Antes de empezar: el álgebra como lenguaje
El álgebra puede parecer rara al principio porque mezcla números, letras y símbolos. Pero, en realidad, es como aprender otra parte del idioma de las matemáticas: el lenguaje algebraico.
Para entenderlo, tenemos que aprender a leer sus símbolos, conocer algunas reglas y descubrir qué nos quieren decir sus expresiones.
Antes de empezar, vamos a pararnos a pensar:
• ¿Recordamos alguna expresión en la que aparezcan letras?
• ¿Cómo se escribía “el triple de un número”?
• ¿Qué era una incógnita?
• ¿Para qué puede servir una letra en matemáticas?
Mi punto de partida
Antes de ver el vídeo de introducción al lenguaje algebraico, vamos a dejar por escrito nuestro punto de partida. Copia estas preguntas en tu cuaderno y respóndelas con sinceridad. No se trata de acertar, sino de pensar qué sabes, qué dudas tienes y qué crees que vas a aprender.
Primeros pasos con el lenguaje algebraico
En este vídeo vamos a ver los primeros pasos para pasar algunas frases sencillas al lenguaje algebraico.
Mientras lo ves, fíjate especialmente en tres cosas:
• qué representa la letra;
• qué operación aparece;
• cómo se construye la expresión algebraica.
Después de ver el vídeo, volveremos sobre estas ideas para practicar y comprobar si sabemos escribir algunas expresiones algebraicas sencillas.
Practico asociaciones
Una vez visto el vídeo, vamos a comprobar si sabemos relacionar algunas expresiones del lenguaje cotidiano con su escritura algebraica.
Relaciona cada frase con la expresión algebraica correspondiente.
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Una vez visto el vídeo, vamos a comprobar si sabemos relacionar algunas expresiones del lenguaje cotidiano con su escritura algebraica.
\nRelaciona cada frase con la expresión algebraica correspondiente.
\nSu navegador no es compatible con esta herramienta.
Trabajo en el cuaderno
Después de practicar en la pantalla, continúa pensando en tu cuaderno:
1. Copia dos asociaciones de la actividad y explica qué representa la letra en cada caso.
2. Inventa dos nuevas parejas: una frase en lenguaje cotidiano y su expresión algebraica.
3. Escribe dos expresiones algebraicas y propónselas a un compañero o compañera para que escriba qué podrían significar en lenguaje cotidiano.
Compruebo lo que he entendido
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Ahora vamos a comprobar si sabemos pasar del lenguaje cotidiano al lenguaje algebraico, y también al revés: del lenguaje algebraico al lenguaje cotidiano.
Fíjate bien: algunas opciones se parecen, pero no significan lo mismo.
Importante: Completa todas las preguntas antes de pulsar el botón Comprobar.
Si compruebas solo una respuesta, las demás contarán como no realizadas.
Puntuación.
Reto: sigo practicando
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Si has terminado la actividad anterior, puedes seguir practicando con este reto.
Ahora encontrarás expresiones un poco más exigentes y tendrás que fijarte muy bien en el orden de las palabras, las operaciones y los paréntesis.
Puntuación.
Trabajo en el cuaderno
Después de practicar con las actividades desplegables, continúa pensando en tu cuaderno:
- Copia dos preguntas en las que hayas dudado y explica con tus palabras por qué la opción correcta era la adecuada.
- Elige una opción incorrecta y escribe qué habría significado realmente.
- Inventa una nueva pregunta desplegable: escribe un enunciado, una respuesta correcta y dos respuestas incorrectas.
- Escribe una frase breve que empiece así: “Ahora entiendo mejor que…”
Caso práctico: la edad de una persona
En muchas situaciones cotidianas usamos expresiones como “dentro de unos años”, “hace unos años”, “el doble de una cantidad” o “la mitad de algo”.
En este caso vamos a utilizar el lenguaje algebraico para representar edades. Para ello, llamaremos x a la edad actual de una persona.
A partir de esta idea, tendrás que interpretar algunas situaciones y escribirlas con lenguaje algebraico.
Actividad 1: Expreso edades con álgebra
Si x es la edad actual de una persona, escribe en lenguaje algebraico:
a) La edad que tendrá dentro de 5 años.
b) La edad que tenía hace 7 años.
c) El doble de su edad actual.
d) La mitad de su edad actual.
e) El triple de la edad que tendrá dentro de 2 años..
Actividad 2: Interpreto expresiones algebraicas
Explica con tus palabras qué significa cada expresión:
a) x + 10
b) x - 4
c) 2x
d) x/2
e) 3(x + 1)
Actividad 3: Invento mi propio caso
Inventa una pequeña situación relacionada con edades.
Después, escribe al menos tres expresiones algebraicas que puedan aparecer en tu situación.
Por ejemplo, puedes usar ideas como:
- dentro de unos años;
- hace unos años;
- el doble de una edad;
- la mitad de una edad;
- la suma de dos edades.
Rúbrica del caso práctico: la edad de una persona
Esta rúbrica sirve para valorar el trabajo realizado en el caso práctico sobre edades y lenguaje algebraico.
Antes de terminar, revisa tu trabajo con atención y comprueba si has representado correctamente las situaciones, si has interpretado bien las expresiones algebraicas y si tu propio caso se entiende con claridad.
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Juego: palabras clave del lenguaje algebraico
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Encuentra en la sopa de letras las palabras relacionadas con el lenguaje algebraico.
Lee la definición de cada palabra antes de buscarla. No se trata solo de encontrar letras: piensa qué significa cada término.
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Su navegador no es compatible con esta herramienta.
Trabajo en el cuaderno
¡Me pongo a prueba como traductor algebraico!
1. Copia la tabla en tu cuaderno y completa las casillas vacías.
2. En algunas filas tendrás que pasar del lenguaje cotidiano al lenguaje algebraico. En otras, tendrás que recorrer el camino contrario: interpretar la expresión algebraica y escribir qué significa con palabras.
3. Usa x para representar el número, la edad, el precio, el dinero o la cantidad desconocida.
4. Después de completar la tabla, elige dos filas que te hayan resultado difíciles y explica cómo has pensado la traducción.
| Nº | Lenguaje cotidiano | Expresión algebraica |
| 1 | El doble de una cantidad de dinero más 15 euros | |
| 2 | La mitad de la suma de un número y 8 | |
| 3 | Un número disminuido en su tercera parte | |
| 4 | 3(x - 4) | |
| 5 | x/2 + x/4 | |
| 6 | Si x es la edad actual de una persona, la edad que tenía hace 6 años | |
| 7 | 2x + x/3 | |
| 8 | La tercera parte del precio de una entrada más 4 euros | |
| 9 | El triple de la diferencia entre un número y 7 | |
| 10 | (x + 12)/2 | |
| 11 | x - x/5 | |
| 12 | 4x - 9 |
Test SCORM: compruebo mi aprendizaje
Antes de terminar esta unidad, responde a este pequeño test. Te servirá para comprobar si sabes pasar del lenguaje cotidiano al lenguaje algebraico y también al revés.
Lee cada pregunta con atención antes de elegir la respuesta.
2
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Galería visual: ideas clave del lenguaje algebraico
El proceso de aprendizaje
Estas cuatro imágenes no representan momentos aislados, sino un proceso que se repite en nuestro aprendizaje:
1. Partimos de lo que sabemos, de nuestras dudas y de lo que creemos que vamos a aprender.
2. Aprendemos a expresar una misma idea de dos formas: con palabras y con lenguaje algebraico.
3. Usamos la pantalla para explorar y comprobar, y el cuaderno para explicar, corregir y ordenar.
4. Revisamos qué entendemos ahora, qué podemos explicar y qué dudas siguen abiertas.
Después de revisar lo aprendido, pueden aparecer nuevas dudas. Por eso, el aprendizaje vuelve a empezar.
