Translating Algebraic Expressions and Equations

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SWBAT: • Identify variables, coefficients, and constants. • Differentiate between an algebraic expression and an algebraic equation. • Translate between a written description of an expression or equation and the actual expression or equation.

Big Idea

Students will translate between the written form and algebraic form using correct mathematical notation.

Do Now

5 minutes

Part of my class routine is a Do Now at the beginning of every class.  Students walk into class and pick up the packet for the day.  They get to work quickly on the problems.  Often, I create do nows that have problems that connect to the task that students will be working on that day.  For this lesson I want students to practice change expressions from word form to numerical form before we start working with algebraic expressions.

To check the do now, display answers from 1 a – h.  I ask students to share with their partner which number sentences result in the same answer.  After a minute of sharing, I ask students to share out.  I want students to share that a and b have the same answer as well as g and h.  for c and d as well as e and h I take quick poll to see if students think these expressions result in the same answer or different answers.  I call on 1-2 students to share their mathematical thinking.  In the past I have found that many students mistakenly think that problems like 5-4 and 4-5 as well as 2 divided by 1 and 1 divided by 2 are equivalent.  I want to address those misconceptions in the do now before moving on to algebraic expressions and equations.

I ask students to share out one thing that they wrote down on their do now that will help make today a productive math class.  I find that students enjoy sharing out these goals – it is a way for them to be held accountable by their teacher and peers.


10 minutes

After the Do Now, I have a student read the objectives for the day.  I tell students that they will be connecting their knowledge operations to algebraic expressions and equations.  I call on students to read the vocabulary words and the examples. 

At the end of the page I write 4 examples on the board (5 – a, 10x = 50, 8b + 4, y + 17 = 24).  Students have to copy each example in the appropriate column, expression or equation, and then identify coefficients, constants, and variables.   I am walking around and making sure students are on task and that they are using their notes to correctly identify the vocabulary words.  When most students are finished I will select a student to display his/her work under the document camera.  I call on 1-2 students to share if they disagree or agree with the student’s work.  We will address any questions or misunderstandings.  If it does not come up I’ll ask what is the coefficient of a and y to make sure students understand that in both cases the coefficient is one.  Here students are using MP3: Construct viable arguments and critique the reasoning of others.


Translating Words Into Algebraic Expressions

10 minutes

I tell students that in algebra they are going to be using variables to represent a situation.  Before we model situations using variables, expressions, and equations we need to be able to translate expressions and equations between word form and algebraic form.  I say that for this page, every time we see a number we will use the variable “n”.  The letter stands in for some number, which we don’t know.  I write example 1 and 2 in algebraic form.  We go through the table and I ask students to identify which operation matches which group of expressions.  I then show students the different ways to represent those expressions (parentheses, dot, fraction bar, etc).  I stress that the order of the variable and the number matter for division and subtraction.  I mention the do now problems where we showed that the quotient of two and one is different than the quotient of one and two. 

I ask students to think about the last two examples in the table, “twelve subtracted from a number” and “twelve less than a number”.  How can write an expression to represent them?  Many students struggle that these phrases are represented by n -12 and not 12 – n, the way that the values appear in the phrase.  I give some examples like ,”Ms. Palmer has n dollars.   Eric has 12 dollars less than her.  How much money does Eric have?”  And, “You have n dollars.  You subtract 12 dollars from your amount of money.  How many dollars do you have now? “.  I encourage students to visualize what is going on.  What value are you starting with?  What is happening to that value? Here students are using MP2: Reason abstractly and quantitatively.


Class Practice Part 1

10 minutes

I have a student read the directions.  I encourage them to look back to their notes on the previous page if they get stuck.  As students are working I walk around and monitor student progress.  I am looking in particular at #3 and 4 to see if they are able to represent them correctly.  When most students are finished I have students share out different ways to represent each problem.  For #3 I may offer an answer like, “2 less than b equals 14” and ask whether students agree of disagree with the answer.

Class Practice Part 2

15 minutes

I read the directions and show students the different cards that will be in their envelopes.  I read the example and I have students volunteer to share two ways that I could model the problem with my cards.  We could use the division symbol, or we could use the fraction bar.  I ask students which value should come first in the expression, the 4 or the n.  Once we have completed the example, I pass out the envelopes.  During this activity, students are engaging in MP1: Make sense of problems and persevere in solving them as well as MP 4: Model with mathematics.  I tell students to work independently and check in with me before they move on to page 6.

As students are working I am walking around and monitoring student progress.  I am looking at particularly at #4-5 and 6-7.  If students are struggling I may ask them what is going on in the problem, what operation is being used?  From there I have them identify the variable and numbers involved.  I re-read the phrase and ask where the student thinks each value belongs.  If a student continues to struggle, I may plug in a value for “a number” to see if that will help. 

If students finish 1-10 correctly, they can partner up with someone and  work on the “Create and Compare” activity on the next page.  Students take turns creating algebraic expressions or equations with cards (out of view of the other student) and reading it aloud to the partner.  Using his/her own cards, the partner must re-create the expression or equation.  Then students compare their work.  This is a great way for students to continue to practice translating expressions and equations and for students to see how the same expression/equation can be represented in multiple ways.    Here students are engaging in MP2, MP3, and MP4.


Closure and Ticket to Go

10 minutes

I ask students to share and compare their answers to questions 4-8.  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. 

If I have time, I ask students to share struggles they had and how they overcame them.  I also ask students if there are still struggles they are having.  I ask other students to give advice.  In my classroom I try to consistently show students that they will struggle with different problems but that they need to use their creative problem solving minds to try a strategy.  If that strategy doesn’t work, try another one!  The main question in this lesson was a difficult one that required students to problem solve and persevere through challenges and set-backs.  I want to acknowledge my students hard work and their persistence.