TEXAS BOARD OF WATER ENGINEERS

Sbanist

Description

• fiche de synthèse - matière potentielle : the mineral resources of the county

TEXAS BOARD OF WATER ENGINEERS R. M. Dixon, Chairman H. A. Beckwith, Member O. F. Dent, Member s··1'fJ. ~ 1\fi l~J r.:\. . ,: ... .- .. ........:........ BULLETIN 5601 GEOLOGY AND GROUND-WATER RESOURCES OF MEDINA COUNTY, TEXAS Prepared in lcooperation with the Geological Survey, __..__ ~;1I!cL printing COI'iE'1.

• county higlxwsys
• northern part of the county
• cretaceous formations
• edwards limestone
• quarry 10.8 miles
• leona formation
• wells
• county seat
• limestone
• county

Sujets

• Crossing
• Relation
• Quaternary
• Medina County
• Printing
• Figure

Informations

• Publié par: udwi
• Nombre de lectures: 19
• Langue: English

Extrait

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Vocabulary List Geometry Altitude- the perpendicular distance from the vertex to the opposite side of the figure (base)  Face- one of the polygons of a solid figure  Diagonal- a line segment that joins two vertices of a polygon but is not a side  Polygon- a closed plane figure formed by three or more line segments  Congruent- having the same size and shape  Similar figures- figures with the same shape but not necessarily the same size  Isosceles triangle- a triangle with exactly two congruent sides  Scalene triangle- a triangle with no congruent sides  Equilateral triangle- a triangle with three congruent sides  Acute triangle- a triangle with all angles less than 90°  Right triangle- a triangle with one right angle  Obtuse triangle- a triangle with one angle greater than 90°  Reflection- a movement of a figure by flipping it over a line  Rotation- a movement of a figure by turning it around a fixed point  Translation- a movement of a figure along a straight line, only the location changes  Dilation- a proportional shrinking or enlargement of a figure   Perpendicular lines- 2 lines that intersect to form a right (90°) angle  Parallel lines- lines in a plane that are always the same distance apart

GEOMETRY (GRAPHIC ORGANIZER)  Using Venn Diagrams, have students show the similarities and differences between the following shapes:  Rectangle, square and rhombus

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 Expand with other shapes- (Two dimensional and three dimensional geometric figures) Students can draw own Venn diagrams on paper if needed

Angle Exploration and Classification (Hands-On Activity)   PREPARATION: To prepare for the lesson, purchase a box of uncooked spaghetti. Cut out small triangle arrows, 6 for each student. To save time, give students a small square of construction paper to cut out the triangle arrows. Students tape the arrows on to one end of the spaghetti pieces to make rays for the angles.  1. Distribute three pieces of uncooked spaghetti and six small arrows to each student. Have  students break one of the spaghetti pieces into half. 2. Instruct students to make rays by taping an arrow to one end of the spaghetti. Tell students that a ray is a line segment that has a beginning point but no end point. 3. Direct students to make an angle from the two large pieces of spaghetti. Observe the spaghetti angles and see which direction the rays are pointing. Assist students who have the rays pointing toward the vertex of the angle. 4. In small groups, have students share their angles. Have them compare the angle sizes and describe them as acute, obtuse, right or straight. 5. Ask students if they can make a larger angle than the one created with the smaller spaghetti pieces. Allow students to think about their response and turn to partner and discuss each others response. Listen to the discussions and make anecdotal notes of the different ideas students have. Select students having different responses to share with the class and record on the board. 6. Ask the students: •What determines the measure of an angle? •What characteristic of the angle is measured? Allow students to discuss in small groups and share responses with the class. 7. Clarify for students that the angle measure is the degree the rays are rotated from one another. Demonstrate on the overhead by rotating spaghetti rays away from and closer to each other. Tell students we measure angles in degrees. 8. Direct students to make a right angle with both sizes of spaghetti. Tell students that a right angle has a measure of 90 degrees. Ask students to think about how to describe the measure of acute, obtuse and straight angles and share with a partner. 9. Ask students to describe the measures of an acute, obtuse and straight angle. An acute angle measures less than 90 degrees, an obtuse angle measures more than 90 degrees and a straight angle measures 180 degrees. If students struggle with a straight angle, have them think about going around the clock. Every three hours, the hour hand rotates 90 degrees. So how many degrees would the hour hand move in six hours or half way around? 10. Direct students to create two angles with equal measures. Allow them to break the spaghetti pieces into different sizes. Encourage students to describe their angles using appropriate mathematical terms. Provide additional practice using a variety of angles with varying degrees and ray lengths. 11. Have students reflect on their learning and record in their journal. a. Review vocabulary by recording and defining terms such as ray, rotate and degrees.

b. Describe how to measure an angle. c. Confirm that the lengths of the sides do not determine the angle measure.  Differentiated Instructional Support: Instruction is differentiated according to learner needs, to help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified indicator(s). •Have six students form two angles with string overlapping, one using string four feet in length and the other eight feet in length. One student, for each angle, represents the vertex of the angle by holding the middle of the four-foot string or middle of the eight-foot string.  Each of the remaining four students holds the end of the strings to complete the rays of the angle. Have students at the end of the string stand close to one another and then have one of the students slowly walk away, increasing the size of the angle. Have students stop at various points to have the class identify and describe the angles as an acute angle, right angle, obtuse angle and straight angle. Students compare the two angles that are formed. At the point when both angles are congruent, students discuss how the two angles can be congruent even if the lengths of the sides are different. •Have students use their arms to create a 90-degree angle and then use fingers to show a 90- degree angle. Show that they are the same measurement. Follow with other angle sizes for comparison. •Have students experiment with a protractor to accurately measure angles.  Extension: Have students draw and label angles and place them in order from greatest to the least using the degrees of rotation.  Home Connection: Have students complete a scavenger hunt to find various objects with angles at home. Have students draw, label, compare and describe the angles.  Materials and Resources: For the teacher: uncooked spaghetti, construction paper, overhead, two lengths of string approximately three feet and six feet in length  For the student:three full-sized pieces of uncooked spaghetti per student (two full- scissors, sized pieces and two half-sized pieces)   Adapted from: https://ims.ode.state.oh.us/ODE/IMS/Lessons/Content/CMA_LP_S03_BD_L05_I07_01.doc     

 Peggys Pizza Parlor (Writing Activity)  Peggys Pizza Parlor offers two 10-inch pizzas for the same price as the 16-inch pizza. Which is the better buy? Explain below.  __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________

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Peggys pepperoni special ad states that every 12-inch pepperoni pizza has 100 pepperoni slices. If the pepperoni slices measure 1-inch across, can the ad be true? If it is, how much of the 12-inch pizza does not have pepperoni on it? __________________________________________________________

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 GEOMETRY GAMES  Below are websites with interactive geometry games for students to explore and play online.  http://www.apples4theteacher.com/math.html#ge ometrygames  http://www.funbrain.com/poly/  http://www.gamequarium.com/geometry.html  http://classroom.jc- schools.net/basic/mathgeom.html  http://www.aaaknow.com/geo.htm#topic18  http://www.coolmath4kids.com/geometrystuff.ht ml  Blokusis a new game out in stores that challenges geometric thinking. This is a great one to have in the classroom. 

   MINUTE DAILY REVIEW Geometry  1. Circle the name of the triangle:

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  Equilateral Isosceles Scalene   2. Are these lines parallel or perpendicular? _____________  _____________ 

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3. Circle the greater number: 54 inches or 5 feet  4. A chord is a line segment with both endpoints on the circle.  Circle: True or False  5. V = l x w x h Circle: True OR False  6. Two names for the line segment are __________________ and _____________.  J ____________ H  7. A ratio is the comparison of two quantities. Circle: True OR False

 8. Is this a regular polygon? 

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