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Words 1838

Pages 8

The following series of worksheets were written to help students discover some relationships with angles that are created by tangents, chords, and secants in circles. Lesson: Central and Inscribed Angles Grade Level: Secondary Level (Geometry) Sunshine State Standard: MA.A.1.4.2, MA.A.2.4.2, MA.B.1.4.2, MA.B.2.4.1, MA.B.4.4.1, MA.C.1.4.1, MA.C.2.4.1, MA.D.1.4.1 Materials: • Students: The use of GeoGebra dynamic worksheets • Teachers: Projection of GeoGebra dynamic worksheets Objectives: 1. Students will discover properties of an angle inscribed in a circle 2. Students will discover properties of the interior angles of a cyclic quadrilateral. 3. Students will discover properties of angles that are formed when two chords of a circle intersect. 4. Students will discover properties of angles formed by two intersecting secants of a circle. 5. Students will be able to find the center of a circle. Vocabulary: tangent line (segment), secant line (segment), central angle, inscribed angle, cyclic quadrilateral, chord, diameter, radius, right angle, arc (major and minor), intercepted arc, measure (angles and arcs), center, perpendicular bisector Lesson Plan: (These lessons should be taught during a unit on circles. Each separate

dynamic worksheet topic will probably take one class setting, approximately 50 minutes.)

-To start a discussion about circles it may be a good idea to discuss some definition of terms that deal with a circle. Displaying a image similar to one shown below and having students recall what different geometrical figures are called may be one way of starting a lesson on circles.

The following descriptions should be mentioned if using the image above: The above circle is called “Circle O”, because the center of the circle is the point “O”. DE is a chord - segment whose endpoints lie on the circle. AB is a diameter - longest chord,…...

...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......

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... i. b. c. d. 8. If the mean of x, x +2, x+4, x+ 6, x+ 8 is 24, then x = j. 22 b. 21 c. 20 d. 24 SECTION – B 9. The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. Assume π = 22/7. 10. In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. 11. The blood groups of 30 students of Class VIII are recoded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. Represent this data in the form of a frequency distribution table. 12. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 13. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc. ar (APB) = ar (BQC). 24. In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = ar (ABC) SECTION – D 25. If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord. 26. Prove that parallelograms on the same base and between same parallels have the same area. 27. ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA......

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...Lesson Plan Teacher Class Subject Date Duration Topic Objectives Material Needed Methodology Shelina.N.Bhamani 5-6 English (Creative Writing) Tuesday, March 29, 2005 45 mins Shape Poem The Student will be able to: 1=Share and write more creactive ideas. 2=Describe different objects Papers Pens Charts Markers Colours OHP(OHT)for the presentation of sample poem(WB can be used too) PRESENTATION: The Teacher will ask the student following questions.(How many of you like butterfly/balloon? Why ou like balloons/butterfly? Do you love poems(yes/no) well,then lets try to write one. Teacher will show an example or two like of balloon(MY RED BALLOON IS LIKE AN AEROPLANE WITHOUT WINGS.IT FLOATS LIKE A BIRD IN THE SKY.A STRONG WIND MAKES MY BALLOON RUN FAST AND TO THE GROUND.POP!OHNO..PIECE OF RUBBER DRIFTING TO THE GROUND)Than SS will asked to choose shapes draw it and write a peom inside that shape) for production you can display all the shapes poems on the school board /bulletin board/soft board.. production stage could be considerd as evaluation Evaluation Lesson Plan Teacher Class Subject Date Duration Topic Objectives Material Needed Methodology Sonia Sham Dupte grades 3-4 language arts Tuesday, March 01, 2005 30 mins telling a story Students will learn how to use descriptive and imaginative language to tell a story. * Telling a Story pictures (allow each student to choose their own picture) * paper * pencils Discuss with students the structure of a good story. Stress that...

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...Lesson Title: You, Your Best Friend and the School Store! Grade Level: Third Subject/Topic Area: Mathematics Designed by: Time needed: 50 minutes Key Vocabulary: Money, Coins, Pennies, Nickels, Dimes, Quarters, Combination, Total, Determine, Pictorially, Scenario, Purchases, Journal Lesson Summary: The purpose of this lesson is for students to use number, operation and quantitative reasoning skills as well as demonstrate the ability to determine the value of a collection of coins. This is primarily an inquiry based lesson where students will be using a performance task which will be used to “place” students in a situation which could occur in “real life” involving money falling from their pocket, and a friend’s pocket, onto the ground. Students will have to use mathematical skills and reasoning to figure out which of the 16 coins they find on the ground belong to them and to their friend and the dollar amount to which each persons coins add up to. In part two of the performance task, students will again use empathy as they “visit” the school store. Students will have figured out how much money they have to spend in the school store in part one of the performance task. Students will be allowed to buy as many items as they can in the school store with one caveat – they must have one coin left over after their shopping spree. Established Goals: MST Learning Standard #3: Math 2. Students use number sense and numeration to ...

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... Circle Section A. 1 Mark Each Q.1 if a line segment, having its end point on a circle, is known as (a) Chord (b) Secant (c) Tangent (d) none of these Q.2 number of tangents that can be drawn through a point which is inside the circle is (a) 3 (b) 2 (c) 1 (d) 0 Q.3 A line through point of contact and passing through centre of circle is known as (a) tangent (b) Chord (c) normal (d) segment Q.4 A circle is inscribed in a triangle with sides 3, 4 and 5 cm. The radius of the circle is (a) 6 cm (b) 5 cm (c) 4 cm (d) none of these Q.5 Distance between two parallel lines is 10 cm. The radius of circle which will touch both two lines is (a) 5cm (b) 7 cm(c ) 12 cm (d) None of these Section B. 2 Mark Each Q.6 In figure, CP and CQ are tangents to a circle with centre O. ARB is anothertangent touching the circle at R. If CP = 12 cm, and BC = 8cm, then find the length of BR. Q.7 In figure AB is a chord of the circle and AOC is its diameter such that ABC 500 . If AT is the tangent to the circle at the point A, find BAT www.cbsesmart.weebly.com “Chase Excellence- Success Will Follow” ll Follow” “Chase Excellence- Success Will Follow” 2011 For more free sample papers and test papers Visit http://jsunilclasses.weebly.com company address] Page 2 Q.8 Two tangents PA and PB are drawn to the circle with centre,......

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...Online Reference & Tools Home>Math>Math symbols> Math symbols Mathematical Symbols List of all mathematical symbols and signs - meaning and examples. Basic math symbols Geometry symbols Algebra symbols Probability & statistics symbols Set theory symbols Logic symbols Calculus & analysis symbols Number symbols Greek symbols Roman numerals Basic math symbols Symbol Symbol Name Meaning / definition Example = equals sign equality 5 = 2+3 ≠ not equal sign inequality 5 ≠ 4 > strict inequality greater than 5 > 4 < strict inequality less than 4 < 5 ≥ inequality greater than or equal to 5 ≥ 4 ≤ inequality less than or equal to 4 ≤ 5 ( ) parentheses calculate expression inside first 2 × (3+5) = 16 [ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18 + plus sign addition 1 + 1 = 2 − minus sign subtraction 2 − 1 = 1 ± plus - minus both plus and minus operations 3 ± 5 = 8 and -2 ∓ minus - plus both minus and plus operations 3 ∓ 5 = -2 and 8 * asterisk multiplication 2 * 3 = 6 × times sign multiplication 2 × 3 = 6 ∙ multiplication dot multiplication 2 ∙ 3 = 6 ÷ division sign / obelus division 6 ÷ 2 = 3 / division slash division 6 / 2 = 3 – horizontal line division / fraction mod modulo remainder calculation 7 mod 2 = 1 . period decimal point, decimal separator 2.56 = 2+56/100 ab power exponent 23 = 8 a^b caret exponent 2 ^ 3 = 8 √a square root √a • √a = a √9 = ±3 3√a cube root 3√a • 3√a • 3√a = a 3√8 = 2 4√a fourth root 4√a...

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... * Solve linear equations in one unknown * Understand and use lines parallel to the axes, y = x and y = -x * Calculate surface area of cubes and cuboids * Understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines | * Know the first 6 cube numbers * Know the first 12 triangular numbers * Know the symbols =, ≠, <, >, ≤, ≥ * Know the order of operations including brackets * Know basic algebraic notation * Know that area of a rectangle = l × w * Know that area of a triangle = b × h ÷ 2 * Know that area of a parallelogram = b × h * Know that area of a trapezium = ((a + b) ÷ 2) × h * Know that volume of a cuboid = l × w × h * Know the meaning of faces, edges and vertices * Know the names of special triangles and quadrilaterals * Know how to work out measures of central tendency * Know how to calculate the range | Counting and comparing | 4 | | | Calculating | 9 | | | Visualising and constructing | 5 | | | Investigating properties of shapes | 6 | | | Algebraic proficiency: tinkering | 9 | | | Exploring fractions, decimals and percentages | 3 | | | Proportional reasoning | 4 | | | Pattern sniffing | 3 | | | Measuring space | 5 | | | Investigating angles | 3 | | | Calculating fractions, decimals and percentages | 12 | | | Solving equations and inequalities | 6 | | | Calculating space | 6 | | | Checking, approximating and estimating | 2 | | | ......

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...for a grade and a subject have been compiled into one comprehensive set, the learner does not have to respond to the whole set in one sitting. The teacher should select exemplar questions that are relevant to the planned lesson at any given time. Carefully selected individual exemplar test questions, or a manageable group of questions, can be used at different stages of the teaching and learning process as follows: 1.1 At the beginning of a lesson as a diagnostic test to identify learner strengths and weaknesses. The diagnosis must lead to prompt feedback to learners and the development of appropriate lessons that address the identified weaknesses and consolidate the strengths. The diagnostic test could be given as homework to save instructional time in class. 1.2 1.3 During the lesson as short formative tests to assess whether learners are developing the intended knowledge and skills as the lesson progresses and ensure that no learner is left behind. At the completion of a lesson or series of lessons as a summative test to assess if the learners have gained adequate understanding and can apply the knowledge and skills acquired in the completed lesson(s). Feedback to learners must be given promptly while the teacher decides on whether there are areas of the lesson(s) that need to be revisited to consolidate particular knowledge and skills. At all stages to expose learners to different techniques of assessing or questioning, e.g. how to answer multiple-choice (MC) questions,......

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...Titles in the series Stories about Maxima and Minima: v.M. Tikhomirov Fixed Points: Yll. A. Shashkin Mathematics and Sports: L.E. Sadovskii & AL Sadovskii Intuitive Topology: V. V. Prasolov Groups and Symmetry: A Guide to Discovering Mathematics: David W. Farmer Knots and Surfaces: A Guide to Discovering Mathematics: David W. Farmer & Theodore B. Stanford Mathematical Circles (Russian Experience): Dmitri Fomin, Sergey Genkin & Ilia Itellberg A Primer of Mathematical Writing: Steven G. Krantz Techniques of Problem Solving: Steven G. Krantz Solutions Manual for Techniques of Problem Solving: Luis Fernandez & Haedeh Gooransarab Mathematical World Mathematical Circles (Russian Experience) Dmitri Fomin Sergey Genkin Ilia Itenberg Translated from the Russian by Mark Saul Universities Press Universities Press (India) Private Limited Registered Office 3-5-819 Hyderguda, Hyderabad 500 029 (A.P), India Distribllted by Orient Longman Private Limited Regisfered Office 3-6-752 Himayatnagar, Hyderabad 500 029 (A.P), India Other Office.r BangalorelBhopaVBhubaneshwar/Chennai Emakulam/Guwahati/KolkatalHyderabad/Jaipur LucknowlMumbailNew Delhi/Patna ® 1996 by the American Mathematical Society First published in India by Universities Press (India) Private Limited 1998 Reprinted 2002, 2003 ISBN 81 7371 115 I This edition has been authorized by the American Mathematical Society for sale in India, Bangladesh, Bhutan, Nepal, Sri Lanka, and the Maldives only. Not for...

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...the Greeks by pretending to be Achilles and thus frightening the Trojans. Leading Achilles’ men, the Myrmidons, into battle, Patroclus fights valiantly but is killed by Hector’s spear. Achilles grieves terribly and decides to return to battle to avenge this death. Thetis, seeing she can no longer hold her son back, gives him armor made by Hephaestus himself. The Trojans soon retreat inside their impenetrable walls through the huge Scaean gates. Only Hector remains outside, clad in Achilles’ own armor taken from Patroclus’s corpse. Hector and Achilles, the two greatest warriors of the Trojan War, finally face one another. When Hector sees that Athena stands by Achilles’ side while Apollo has left his own, he runs away from Achilles. They circle around and around the city of Troy until Athena disguises herself as Hector’s brother and makes him stop. Achilles catches up with Hector, who realizes the deception. They fight, and Achilles, aided by Athena, kills Hector with his spear. Achilles is still so filled with rage over Patroclus’s death that he drags Hector’s body over the ground, mutilating it. He takes it back to the Greek camp and leaves it beside Patroclus’s funeral pyre for dogs to devour. Such disrespect for a great warrior greatly displeases the gods, who convince Priam to visit Achilles and retrieve Hector’s body. Priam speaks to Achilles, who sees the error of his ways. The Iliad ends with Hector’s funeral.......... The war itself does not end with Hector’s......

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...discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts. It was used in Babylonia and in the Indus Valley by the Egyptians, Babylonians, and the people of the Indus Valley but the creators were Pythagoras, Euclid, Archimedes, and Thales. Pythagoras was the first pure mathematician although we know little about his mathematical achievements. He was also, a greek philosopher and created a movement called Pythagoreanism. Euclid is sometimes called Euclid of Alexandria. He is also called the “Father of Geometry” and his elements were one of the most influential works in the history of mathematics, which served as a textbook used for teaching mathematics (especially Geometry) from when it was published till the late 19th century to early 20th century. In the Elements he included the principles of what is now called Euclidean Geometry. Euclidean Geometry is a mathematical system and consists of in a small set of appealing postulates that are accepted as true. In fact, Euclid was able to come up with a great portion of plane geometry from five postulates. These postulates include: A straight line segment can be drawn joining any two points, to extend a finite straight line continuously in a straight line, given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center, all right angles are congruent, and if two......

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...activity without much help? 3. Did the students talk about their hypotheses with one another? 4. Did the students make predictions about other insects, and creatures? 5. Did the students use words from the lesson in their play following the activity? 6. Did this lesson lead students to talk about other creatures and their possible skeletons? 7. Did this lesson create a desire to learn about other insects? 8. Was this lesson able to flow into another lesson allowing for connected, continuous learning? EXTENSION: 1. What if we had a skeleton like an ant? 2. What if ants had a skeleton like us? 3. What if we had both types of skeleton? 4. What if we did not have a skeleton? Out for the Count, by Kathryn Cave and Chris Riddell, is a counting storybook featuring numbers up to 100. The rhyming story describes the night-time adventures of Tom, who lies in bed counting sheep trying to fall asleep. Soon, Tom finds the sheep leading him, and his trusty stuffed-rabbit companion, into a wild woodland that is anything but restful. He meets wolves, pythons, mountain goats, pirates, penguins, vampire bats, tigers and ghosts in ever increasing quantities. To survive, he hides or races away by car, on foot, or on skis, but always counting. This book focuses on the math concepts of number sense and counting. An extension activity for this book would be to have the students create their own “Out for the Count” book. The book would start at 100, and increase by......

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...Detailed Lesson Plan in Mathematics II I. Objectives At the end of the lesson, the pupils will be able to: * Visualize unit fractions with denominators 10 and below. * Identify unit fractions with denominators 10 and below. * Work cooperatively with teammates. II. Subject Matter Topic: Unit Fractions Reference: Teacher Guide for Mathematics Grade 2 pp. 216-217 Materials: chalkboard, illustrations, realias, worksheets, sticks III. Procedure Teacher’s ActivityA. Preparatory Activities 1. Prayer“Sunny will you lead ou prayer?” 2. Greetings “Good morning, class!” “Take your seat.” 3. Checking of Attendance“Class monitors, who are absent today?” 4. Energizer“To start our day, let us first do an ice breaker. So kindly stand up.”“Let us have an exercise. I will show you the steps and you will repeat after me.” 5. Drill“I have here a basket of different fruits and vegtables. Classify whether it is divided into halves or fourths. State your answer by raising your sticks. 6. Motivation“Do you want to hear a story? ”“Alright then, I will tell you a story entitled Snack Time”. Pay attention and listen to me carefully.”SNACK TIMEOne day Sunny is playing outside when she heard her mom calling “Sunny come here quickly! I prepare some snacks for you.” said Sunny’s mom.“ I’m hungry! I’m going to eat some snacks. I’ll continue playing later.” she thought.So she went into the kitchen. She found some snacks that her mom......

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...which is obtained in a very precise way. Imagine a vertical line, and a second line intersecting it at some angle f (phi). We will call the vertical line the axis, and the second line the generator. The angle f between them is called the vertex angle. Now imagine grasping the axis between thumb and forefinger on either side of its point of intersection with the generator, and twirling it. The generator will sweep out a surface, as shown in the diagram. It is this surface which we call a cone. Notice that a cone has an upper half and a lower half (called the nappes), and that these are joined at a single point, called the vertex. Notice also that the nappes extend indefinitely far both upwards and downwards. A cone is thus completely determined by its vertex angle. Now, in intersecting a flat plane with a cone, we have three choices, depending on the angle the plane makes to the vertical axis of the cone. First, we may choose our plane to have a greater angle to the vertical than does the generator of the cone, in which case the plane must cut right through one of the nappes. This results in a closed curve called an ellipse. Second, our plane may have exactly the same angle to the vertical axis as the generator of the cone, so that it is parallel to the side of the cone. The resulting open curve is called a parabola. Finally, the plane may have a smaller angle to the vertical axis (that is, the plane is steeper than the generator), in which case the plane will......

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...9:55 – 11:15 Math III – 1 1:00 - 2:20 Math III - 2 I. Objective: * Compare values of the different denominations of coins and bills through P1000 Value: Gratitude II. Subject Matter: Comparing values of the different denominations of coins and bills through P1000 References: BEC PELC – I A. 4. 3. Materials: Philippine money, play money, flashcards, charts III. Procedure: A. Preliminary Activities: 1. Drill: Write greater than, less than or equal to the following a. P50.00 __ P100.00 b. 2 ten peso bills __ P30.50 2. Review: Write the money values in symbols. a. nine hundred fifty pesos and fifty centavos b. seven hundred seventy-eight pesos and twenty five centavos 3. Motivation: Did you also receive Christmas gifts from your godparent? What did you say after you receive such gift? B. Developmental Activities: 1. Presentation: a. Last Christmas Edmar’s godparents gave him P500 P100P100 P50 . Allyssa’s godparents gave her P1 000 Edmar received P750 while Alyssareceived P1000. Let us compare the amounts. Use >, < or =. Which is more, 750 or 1000? Which is less? 2. Guided Practice Compare the following. Write >, < or = 1. P 955 ____ P 595 2. P 1 000 ____ P 100 3. P 99 ____ P59 4. P......

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