Estimemos la longitud de lado a partir del área (parte 1)
¿Cuál es la longitud de lado del cuadrado A?, ¿cuál es su área?
¿Cuál es la longitud de lado del cuadrado C?, ¿cuál es su área?
¿Cuál es el área del cuadrado B?, ¿cuál es su longitud de lado? (Usa papel de calcar para verificar tu respuesta).
2.2
Activity
Estimemos la longitud de lado a partir del área (parte 2)
Standards Alignment
Building On
Addressing
8.NS.2
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Usa el círculo para estimar el área del cuadrado que se muestra. Explica tu razonamiento.
A coordinate plane with the origin labeled “O.” x-axis, scale -6 to 6 , by 1's. y-axis,-6 through 7, by 1's. Circle and square graphed. circle’s circumference passes through 2 of the squares vertices. The circle’s center is the origin and it’s circumference is indicated by a dashed line that passes through the following approximate points on the axes: Negative 5 point 3 comma 0, 0 comma 5 point 3, 5 point 3 comma 0, and 0 comma negative 5 point 3. The square is tilted so that all its sides are diagonal to the coordinate grid. It has vertices at: 0 comma 0, negative 2 comma 5, 3 comma 7, and 5 comma 2. The circumference of the circle passes through the square’s vertices at negative 2 comma 5 and 5 comma 2 so that the sides of the square, extending from the origin to those 2 vertices, are within the circle. @Kia Johnson I didn't want to say that the sides of the square were the radius felt like taking away some of the cognitive demand) but felt a little wordy. REPLY 11:44 (Fixed some language, now that I am writing for same image on grid): A coordinate plane with the origin labeled “O.” The x-axis has the numbers negative 6 through 6 indicated with tick marks. The y-axis has the numbers negative 6 through 7 indicated with tick marks. A square and a circle are drawn on the plane so that the circle’s circumference passes through 2 of the squares vertices. The circle’s center is the origin and it’s circumference is indicated by a dashed line that passes through the following approximate points on the axes: Negative 5 point 3 comma 0, 0 comma 5 point 3, 5 point 3 comma 0, and 0 comma negative 5 point 3. The square is tilted so that all its sides are diagonal to the coordinate grid. It has vertices at: 0 comma 0, negative 2 comma 5, 3 comma 7, and 5 comma 2. The circumference of the circle passes through the square’s vertices at negative 2 comma 5 and 5 comma 2 so that the sides of the square, extending from the origin to those 2 vertices, are within the circle.
Usa la cuadrícula para verificar tu respuesta al primer problema.
A coordinate plane with the origin labeled “O.” x-axis, scale -6 to 6 , by 1's. y-axis,-6 through 7, by 1's. Circle and square graphed. the circle’s circumference passes through 2 of the squares vertices. The circle’s center is the origin and it’s circumference is indicated by a dashed line that passes through the following approximate points on the axes: Negative 5 point 3 comma 0, 0 comma 5 point 3, 5 point 3 comma 0, and 0 comma negative 5 point 3. The square is tilted so that all its sides are diagonal to the coordinate grid. It has vertices at: 0 comma 0, negative 2 comma 5, 3 comma 7, and 5 comma 2. The circumference of the circle passes through the square’s vertices at negative 2 comma 5 and 5 comma 2 so that the sides of the square, extending from the origin to those 2 vertices, are within the circle.
Student Lesson Summary
El área del cuadrado es 73 unidades2.
Como el área está entre y , la longitud de lado debe estar entre 8 unidades y 9 unidades. Podemos usar papel de calcar para trazar la longitud de lado y compararla con la cuadrícula, lo que también muestra que la longitud de lado esta entre 8 y 9 unidades.
Para hablar de la longitud de lado exacta, podemos usar el símbolo de la raíz cuadrada. Decimos “la raíz cuadrada de 73”, que se escribe y significa “la longitud de lado de un cuadrado cuya área es de 73 unidades cuadradas”. Observa que .
Glossary
raíz cuadrada
La raíz cuadrada de un número positivo es el número positivo que al elevar al cuadrado da . También es la longitud de lado de un cuadrado de área . La raíz cuadrada de se escribe .
La raíz cuadrada de 16 se escribe . Su valor es 4 porque es 16.
también es la longitud de lado de un cuadrado de área 16.
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Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.