Working with Expressions and Equations Part 1

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Objective

SWBAT: • Create algebraic expressions and equations to model situations. • Use substitution to evaluate algebraic expressions. • Graph an equation on a coordinate grid.

Big Idea

Students use their knowledge of algebraic expressions and equations to write expressions and equations using appropriate math symbols.

Do Now

7 minutes

See my Do Now video for more details about my routines to begin class.  For this lesson I want students to review the vocabulary of the previous lesson. 

I ask students to share which answers are incorrect for #1-2 and how they know.  For #1, a common mistake I see is that students select c as there answer, not realizing that k-8 and 8-k are two distinct expressions. 

I created problem 3 so that students are thinking about the relationship between the number of tickets purchased and the cost.  I want students to be able to articulate that for each additional ticket you buy, your cost is $9 more. 

 

Problem: Representing a situation with an expression

7 minutes

After the Do Now, I have a student read the objectives for the day.  I tell students that they will be creating expressions and equations to model situations.    

To get students making the connections between skills in manipulating numbers and variables, I have students work on the problems on page 2.  Typically my students are able to easily answer a-d for the first situation.  Some students may need a reminder that a decade = 10 years. 

Some students struggle to take those same skills and use them with variables, like in the second example.   If students are struggling, I will reinforce that we don’t know Mr. Haskin’s age, so we will just use the variable x to represent how old he is in years.  If he is x years old now, how old will he be in 4 years?  Some students think of x + 4 but are uncomfortable because it is not a single number.  Or students may try to add x+4 and get 4x.  I explain that x + 4 is the most specific we can get, since we don’t know the value of x.  If students continue to struggle, I make connections back to the first example.  How did you find out how old Ms. Palmer was 5 years ago? I am looking for students to say that they subtracted 5 from 28 to get 23.  Then I push students to apply that same strategy to find Mr. Haskin’s age 5 years ago.

After students have had a few minutes to work, we review the answers.  I give students values for Mr. Haskin’s age and have them calculate the answers.  What if Mr. Haskin’s is 29 years old now?  What if he is 41 years old now?  70?  Students are using substitution to find the answers.

Ben's Family Corn Maze

23 minutes

In this lesson students will set the foundation for the next two lessons where they are writing expressions and equations to model situations and then using those equations to answer further questions.  Therefore, today’s work is mostly guided and the following days have much more independent and group work time.

I have a student read the first paragraph on p. 3 about Ben’s Family Farm.  I ask a series of questions to help students write an expression.  For each visitor that comes to the farm, they collect how much money?  How much money would they collect if there were 6 visitors?  10 visitors?  100 visitors?  Then how can we represent the amount of money they will collect if there are n visitors? I want students to connect the operation they are using to answer questions with numbers to the expression.  I ask for different ways to write the expression (switching the order of the number and variable, using a dot, using parentheses, using 8n). 

I tell students that they need to substitute values for n into the expression in order to find the amount of money collected.  Students work to complete the table independently.  They check in with their partner when they complete it to compare answers.  I ask questions to the class before moving on.  What do you notice about the table?  I am looking for students to share that the amount of money increases as more visitors come.  They might also notice that for every 5 more visitors the amount of money increases $40.

We move on to page 4.  The terms independent and dependent are just being introduced here, they will show up in the next lesson as well.  Before students create the graph I ask them to predict what they think it will look like and why they think that.  Students create the graph independently using the table they created on page 3.  I walk around and monitor student progress.  Once most students are finished, we come together to share what we notice.  I am looking for students to connect the graph with the table.  They may notice that, like the table, the amount of money collected is increasing as the number of visitors increases.  They may notice that the values in the table represent the coordinate points on graph.  Students are engaging in MP2: Reason abstractly and quantitatively and MP4: Model with mathematics.

I ask for students to brainstorm with their partner about what the point (0, 0) represents.  I want students to make the connection between the point and the table.  I am looking for them to articulate that (0,0) shows that if there are no visitors, the farm will not collect any money.

 

Extra Practice

10 minutes

Students work independently on these problems.  I walk around and monitor student work.  I am looking specifically at # 1, 3, and 6.  For number 1, are my students able to see that they need to use division to represent this situation?  Do they place the number and variable in the correct places?  For number 3, some students struggle and mistakenly use subtraction in their expression.  For number 6, I check that students know what to do when they see the fraction bar.  I am also looking to see that they use the order of operations correctly.

If students are struggling I may ask them the following questions:

  • What are the values in the problem?  What does the variable represent?
  • What if we plug in ___ (insert plausible number) for the variable?  How would you figure out the answer?
  • What operation is happening between this value and variable?

If students correctly answer problems on page 5 they can move onto page 6.  I may ask them these questions?

  • How does your expression represent the number of dimes Ella has?
  • What is an efficient way to calculate the amount of money Ella has?
  • How can/did you figure out the number of dimes she has for part e? 

 

Closure and Ticket to Go

13 minutes

I ask students to share and compare their answers to questions 1-3 on page 5.  After they share, I ask for volunteers to share out their thinking about the problems to the class.  I ask students how they know that their expression/equation matches the phrase.  Students are using MP3: Construct viable arguments and critique the reasoning of others.  For more details see my Closure video in my Strategy Folder

For the last 5 minutes of class I give students the Ticket To Go and have them work on it independently.  See my Ticket to Go video in my Strategy Folder for more details.