...INTERVENTION MATERIAL 1 RIZAL HIGH SCHOOL SY 2011 - 2012 Prepared by: Asakil, Flordeliza V. Casumbal, Epifania J. Dela Cruz, Lorena O. Pagulayan, Rowena H. Reluba, Ma. Theresa C. Unida, Francisca R. 2 2 Purpose of Strategic Intervention Material (SIM) This learning package is intended to supplement your classroom learning while working independently . The activities and exercises will widen your understanding of the different concepts you should learn. How to use this Strategic Intervention Material (SIM)? • • • • • • • Keep this material neat and clean. Thoroughly read every page. Follow carefully all instructions indicated in every activity. Answer all questions independently and honestly. Write all your answers on a sheet of paper. Be sure to compare your answers to the KEY TO CORRECTIONS only after you have answered the given tasks. If you have questions or clarifications ask your teacher. 3 Honey, I shrunk the kids !!! Title Card Topic: SUM OF INTERIOR ANGLES OF POLYGON 4 Are you kind enough to help them regain their normal self ? Do you want to know how the kids got shrunk ? 5 Thank you. I know you are more than willing to help. Sit tight and let’s try to do the following activities so that we can unfold their story. 6 Guide Card P 2 Activity 1 1 • Do this paper-folding activity using a cutout of a triangle. • Name the triangle RPS and label the corresponding ∠1...
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...because it has thickness! And it should extend forever, too. So the very top of a perfect piece of paper that goes on forever is the right idea! Also, the top of a table, the floor and a whiteboard are all like a plane. Imagine Imagine you lived in a two-dimensional world. You could travel around, visit friends, but nothing in your world would have height. You could measure distances and angles. You could travel fast or slow. You could go forward, backwards or sideways. You could move in straight lines, circles, or anything so long as you never go up or down. What would life be like living on a plane? Regular 2-D Shapes - Polygons Move the mouse over the shapes to discover their properties. Triangle Square Pentagon Hexagon Heptagon Octagon Nonagon Decagon Hendecagon Dodecagon These shapes are known as regular polygons. A polygon is a many sided shape with straight sides. To be a regular...
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...User’s Guide For fx-9860G Series/GRAPH 75/85/95 Series CASIO Worldwide Education Website http://edu.casio.com CASIO EDUCATIONAL FORUM http://edu.casio.com/forum/ = Page 1 = 20060601 Contents Contents 1 Geometry Mode Overview 2 Drawing and Editing Objects 3 Controlling the Appearance of the Geometry Window 4 Using Text and Labels in a Screen Image 5 Using the Measurement Box 6 Working with Animations 7 Error Messages = Page 2 = 20060601 1-1 Geometry Mode Overview 1. Geometry Mode Overview The Geometry Mode allows you to draw and analyze geometric objects. You can draw a triangle and specify values to change the size of its sides so they are 3:4:5, and then check the measurement of each of its angles. You can also lock the coordinates of a point or the length of a line segment, and you can draw a circle and then draw a line that is tangent to a particular point on the circle. The Geometry Mode also includes an animation feature that lets you watch how an object changes in accordance with conditions you define. Geometry Mode Menus Unlike other modes, the Geometry Mode does not have function menus along the bottom of the screen. Instead, it uses menus named [F1] through [F6] and [OPT], like the ones shown below. The following is a general explanation of Geometry Mode menus. • Pressing a key that corresponds to a menu ([F1] through [F6] or [OPT]) will display the Pressing...
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...http://www.aquapoolcopoolandspa.com/Octagon.html http://upload.wikimedia.org/wikipedia/commons/4/41/Parallelogram.svg http://www.freemathhelp.com/feliz-trapezoids.html http://0.tqn.com/d/altreligion/1/0/_/1/-/-/circle.jpg http://www.northstarmath.com/sitemap/AcuteTriangle.html * A triangle in which one angle is a right angle (that is, a 90-degree angle) * A triangle that has one interior angle that measures more than 90° is an obtuse triangle. * Lines are parallel if they lie in the same plane, and are the same distance apart over their entire length. * A line is perpendicular to another if it meets or crosses it at right angles (90°). * plane figure with four equal straight sides and four right angles. * An 8-sided polygon. * A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. * A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. * A 2-dimensional shape made by drawing a curve that is always the same distance from a center. * A triangle in which all three angles are acute...
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...for kindergarten or first grade as I will be instructing either grade level. Before I attempt to play this game, I will make sure that my students are aware of the different shapes. Detailed Description/Instructions for the Activity-I as the teacher say I spy something with eight sides, three sides, four sides, five sides, or six sides. I can put my class into three groups and then call out the sides, I will give each group a couple of minutes to figure out what geometric shape I am speaking of whether it is a triangle, rectangle, hexagon, trapezoid, parallelogram, or pentagon. I would then ask the children to describe the shape, for example a rectangle can be used for a computer screen. This game will help my students better understand these different geometric shapes, and it can also be quite fun, as the children will play by themselves eventually. Materials needed- Pictures of a pentagons, trapezoids, triangles, hexagon, rectangle, and a parallelogram, these items are going to be large enough so the children are able to see them. I will also have pictures from magazines as well, so they are able to see these geometric shapes in a real-life manner. National Council of Teacher Mathematics Standards. –This activity meets many of the National Council of Teacher Mathematics Standards, including showing the different characteristics of two and three dimensional geometric shapes as well as developing mathematical arguments about geometric relationships. According to "Geometry...
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...When watching The Bare Bears, one amazing thing I have noticed is that the friendship among them. They are so close to each other, but when a girl later involved in the friendship. Things seems have changed. Panda fell in love with the girl, but they other bears see the girl as a good friend. Later, there are funny things happen because of this. I was wondering what is this thing that makes friendship different between opposite sex. According to this, the question I used to lead my research is “What is the difference between same sex and different sex friendship?” This question is kind of broad and what I intend to do is looking to some specific aspects about it, especially gender. I searched a few research articles and found some that fits...
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...put into two major types - * biting and chewing * Sucking, this can also include piercing or lapping. How does this affect the geometry of the insect's mouth structure? Give two examples of insects with each type of mouth structure. They are bilaterally symmetric meaning that they are same on both sides of the body 5. Often times we look as insects at things that "bug you" or are a nuisance, but they are an important part of the world three surround you. Why are insects important in our world? Interior angle of a triangle add up to 180 degrees 6. What are polygons? What does it mean to have a closed polygon? A simple polygon? A regular polygon? A polygon is a figure with at least three straight sides and angles. Its means all sides are connected and there no curved side. 7. What is an interior angle of a polygon? Is there a formula for finding the measure of an interior angle of a regular polygon? Interior angle of triangle add up to 180◦ 8. How does geometry influence the lives of biologists and artists? Why would knowing and being able to work with geometry make their work more interesting and sometimes easier? The branch of mathematics that is concerned with the properties and relationships of...
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...Geometry Charades Objective: Learn basic geometrical terms playing games of charades. Materials: Charades cards with geometrical terms on them, pictures of each geometrical term so that the students can learn what each of them are before the game begins. A prize is needed for the student that wins the most amount of points at the end of the game. Directions: Each student will get a turn in the order of seating positions. The student who is up will draw a Charades card from the pile and act out whatever geometrical term is on the card. The student who is acting out the term has two minutes to get the crowd to guess what they are acting out. Students can raise their hands and guess what the person is trying to act out. The student that guesses the term correctly first wins a point. The student that acts out the term and gets someone in the crowd to guess what he or she is doing wins a point as well. I will keep account of each student’s point balances. Each student will get a turn regardless of who guesses the right answer. Cards: These are the following cards that students can choose: Parallel lines, line, line segment, intersecting lines, ray, right angle, acute angle, obtuse angle Accompanying Lesson Plan: Students will learn the geometry terms definitions, and what each term looks like in a picture before the game is played. The students will use their creativity to create the geometry term that they draw with their bodies in the game of...
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...Chapter 3: Triangles / Polygons Lesson 3-3: Triangle Inequalities Homework name ________________________ date ______________ period ___ For each set of lengths, determine whether it is possible to draw a triangle with sides of the given measures. If possible, write yes. If not possible, write no. 1. 3, 4, 5 _____ 2. 4, 9, 5 _____ 3. 5, 6, 12 _____ 4. 7, 3.5, 4.5 _____ 5. 4, 5, 8.5 _____ 6. .5, 1.2. .6 _____ The lengths of two sides of a triangle are given. Find the two numbers that the third side must fall between. 7. 3 and 8 _____ < x < _____ 8. 12 and 25 _____ < x < _____ 9. 13 and 4 _____ < x < _____ 10. 13 and 21 _____ < x < _____ Arrange the letters in order from greatest to least. 11. ___ > ___ > ___ 12. ___ > ___ > ___ 9 b c 35° 70° b 5 a c 12 a 13. ___ > ___ > ___ b 55° 14. ___ > ___ > ___ c a 15. ___ > ___ > ___ c a 26 b 22 15 c b 68° 24 a 17 28 16. What conclusion can we draw from this triangle? b a 61˚ 58˚ c c 24 a b 26 a b 58˚ 61˚ c 22 For questions 17 - 20 refer to the diagram below. A E 55° 30° B 40° 100° 50° C 17. What is the longest segment in CED ?_____ 18. Find the longest segment in ABE ._____ 19. Find the longest segment in the figure._____ 20. What is the shortest segment in BCDE?_____ D...
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...ships inside the Lager. In describing the gray zone, Levi discusses the different roles of prisoners assigned by the Nazi. The prisoners that did the work were seen as being more privileged which at the end of the day helped them get more food and live better. Therefore, the concept of the gray zone is analyzing the difference between the privileged and the non-privileged in the Lager. The difference can be seen by the tasks that the prisoners carried out, for example, one of the groups were seen as, “Low ranking functionaries... sweepers, kettle washers, night watchmen, bed smoothers... checkers of lice and scabies, messengers, interpreters, assistants’ assistants. In general, these people poor devils like ourselves, who worked full time like everyone else but who for an extra half liter of soup were willing to carry out these and other ‘tertiary’ functions.” This group was seen as harmless and not much different than the underprivileged. The other group of prisoners in the Lager was seen as the enemies to their own people. They were referred to as the Kapos who were “free to commit the worst atrocities on their subject as punishment for any transgressions, or even without any motive whatsoever: until the end of 1943 it was not unusual for a prisoner to be beaten to death by a Kapo without the latter having to fear any sanctions.” The prisoners that became part of the Kapo were seen as permanent. They were not accepted back by their people if they were willing to give...
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...Let the coordinates of point A be (x1 y1), the coordinates of B be (x2 y2), and the coordinates for C, which is a right angle, be (x2 y1) It is understood from the image that triangle ABC is a right angle triangle. AB is, in fact, the hyptenouse, and AC & BC are the corresponding sides. The length of the long leg, side AC, is equal to the difference in the x-coordinates of points C and A. Points C and B have the same x-coordinate, so the length of side AC is also equal to the difference in the x-coordinates of points B and A. So, AC = x2 − x1 The length of the short leg, side BC, is equal to the difference in the y-coordinates of points B and C. Points A and C have the same y-coordinate, so the length of side BC is also equal to the difference in the y-coordinates of points B and A. So, BC = y2 − y1 Thus, from pythagorous theorum... a2 + b2 = c2 We substitute... AB2 = AC2 + BC2 We substitute again... d2= (x2-x1)2 + (y2-y1)2 Now, we will take the square root of either side and arrive at the distance forumla... d = √(x2-x1)2 + (y2-y1)2 B. Let the coordinates of point A be (x1 y1 z1), of B be (x2 y2 z1), C be (x3 y3 z1), D be (x2 y2 z2) This derivation is two step process. First, we will find AB and, using it, we will find AD It is understood from the image that triangle ABC is a right angle triangle. AB is, in fact, the hyptenouse, and AC & BC are the corresponding sides Let's suppose that AC is actually along the x-axis while BC is along the y-axis Now triangle...
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...Philippine Normal University Taft Avenue, Manila Department of Mathematics A Detailed Lesson Plan in Grade 7 Mathematics on Angle-Sum Theorem of Polygons Submitted By: Kevin Emmanuel S. Deniega III- 34 BSE Mathematics Submitted to: Dr.Gladys Nivera February 5, 2013 Original Copy I. Objectives: At the end of a 30-minute period class the students should be able to: A. Explain how to get the sum of the interior angles of a convex polygon. B. Solve for the sum of the interior angles of an n-sided convex polygon. C. Determine the number of sides of a polygon based on the given sum of all the interior angles. D. Foster cooperation with his group mates in accomplishing the task assigned to their group. E. Present to the class the output of their group activity. F. Develop the act of helping his/her classmates in some of their difficulties in answering some problems. G. Respond to the questions of his/her classmates with regards to the question that he/she is answering. II. Subject Matter: Topic: Angle Sum Theorem of Polygons Materials: Puzzle, chart, worksheets, protractor References: Nivera, Gladys C. (2012).Patterns and Practicalities (K-12).Grade 7 Mathematics. Makati City: Don Bosco Press. Jose-Dilao, S. & Bernabe, J. (2002). Geometry. Quezon City: SD Publications. III. Instructional Strategies: A. Preparatory Activities 1. Prayer 2. Greetings 3. Checking of attendance ...
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...My Mathematical Understandings After completing this lesson, I have learned several things about geometric shapes. By physically manipulating strings into the desired shapes, I am now better able to grasp the relationships between sides and angles. It now makes sense that in order for lines to be parallel, the distance between the two lines must always be equal. However, the length of the lines does not need to be equal in order for the lines to be parallel (as seen in a trapezoid). In addition, these parallel lines must be in the same plane. Also, from this lesson, I learned some constraints and properties of shapes with four sides. Since I was physically able to manipulate a string and test several hypotheses surrounding quadrilaterals, it now makes sense that a quadrilateral with two pairs of parallel sides must have two pairs of congruent (meaning equal) sides. It is physically impossible to construct a quadrilateral with two pairs of parallel sides and only one pair of congruent sides. Moreover, from this activity, I learned some concepts surrounding angles in certain geometric shapes. It seems logical that opposite angles in a quadrilateral must equal 180 degrees. Otherwise, the shape would be impossible to construct. This activity raised many hypotheses for our group. First of all, the desired shapes that needed to be constructed made us question whether the shape was impossible. In addition, it also made us question whether our...
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...Geometry III Unit Test I. Fill in the blanks. 1. A plane is determined by _______________ non collinear points. 2. Points lie on one line are__________________. 3. __________________ points determine a line. 4. _______________points that lie in one plane. 5. Three or more points are _____________ if they lie in one line. 6. Line segment has______________ endpoints. 7. A portion of the line with only one end and which extends endlessly in only one direction is called _____________ 8. __________ has no length no width and no thickness and is represented by a dot. 9. __________ can be represented by the edge of the table. 10. ____________ has infinite length and width but no thickness. 1. Find the surface area of a rectangular prism with base length 10 cm, width 7 cm and height is 9 cm. 2. Find the volume of the square pyramid, the base side is 8 cm and the height is 12 cm? 3. The angles of a triangle have the ratio 2:5:8. What is the measure of the largest angle? a. 60 b. 72 c. 84 d.96 4. The perimeter of a regular hexagon with side length of 4.5cm. a. 22.5 cm b. 27 cm c. 31.50cm d. 40.5 cm 5. A rectangle has a width of 9cm and a length of 19cm. What is the perimeter? a. 40 cm ...
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...The Fencing Problem - Math The task -------- A farmer has exactly 1000m of fencing; with it she wishes to fence off a level area of land. She is not concerned about the shape of the plot but it must have perimeter of 1000m. What she does wish to do is to fence off the plot of land which contains the maximun area. Investigate the shape/s of the plot of land that have the maximum area. Solution -------- Firstly I will look at 3 common shapes. These will be: ------------------------------------------------------ [IMAGE] A regular triangle for this task will have the following area: 1/2 b x h 1000m / 3 - 333.33 333.33 / 2 = 166.66 333.33² - 166.66² = 83331.11 Square root of 83331.11 = 288.67 288.67 x 166.66 = 48112.52² [IMAGE]A regular square for this task will have the following area: Each side = 250m 250m x 250m = 62500m² [IMAGE] A regular circle with a circumference of 1000m would give an area of: Pi x 2 x r = circumference Pi x 2 = circumference / r Circumference / (Pi x 2) = r Area = Pi x r² Area = Pi x (Circumference / (Pi x 2)) ² Pi x (1000m / (pi x 2)) ² = 79577.45m² I predict that for regular shapes the more sides the shape has the higher the area is. A circle has infinite sides in theory so I will expect this to be of the highest area. The above only tells us about regular shapes I still haven't worked out what the ideal shape is. Width...
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