IDENTIFICACIÓN DEL MATERIAL AICLE TÍTULO Plane figures NIVEL LINGÜÍSTICO A2.1 IDIOMA Inglés MATERIA Matemáticas NÚCLEO TEMÁTICO Geometría GUIÓN TEMÁTICO Identificación de figuras planas. Descripción y clasificación de las mismas utilizando el vocabulario básico de la unidad. Aplicación del Teorema de Pitágoras a la resolución de problemas. Cálculo de perímetros y superficies y su aplicación a la resolución de problemas de la vida cotidiana. FORMATO PDF CORRESPONDENCIA 1º de E.S.O. CURRICULAR AUTORÍA Eva Mª Espinosa Pulido TEMPORALIZACIÓN 8 sesiones COMPETENCIAS BÁSICAS Competencia en comunicación lingüística: Conocer, adquirir, ampliar y aplicar el vocabulario básico del tema. Ejercitar una lectura comprensiva de textos relacionados con el núcleo temático Dialogar y discutir con los compañeros sobre las actividades propuestas Competencia matemática Conocer e identificar los diferentes figuras planas Calcular sus perímetros y áreas. Resolver problemas cotidianos y reales en los que aparezcan figuras planas. Utilizando el Teorema de Pitágoras o el perímetro o el área de las mismas. Aprender a aprender Reconocer figuras planas en su entorno para poder aplicar los conocimientos de la unidad en la resolución de problemas reales. Ser capaces de aprender a calcular perímetros y áreas a partir de la información de la secuencia. Autonomía e iniciativa personal Conocer y poner en práctica las fases de desarrollo de un proyecto. Planificar, identificar objetivos y gestionar el tiempo con eficacia. Social y ciudadana Ser capaz de trabajar en grupo Tratamiento de la información y competencia digital Buscar y seleccionar información con distintas técnicas según la fuente o el soporte, valorando su fiabilidad. OBSERVACIONES La unidad está pensada para 1º de ESO pero también puede utilizarse para trabajar esto contenidos en cursos posteriores fundamentalmente en 2º de ESO. La unidad puede ir acompañada de más actividades de aplicación de lo aprendido a situaciones de la vida cotidiana del alumno. 1º de ESO: Plane figures 2
TABLA DE PROGRAMACIÓN AICLE OBJETIVOS DE ETAPA Asumir responsablemente sus deberes, conocer y ejercer sus derechos en el respeto a los demás, practicar la tolerancia, la cooperación y la solidaridad entre las personas y grupos. CONTENIDOS CURSO/CICLO DE Desarrollar y consolidar hábitos de disciplina, estudio y trabajo individual y en equipo. Desarrollar destrezas básicas en la utilización de las fuentes de información para, con sentido crítico, adquirir nuevos conocimientos. Adquirir una preparación básica en el campo de las tecnologías, especialmente las de la información y la comunicación. Concebir el conocimiento científico como un saber integrado, así como conocer y aplicar los métodos para identificar los problemas en los diversos campos del conocimiento y de la experiencia. Desarrollar el espíritu emprendedor y la confianza en sí mismo, la participación, el sentido crítico, la iniciativa personal y la capacidad para aprender a aprender, planificar, tomar decisiones y asumir responsabilidades. Comprender y expresarse en una o más lenguas extranjeras de manera apropiada. Apreciar la creación artística y comprender el lenguaje de las distintas manifestaciones artísticas, utilizando distintos medios de expresión y representación. Figuras planas. Perímetros y áreas de figuras planas. Teorema de Pitágoras TEMA O SUBTEMAS Clasificación de figuras planas. Elementos de las figuras planas. Teorema de Pitágoras. Aplicaciones. Perímetros y Áreas de figuras planas. Presencia de las figuras planas en el entorno del alumno. MODELOS DISCURSIVOS Clasificar las distintas figuras planas y describirlas utilizando sus elementos. Explicar en qué consiste el Teorema de Pitágoras y cuál es su aplicación en la resolución de problemas. Identificar las fórmulas para el cálculo de perímetros y áreas de figuras planas. Explicar cuál es la presencia de distintas figuras planas en el entorno del alumno. 1º de ESO: Plane figures 3
Dialogar para la resolución de actividades que requieren la colaboración y el trabajo en grupo del alumnado. TAREAS Lluvia de ideas relacionada con la identificación de figuras planas en el entorno del alumno. Audición y lectura comprensiva de textos. Realización de sopa de letras y crucigramas para el conocimiento y la consolidación de vocabulario. Realización de mapas conceptuales para relacionar los contenidos de la secuencia. Búsqueda de información acerca del cálculo de perímetros y áreas. Proyecto final de identificación de figuras planas en el entorno del alumno. Exposición oral de la información obtenida. Construcción de circunferencias asociadas a un triángulo. Autoevaluación. CONTENIDOS LINGÜÍSTICOS FUNCIONES: Comprender información general y específica de textos escritos. Escuchar y comprender información de mensajes orales. Sintetizar y seleccionar datos de las diferentes fuentes de información y transmitirlas de manera coherente al resto. Describir y clasificar las figuras planas presentes en el entorno del alumno. Explicar el procedimiento necesario para calcular el perímetro y el área de una figura plana. Dialogar y expresar opinión sobre los diferentes aspectos de la unidad, respetando las opiniones diferentes a las propias. ESTRUCTURAS: I think / In my opinion I can use to It s difficult/easy to say if /that Do you find? What direction is in? Can you show me where is? It s in column and row The biggest difference between and is that I agree/ disagree with you because Can you help me with the word? Do you know the first letter of? What do you think is? How do you spell? Where would you put? Please tell us what is connected with. I wrote next to 1º de ESO: Plane figures 4
Can you show me..? This is called. The height is.. cm To calculate you have to Do you have any doubt? Do you understand me? / Can you repeat? I haven t understood What is the perimeter/surface of..? Calculate the.. of.. whose What figure appears in.? Can you remind me of? LÉXICO: Triangles, quadrilaterals, polygons, circles, circumference, area and perimeter, equilateral, isosceles, scalene, acute, obtuse, right, perpendicular, bisector, circumcentre, altitude, orthocenter, angle bisector, incentre, medians, barycentre, hypotenuse, leg, octagon, area, diagonal, kite, Rhombus, apothem, radius. CRITERIOS EVALUACIÓN DE Distingue los tipos de figuras planas y sus elementos. Identifica triángulos rectángulos, así como sus elementos y características. Resuelve problemas utilizando el Teorema de Pitágoras. Reconoce los puntos y rectas asociados a un triángulo. Construye circunferencias inscritas y circunscritas a un triángulo dado. Calcula el perímetro y el área de las diferentes figuras planas. Resuelve problemas que impliquen el cálculo de perímetros y áreas de las figuras planas estudiadas. Reconoce y valora la presencia de figuras planas en su entorno. 1º de ESO: Plane figures 5
Plane Figures 1.- Brainstorm Look around you and answer the questions. Try to use the words on the right in your answers. What shape is each of the traffic signs you see in the pictures? Do you know another traffic signs with the same shape? What other shapes can you find around you? In my opinon the is I can use to measure It s difficult to say if is It s easy to say that is 1º de ESO: Plane figures 6
2.- Word search Find the words in the list on the right: Do you find? What direction is in? (Forward/ backward/ up/ down/ diagonal) Can you show me where is? It s in column and row 1º de ESO: Plane figures 7
3.- Listen to the text about points and lines associated with a triangle. Then, fill the gaps with some words from the previous activity: A perpendicular of a triangle is a straight line passing through the midpoint of a side and perpendicular to it. The three perpendicular meet in a single point, it is called the triangle s ; this point is the centre of the circumcircle. An of a triangle is a straight line through a vertex and perpendicular to the opposite side. The three altitudes intersect in a single point, called the of the triangle. An angle of a triangle is a straight line through a vertex, which cuts the corresponding angle in half. The three angle intersect in a single point called the, which is the centre of the triangle s incircle. A of a triangle is a straight line through a vertex and the midpoint of the opposite side. The three intersect in a single point, the triangle s. 4.- a) Match each point with the corresponding lines. 1. Barycentre a. Perpendicular bisectors 2. Incentre b. Altitudes 3. Circumcentre c. Medians 4. Orthocentre d. Angle bisectors b) What is the difference? Perpendicular bisectors-angle bisectors Altitudes-Medians Incentre-Circuncentre The main difference between and is I think they are similar but with a little difference, that is In my opinion, you re right but it s more important to emphasize that I agree/ disagree with you because 1º de ESO: Plane figures 8
5.- Read the following text and watch the video: PYTHAGOREAN THEOREM In all right triangles, the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse. PYTHAGOREAN EQUATION Leg 2 + Leg 2 = Hypotenuse 2 6.- Then, solve the following problems: a) A painter is on top of a 35 feet ladder that is leaning against a house. The base of the ladder is 21 feet from the base of the house. If the painter were to fall, how far down would his fall be? b) John wants to put his TV on sale. The problem is that John forgot the inches of his TV. TVs are advertised by the inches of the diagonal. John knows the width of the TV is 45in and the high is 28in. How many inches should John advertise his TV as? 7.- Now, have fun with the following video (from mathstory.com): Hypotenuse, (right triangle) Is the longest side... (right triangle) Hypotenuse, (right triangle) Is the longest side...(right triangle) It's not the shortest, Or the next, It's the longest side, Like the kiddies like to ride, Like a playground slide... Obtuse, they must be playin', They won't wanna' tangle, Acute's don't have hypotenuse, Like a right triangle... Acutes and obtuse, Have no hypotenuse now, No angles of 90 degrees... Acutes and obtuse, Have no hypotenuse now, No angles of 90 degrees... Hypotenuse, (right triangle) Is the longest side...(right triangle) Hypotenuse, (right triangle) Is the longest side...(right triangle) It's the hottest of the hot, It's the hottest one, It's so burning like a flame, Like the hot summer sun... Measuring degrees, 90 is the angle, Opposite hypotenuse in a right triangle Opposite 90, yes, opposite 90, Yes,opposite 90 degrees... Opposite 90 yes, opposite 90 Yes, opposite 90 degrees... Hypotenuse, (right triangle) Is the longest side...(right triangle) Hypotenuse, (right triangle) Is the longest side...(right triangle) Pythagoras my man, Discovered a math theorem, You didn't live in ancient Greece, I know you couldn't hear him A rule of right triangles, Pythagoras, devised, A squared plus B squared, Is what he advised! a 2 + b 2 = c 2 Hypotenuse is letter c 1º de ESO: Plane figures 9
8.- Crossword: PLANE FIGURES Across 2. An angle formed by two perpendicular lines; a 90 degrees angle. 5. The line segment joining a vertex with another (non-adjacent) vertex. 9. The center of the circumscribed circle. 11. The amount of surface contained by a figure. 12. The length of a straight line drowns from the center of a circle to a point on its circumference. 14. The line from a vertex to the midpoint of the opposite side. Down 1. The line segment from the center of a regular polygon to the midpoint of a side. 3. The longest side of a right triangle. 4. Trapezoid in which the adjacent sides are equal and diagonals intersect each other at right angles. 6. An angle that is less than 90 degrees. 7. A polygon with 8 sides. 8. Either of the sides in a right triangle opposite an acute angle. 10. Opposite sides are parallel. Opposite angles are equal and diagonals intersect each other at right angles. 13. The line segment from one vertex that is perpendicular to the opposite side. 1º de ESO: Plane figures 10
Can you help me with the word? Do you know which is the first letter of? I think that the first letter is What do you think is? How do you spell? 9.- Complete in your notebook this C-map with the words below: Four Apothem Angle bisectors Obtuse Kite Decagon Barycentre Hexagon Rectangle Scalene Circumcentre seven Discussion: Where would you put? Please tell us what it is connected with. I wrote next to In my opinion, this concept might be situated here, joined with I think that 1º de ESO: Plane figures 11
10.- Project 1: Work in groups of three. a) Take photos by yourself of plane figures that appear around you. b) Make a presentation with the best photos. c) Finally, explain to your mates the name of each figure, its properties and where they are. 11.- Project 2: a) Draw the inscribed and circumscribed circumference of a triangle. b) Then, draw all points associated with a triangle. c) What is the relationship between all points associated with a triangle? 12.- Make a WORD MAT with the areas and perimeters of plane figures that appear in the C-map in exercise 9. EXPLANATION: To sum up, you have to do a table with four columns. In the first column has to appear the name of the plane figure, the second column has to contain a graphic representation for each plane figure, in the third one has to appear the formula to calculate the perimeter and in the last column has to appear the formula to calculate the area. 1º de ESO: Plane figures 12
13.- Self-assessment I CAN Know different kinds of triangles. YES NO NOT Understand the difference between Leg and Hypotenuse. YES NO NOT Draw points and lines associated with a triangle. YES NO NOT Draw the inscribed and circumscribed circumference of a triangle. Solve real situations exercises by using the Pythagorean theorem. YES NO YES NO NOT NOT Know different kinds of quadrilaterals. YES NO NOT Know different kinds of polygons. YES NO NOT Distinguish the different elements of a polygon. YES NO NOT Distinguish between a circumference and a circle. YES NO NOT Distinguish the different elements of a circumference. YES NO NOT Know the difference between area and perimeter. YES NO NOT Solve real situation exercises by using areas and perimeters. YES NO NOT Recognize the presence of plane figures in my environment. YES NO NOT Seek information from various sources and Make a short presentation. YES NO NOT Classify and describe plane figures in my environment. YES NO NOT Describe the components of a plane figure. YES NO NOT 1º de ESO: Plane figures 13