™ a nd a de co mp res so r are needed to s ee this pic ture. a re ne ed ed to se e th is pi c tu re. Concave or convex? Qu i ckTi me ™ a nd a QuickTime™ and a de co mp res so r decompressor a re ne ed ed to se e thi s pi ctu re . are needed to see this picture. Quic kTim e™ and a decompress or are needed to s ee this pic ture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor QuickTime™ and a are needed to see this picture. decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. Classwork New Purple 531-532 Problems: 1- 22 Checkpoints: 4, 10, 22 Closure What shapes do you see represented in the classroom? Homework Pages 192-193 Problems (1-13) Lesson 6 7-g: Identify and Classify Triangles 7-h: Sum of Interior Angles What are the differences between the two triangles? A triangle is a closed plane figure bounded by three line segments. 2 Ways to Classify Angles Way 1 is by its angles Way 2 is by it sides Let’s explore more in depth! Classifying Triangles by its Angles Acute: An acute-angled triangle has all angles less than 90º Obtuse: An obtuse-angled triangle has one angle greater than 90º. That is, one angle is obtuse. Right: A right-angled triangle has one angle equal to 90°. That is, one angle is a right angle. What are these? Classifying Triangles by its Sides Scalene: A scalene triangle has no equal sides. Equilateral: An equilateral triangle has all sides equal. Isosceles: An isosceles triangle has two sides equal. What are these? Sum of the interior angles in a triangle equal 180 degrees. QuickTime™ and a decompressor are needed to se e this picture. QuickTime™ and a decompressor are neede d to se e this picture. QuickTime™ and a decompressor are needed to see this picture. Qui ckTi me™ and a decompresso r are ne ede d to see thi s pi cture. QuickTime™ and a decompressor are neede d to se e this picture. Classwork New Purple Pages 524-526 Problems: 1-34 Checkpoints: 5, 9, 15, 21, 26, 34 Closure What do you think the angles of a quadrilateral add up to be? Homework Pages 198-199 Problems (1-15) Lesson 7 7-i: Quadrilaterals QuickTime™ an d a decompressor are need ed to see this picture . Explore Some Shapes http://www.learnalberta.ca/content/mejhm/i ndex.html?l=0&ID1=AB.MATH.JR.SHAP&I D2=AB.MATH.JR.SHAP.SHAP&lesson=ht ml/object_interactives/shape_classification/ explore_it.html Classzone.com Quic kTime™ and a Chapter 10: Polygons and Angles decom pres sor are needed to s ee this picture. Classwork Old Purple Pages 384-385 Problems: 1-22 Checkpoints: 3, 8, 14, 19, 22 Closure Is a rectangle a square? Is a square a rectangle? I’m confused! Homework Pages 204-205 Problems (1-8) Lesson 8 7-j: Relationship between Interior Angles and Polygons The angles in a triangle add up to 180 degrees. The angles in a quadrilateral add up to 360 degrees. What about other polygons? You can use a formula to determine the measures of the interior angles. Draw the diagonals from one vertex in several regular polygons to form triangles. Number of Number of Total angle Measure of Angles Triangles measure each angle 3 1 or (3-2) (1 x 180), or 180 (180/3), or 60 4 2 or (4-2) (2 x 180), or 360 (360/4), or 90 5 3 or (5-2) (3 x 180), or 540 (540/5), or 108 6 4 or (6-2) (4 x 180), or 720 (720/6), or 120 n (n-2) (n-2) x 180 (n-2) x 180 divided by n Classwork Practice drawing and measuring angles! Closure What is your favorite part of geometry? Why? Homework Page 206 Read carefully Page 207 Problems (1-8) Lesson 9 7-k: Legs and Hypotenuse 7-l: Pythagorean Theorom The Pythagorean Theorem The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students. The Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. The later discovery that some numbers were irrational greatly troubled him. It is even said that the man who proved some numbers were irrational was drowned at sea by Pythagoras. Doesn’t sound very rational to me! The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that: QuickTime™ and a decompressor are need ed to see this picture. “The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.” 2 2 2 a +b =c The lengths of the two shorter sides of the right QuickTime™ and a decompressor triangle, the legs, are neede d to see this picture. are a and b. The length of the longest side, the hypotenuse, is c. Classzone.com Chapter 11 Animations The Pythagorean Theorem Quic kTime™ and a decom pres sor are needed to s ee this picture. Classwork New Purple Pages 590-592 Problems: 1-29 Checkpoints: 5, 11, 17, 24, 29 Closure What is the formula and how does it work? Homework Pages 482-483 Problems (1-15) Lesson 10 7-m: Coordinate Planes What is this? What does it represent? http://www.learningwave.com/lwonlin e/algebra_section2/alg_coord.html http://www.shodor.org/interactivate/ac tivities/MazeGame/ Classwork New Purple Pages: 315-316 Problems: 1 - 40 Check Points: 10, 22, 30, 40 Closure How are the quadrants labeled? Homework Pages 310-311 Problems (1-21) Lesson 11 7-n: Similar and Congruent 7-o: Transformations 7-p: Transformations in Coordinate Planes Which ones are which? QuickTime™ and a decompressor are need ed to see this picture. Which ones are which? QuickTime™ and a decompressor are need ed to see this picture. Similar: So what are the measurements? Are these the same figures? What happened to them? Types of Transformations (changes) Translations: you can slide a figure along a straight line Rotations: you can turn the figure around a point Reflections: you can flip the figure over a line Blue: original figure Red: transformed figure Slide 6 to the right! Original Figure A (-5, 6) QuickTime™ and a B (-5, 3) decompressor C (-2. 3) are neede d to se e this picture. New Figure A (1, 6) B (1, 3) C (4, 3) Rotate 90 degrees to the right around point B! Original Figure A (-5, 6) QuickTime™ and a B (-5, 3) decompressor C (-2. 3) are neede d to se e this picture. New Figure A (-2, 3) B (-5, 3) C (-5, 0) Reflect or flip over a line of symmetry Original Figure A (-5, 6) QuickTime™ and a B (-5, 3) decompressor C (-2. 3) are neede d to se e this picture. New Figure A (3, 6) B (3, 3) C (0, 3) Slide 7 to the right and down 8! Original Figure A (-5, 6) QuickTime™ and a B (-5, 3) decompressor C (-2. 3) are neede d to se e this picture. New Figure A (2, -2) B (2, -5) C (5, -5) Classzone.com Chapter 10 Animations Translations, Reflections, and Rotations Quic kTime™ and a decom pres sor are needed to s ee this picture. Classwork New Purple Pages 558-561 Problems: 1 - 20 Checkpoints: 4, 8, 16, 20 Closure When do we see transformations in real life? Homework You Choose one group Pages 414-415 Problems (1-18) or Page 419 (1-4) and 421 (1-6) Lesson 12 7-q: Parts of a Circle What are the parts of a circle? Vocabulary Circle: a special closed figure made up of all the points in a plane that are the same distance from the point called the center. Chord: a line segment with endpoints on a circle Diameter: a chord that passes through the center of the circle Radius: a line segment with one endpoint at the center of the circle and the other on the circle. http://www.mathgoodies.com/lesso ns/vol2/geometry.html Closure Do you think Sir Cumference and the First Round Table is a good way to introduce the parts of a circle to a class of 4th grade GT Math students? Why or why not? Homework Model/Label a circle with chord, Make a model of a diameter, radius, arc, circle, label all circumference parts! Be creative! Center Lesson 13 7-r: Classifying Solids Prisms and Pyramids 7:s: Euler’s Formula V-E + F = 2 7:t: Nets What do you see? QuickTime™ and a decompress or are needed to see this picture. http://www.harcourtschool.com/jin gles/jingles_all/1what_am_i.html In the mood for a tune? Types of Solid Figures (pull them out) Shape of Base Figure with One Base Figure with Two Congruent Bases Triangular Pyramid Triangular Prism QuickTime™ and a dec ompress or are needed to see this picture. QuickTime™ and a decompressor are neede d to see this picture. Rectangular Pyramid Rectangular Prism Quic kTime™ and a Qu i ckTi me ™ a nd a dec ompress or de co mp res so r a re ne ed ed to se e th is pi ctu re. are needed t o see t his pict ure. Cone Cylinder QuickTime™ and a QuickTime™ an d a decompressor decompressor are neede d to see this picture. are need ed to see this p icture . Hexagonal Pyramid Hexagonal Prism QuickTime™ and a a dna ™emi Tk ciu Q ros serpmoced decompressor .eru tcip sih t ee s o t d edeen e ra are neede d to see this picture. http://www.bgfl.org/bgfl/custom/re sources_ftp/client_ftp/ks2/maths/3 d/index.htm Copy Chart first! Name of shape Number of bases Number of Number of and faces edges vertices Cone Cylinder Triangular Pyramid Triangular Prism Rectangular Pyramid Rectangular Prism Pentagonal Pyramid Pentagonal Prism Hexagonal Pyramid Hexagonal Prism Euler’s Formula http://www.math.ohio- state.edu/~fiedorow/math655/Euler.html Classwork New Purple Pages 633-635 Problems: 1 - 26 Checkpoints: 8, 13, 19, 22, 26 Homework Pages 430-433 (1-10) Closure What is the difference between pyramids and prisms?

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