# Distributive property to write an equivalent variable expression

Students struggle to understand that x5 and 5x are equivalent expressions, because it conflicts with their previous experiences with numbers 53 and 35 are not equivalent. Can you find yours among them.

So, you have 20 and 30m. Now I'd like you to work with your partners to generate 3 more equivalent expressions for the area of the rectangle.

I know that properties are somewhat like laws; they always work. Then take the sum of those two products. Students will benefit from a discussion of what the word equivalent means.

Just going to be left with 3m. How long will Marly have to wait if there are 60 people in front of her. How do you suggest we write the expression. The associative property is about grouping. Yes, but remember - the commutative property only works for multiplication and addition.

Or as you can say, eight halves is equal to four wholes.

If you change the order of the numbers when performing those operations you'll get different answers. It's because you only multiplied the 5 by 3, and didn't multiply the x by 3.

That's one way of kind of very systematically figuring out a greatest common factor. For the Example 1, I don't use the words 'distributive property. I hope students solve a problem like 11, using mental math. Use the distributive property to rewrite this expression. Because we usually write the numbers first.

I'll underline the 10 x 60 in one color, and ten the 10 x 5 in another color. You could say 60 is two times 30, which is two times 15, which is three times five. Common Core For Grade 6 Examples, videos, and solutions to help Grade 6 students model and write equivalent expressions using the distributive property.

I'm having a little trouble making sense of what you wrote, because you've used an x to represent the variable and an x to indicate multiplication. These students may benefit from discussion about how x is not usually used to represent multiplication in algebraic expressions to avoid confusion with the variable x, and that a dot is often used when a multiplication symbol is needed to prevent confusion.

The algebra tiles show that there are 3 x s and 15 units.

What is blocks. So, you could actually factor out a To help us think about this, let's start by using algebra tiles to represent this rectangle. Finally, students put their conclusions to work by expanding and evaluating 4 more expressions. The area model presents a nice visual model of the distributive property.

Use the new model and the previous model to answer the next set of questions. This part is to help students start to focus in on the appearance of equivalent expressions generated by the distributive property MP7.

What is the coefficient. As students are working on these, I will be watching to make sure values are being expanded correctly. Here is the Venn diagram of the results.

Why do you have to write any symbol at all. How many a's are in the expression. How many blocks does John need?. The distributive property is the ability of one operation to "distribute" over another operation contained inside a set of parenthesis.

Most commonly, this refers to the property of multiplication distributing over addition or subtraction, such that $$x(a+b) = xa + xb$$. Equivalent Expressions with the Distributive Property Short description: Learn how the distributive property can be used to model and create equivalent expressions in this animated Math Shorts video.

Long description: This animated Math Shorts video explains how the distributive property can help students model and create equivalent expressions. Understanding Polynomial Expressions A term is a constant, variable, Now, use the distributive property to write an equivalent expression for (𝑎𝑎+3)(𝑎𝑎+2).

Let’s Practice! 1. Write an equivalent expression for 3(𝑥𝑥+2𝑦𝑦−7𝑧𝑧) by. A variable can be distributed into a set of parentheses just as we distributed a negative sign or a number. We can now apply the distributive property to the expression by multiplying each term inside the parentheses by x.

x * y + x * 1 Imagine they are in a 3 x 3 box The question is in the description. imagine it is a 3 x 3 box Write. This part is to help students start to focus in on the appearance of equivalent expressions generated by the distributive property (MP7).

In other words, it creates expressions that can be seen as a product of two factors, * We can instead write the expression as $$2\left (3p+5 \right)+\left (-1 \right)\left (p+2 \right)$$ By using the distributive property we can rewrite the expression as.

Distributive property to write an equivalent variable expression
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Illustrative Mathematics