Writing Algebraic Expressions

Students work independently on the Think About It problem.  After 2 minutes of work time, I have students share out their expressions.  I ask them:

• How did you come up with the first expression?  
• How did you come up with the second expression?  
• What did you use to represent the amount of money Keith has in the second? Why did you do that?

The key idea that I want to come out of this discussion is that we need a variable for the second expression, because we don't know how much money Keith initially has. 

In the previous lesson, students translated words into numeric expressions.  In this lesson, the expressions will all require variables.

In the notes section, students fill in the guided notes with the following steps:

Steps for Writing Simple Expressions

1. Read and annotate
2. Use a variable to represent unknowns and digits/operations for different values
3. Define the variable
4. Identify what amount you're starting with
5. Determine the operation performed on the starting amount and translate
6. Check by restating and comparing to the verbal/written expression

I guide my students through Example One in the Intro to New Material section.  First, I cold call on a student to share the operation we need to use in the expression.  Then, I have students turn to their partners and decide what we should use to represent 'a number' in the problem.  I ask for two volunteers to share out what they have decided to use.  I use this as an opportunity to reinforce the idea that we do not use 'o' or 'l' as variables, because they look like the numbers 0 and 1, respectively.  I don't want students to feel like they will always be given a variable that starts with the same letter as something in the context of the problem.  So while many students will use n to represent 'a number,' it is important that students also experiment with picking other variables, so long as they define the variable in their work space.  

Once we've gone through the steps and written our expression for Example One, I add an additional check.  The 'less than' language can be tricky for kids, with some wanting to write '12-n'  I ask students to pick a value for the variable, say 20.  We then replace the 'a number' with 20, and check to see that our expression in reasonable for '12 less than 20.'  

For Example Two, we go through the same process.  We discuss that there are two options here:  1/3n and n ÷ 3, as they both involve splitting n into three equal pieces.

Students work in pairs on the Partner Practice problem set.  As they work, I circulate around the classroom and check in with each group.  I am looking for:

• Are scholars correctly identifying the variable?
• Are scholars correctly identifying the constant?
• Are scholars correctly translating the verbal expression into numerical form?

I'm asking:

• How did you know what the variable was?
• How did you know what the constant was?
• What amount are you starting with?
• Will the expression have the same answer if you changed the order of the terms?
• How did you know what operation to use?
• What does this coefficient mean?
• What does the variable represent given the context of the problem? What does the constant represent given the context of the problem?

I also ask students if, in Problem 1C, '9 minus a number' would produce the same algebraic expression as '9 less than a number.'

Students independently complete the Check for Understanding problem, before moving on to the Independent Practice.

Students work on the Independent Practice problem set. 

As they are working, I am looking specifically at problems 4 - 7.  Some students will not read carefully, and will not use a to represent their age now.  If I see things like 12 - 6 for Problem 4 or 10 for Problem 5, then I know that students are not thinking about using an unknown (and are using their actual ages).

In this set, there are problems that ask students to write numeric expressions (without variables).  I want to give students practice with writing all types of expressions.

Problem 23 will confuse some students, because the expression will be 6 - 14.  Students do not learn to perform integer operations in 6th grade, but students will be suspicious that something is wrong because of the order of their terms. 

After independent work time, I have students come back together for a quick discussion.  I ask which expression is correct for Problem 1:  70 + q or q + 70?  I want to discuss that addition is commutative, and either expression will work.  However, q + 70 is the translation of '70 more than q,' because q is the initial value in the problem.

I then cold call on students to read the verbal expressions for Problems 26 - 29.

Students work independently on the Exit Ticket to close the lesson.