Are We Alike?

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SWBAT combine like terms and simplify expressions with multiple terms and variables.

Big Idea

Combining like terms and simplifying expressions is the precursor to solving equations


10 minutes

The do now is a set of numerical expressions that the students are asked to simplify.  My goal here is to get the students to use the commutative property to make this more of a mental math challenge than a pencil paper task.  I’m going to ask students to simplify the numerical expressions.  Then I want them to explain in writing what they did first, second, and so on.  As students are working out these problems, I’m going to watch for students that are using the commutative property to solve.  Ask the students why they can combine those two numbers together. (SMP 6)

When students finish simplifying these expressions, have them do a HUSUPU to share solutions and strategies

These problems will help ease students in to combining like terms.  Let them know that they combine like terms all the time when they are using operations.  Today, we will be incorporating variables into our expressions and combining those terms. 

Writing Expressions

15 minutes

Time: 15 minutes

My students have already been writing expressions.  They should easily come up with one expression.  The challenge will be to come up with the second expression.  According to CCSS, students need to recognize that y + y + y is the same as 3y no matter what the value of the variable.  So I thought of 3 common expressions for the students to write about.  In order to get students thinking about the 2nd expression, ask them how addition can be written using multiplication.  Students should know that multiplication is repeated addition.  (SMP 2)

The problem they may struggle with is finding the area of a square.  They should be able to tell you that the area is s x s, but they may say the other expression is 2s.   Ask the students to plug in a side length using both of their expressions.  Are they the same? (NO).  Then say, what happens when we multiply 2 of the same factors?  Using this vocabulary, should get them thinking about exponents. (SMP 4)

We are going to do one slide at a time.  Students should work independently.  When they are done, I’m going to have them do a round robin share to check solutions. (SMP 3)

Tools:  3 writing expression problems

Combining like terms

20 minutes

This section of the lesson is new to the students.  Bring them back to the do now problem and explain that they were combining like terms when they simplified those expressions.  Remind them that a term is separated by plus and minus signs.  Terms that have the same variable are considered like terms and can be added or subtracted depending on the expression.  I have 2 slides examples to show them what this means.

After I show them about combining like terms, we will do some examples together and they will get to try some on their own.  Students will be taking notes while I show them the examples.  In the examples, I’ve circled and boxed in the like terms as a visual for the students.  I also like to circle/box the second term in with the sign in front of it.  This helps students remember to either add or subtract.  Knowing what operation to do is a major struggle for students when they are first learning about combining like terms.   When students are done trying one out on their own, have them work with a tablemate to discuss solutions and strategies.

Tools:  Combining like term examples

Simplifying Expressions

15 minutes

Explain to the students that simplifying an expression usually indicates that there is multiplication or division in the problem that is done first, before you add or subtract.  Ask the students, where they have heard that before? (orders of operations).  If they see a number being multiplied by a quantity (3(4x+2)), they should use the distributive property to simplify it before combining the like terms. (SMP 6)

I will be giving them an example for their notes and then they will try one on their own.  Once they have tried a problem on their own, have them share strategies and solutions with a tablemate (SMP 3)

Tools:  Simplifying expressions examples


Match Game

15 minutes

For this game, I would laminate the cards so you can use them for other classes.  Otherwise, make a set of cards for each class as they will get ripped or lost.

The students will be working with partners to match equivalent expressions.  Students will be simplifying and combining like terms for this activity.  Each person should get the opportunity to match an expression.  When one partner gets a match, the other partner will check their work.  If the solution is correct, the two cards can be moved off to the side.   By having the partners check work, each person in the group is responsible for their own learning.

Tools:  Match game cards


10 minutes

The students will be completing a connect 3: writing expressions, combining like terms, and simplifying expressions.  I chose these 3 words because they were the focus of our learning today.  Students should recognize that whenwriting expressions we need to simplify them and combine like terms to make the math easier to solve. If time permits, have the students share their connections with a partner.

Tools:  Are we alike notes