Introduction to Factoring with Area Models
Introduction to Factoring with Area Models is a Grade 7 math skill from enVision, Mathematics, Grade 7, covering Generate Equivalent Expressions. Factoring is the process of using the distributive property in reverse. To factor an expression, find the greatest common factor (GCF) of the terms, write it outside the parentheses, and then determine what remains inside the parentheses. Explanation Factoring is like being a math detective. You start with the final expression and work backward to find the original factors that were multiplied together.
Key Concepts
Property Factoring is the process of using the distributive property in reverse. To factor an expression, find the greatest common factor (GCF) of the terms, write it outside the parentheses, and then determine what remains inside the parentheses. $$ab + ac = a(b+c)$$ This can be modeled by arranging algebra tiles into a rectangle and finding the dimensions.
Examples To factor $6x + 18$, find the greatest common factor of $6x$ and $18$, which is $6$. Write $6$ outside parentheses. This gives $6(x + 3)$. To factor $8a + 12b$, the greatest common factor of $8a$ and $12b$ is $4$. The factored expression is $4(2a + 3b)$.
Explanation Factoring is like being a math detective. You start with the final expression and work backward to find the original factors that were multiplied together. It's the opposite of distributing; you're 'un distributing' the expression.
Common Questions
What is introduction to factoring with area models?
Factoring is the process of using the distributive property in reverse.. To factor an expression, find the greatest common factor (GCF) of the terms, write it outside the parentheses, and then determine what remains inside the parentheses.. This can be modeled by arranging algebra tiles into a rectangle and finding the dimensions.
How do you use introduction to factoring with area models in Grade 7?
Explanation Factoring is like being a math detective.. You start with the final expression and work backward to find the original factors that were multiplied together.. It's the opposite of distributing; you're 'un-distributing' the expression.
What is an example of introduction to factoring with area models?
Examples To factor , find the greatest common factor of and , which is .. Write outside parentheses.. To factor , the greatest common factor of and is .
Why do Grade 7 students learn introduction to factoring with area models?
Mastering introduction to factoring with area models helps students build mathematical reasoning. You start with the final expression and work backward to find the original factors that were multiplied together.. It's the opposite of distributing; you're 'un-distributing' the expression.
What are common mistakes when working with introduction to factoring with area models?
A common mistake is overlooking key conditions. This can be modeled by arranging algebra tiles into a rectangle and finding the dimensions.
Where is introduction to factoring with area models taught in enVision, Mathematics, Grade 7?
enVision, Mathematics, Grade 7 introduces introduction to factoring with area models in Generate Equivalent Expressions. This skill appears in Grade 7 and connects to related topics in the same chapter.