Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Selecciona todas las expresiones que representan el área del rectángulo grande exterior de la figura A. Explica tu razonamiento.
A
One rectangle diagram. Labeled A. Large outer rectangle partitioned into 2 smaller rectangles, vertical side 6. First rectangle bottom side length 3. Second rectangle bottom side length 2.
Selecciona todas las expresiones que representan el área del rectángulo sombreado en el lado izquierdo de la figura B. Explica tu razonamiento.
B
One rectangle diagram. Labeled B. Large rectangle with bottom side length 7, partitioned into 2 smaller rectangles. First rectangle vertical side 4, bottom side length blank, area shaded blue. Second rectangle vertical side 4, bottom side length 2.
8.3
Activity
Práctica distributiva
Standards Alignment
Building On
Addressing
6.NS.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Completa la tabla. Si tienes dificultades, puedes saltarte un elemento de la tabla y volver a él después. También puedes dibujar un diagrama de dos rectángulos que compartan un lado.
columna 1
columna 2
columna 3
columna 4
valor
Student Lesson Summary
Cuando necesitamos hacer cálculos mentales, a menudo se nos ocurren formas de hacer el cálculo más fácilmente.
Supongamos que estamos haciendo compras y necesitamos saber cuánto costará comprar 5 latas de frijoles a 79 centavos cada una. Podemos hacer el cálculo mental de esta manera:
Cuando pensamos “79 es lo mismo que . Puedo simplemente multiplicar y y sumar los productos” estamos usando la propiedad distributiva.
En general, cuando multiplicamos dos factores, podemos separar uno de los factores en partes, multiplicar cada parte por el otro factor y luego sumar los productos. El resultado será el mismo que el producto de los dos factores originales. Cuando separamos uno de los factores y multiplicamos las partes, estamos usando la propiedad distributiva de la multiplicación.
La propiedad distributiva también funciona con la resta. Esta es otra forma de encontrar :
Glossary
None
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Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).