# Apply the distributive property to write an equivalent expression

Students' written responses will be collected and analyzed by the teacher.

## Apply the distributive property to create an equivalent expression 6 a 2b 3c

Then, you can add the products. Export To We could say that the number 12 is the product of say two and six; two times six is equal to Then simplify the result. The teacher will circulate around the classroom while students are playing the game and will be taking note of any student misconceptions. So because if you take the product of two and six, you get 12, we could say that two is a factor of 12, we could also say that six is a factor of By substituting a number for a variable, this will allow students having difficulty to better understand equivalent expressions. What we're going to do now is extend this idea into the algebraic domain. Notice that the result is the same in each case. And so the general idea, this notion of a factor is things that you can multiply together to get your original thing. Remember that there are several ways to write multiplication. English Language Learners may need support for unfamiliar vocabulary. Well, one thing that might jump out at you is we can write this as two times one plus two X. Feedback to Students The teacher will provide feedback to the students in the introduction activity.

The teacher will assess students' understanding through formative feedback during the guided inquiry class discussion. What we're going to do now is extend this idea into the algebraic domain. Student have to be flexible thinkers in that they have to see numbers in different ways.

## Distributive property equivalent expressions worksheet

By substituting a number for a variable, this will allow students having difficulty to better understand equivalent expressions. So in that case you could break the six into a two and a three, and you have two times two times three is equal to Have them write story word problems that reflect equivalent expressions. Notice that the result is the same in each case. We broke 12 into the things that we could use to multiply. And you probably remember from earlier mathematics the notion of prime factorization, where you break it up into all of the prime factors. Formative Assessment At the beginning of the lesson, the teacher will have students demonstrate their knowledge by answering the essential question, "How do you know if algebraic expressions are equivalent? The teacher will provide feedback to students after the summative assessment. This is called distributing the 3. The teacher will circulate around the classroom while students are playing the game and will be taking note of any student misconceptions.

So let's do another one. You have broken this thing up into two of its factors. The multiplication of 3 10 and 3 2 will each be done before you add.

Then, you can add the products.

So one way to think about it is can we break up each of these terms so that they have a common factor? In this lesson, students are asked to apply the properties of operations to identify and generate equivalent expressions.

### Commutative property

You take the product of these things and you get 12! People don't really talk that way but you could think of it that way. Note that the answer is the same as before. So in our algebra brains, this will often be reviewed as or referred to as this expression factored or in a factored form. Let me get a new color here. Sometimes people would say that we have factored out the two. So in that case you could break the six into a two and a three, and you have two times two times three is equal to You have broken this thing up into two of its factors. And you'd say, "Well, this would be 12 "in prime factored form or the prime factorization of 12," so these are the prime factors. We broke 12 into the things that we could use to multiply. Remember that there are several ways to write multiplication. So I'm essentially undoing the distributive property, taking out the six, and you are going to end up with, so if you take out the six, you end up with six times, so if you take out the six here, you have an X, and you take out the six here, you have plus five. The expression is rewritten using the distributive property on the right side, where we distribute the 3, then multiply each by 3 and add the results. Well, this one over here, six X literally represents six times X, and then 30, if I want to break out a six, 30 is divisible by six, so I could write this as six times five, 30 is the same thing as six times five.

So I'm essentially undoing the distributive property, taking out the six, and you are going to end up with, so if you take out the six, you end up with six times, so if you take out the six here, you have an X, and you take out the six here, you have plus five.

The same process works if the 3 is on the other side of the parentheses, as in the example below.

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