In Plain English: Mathematical Expressions in Words

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SWBAT write mathematical expression given the expression in words as well as write a mathematical expression in words given the mathematical expression.

Big Idea

There is Power in Words: The power behind problem solving is understanding mathematical language.


10 minutes

Today for our opening activity, I will have my students participate in a carousel activity where they will walk around and write on chart paper as many words as they can that mean to add, subtract, multiply, and divide. Each group will have 45 seconds at each chart paper.

The manner in which I will accomplish this is by first placing four pieces of chart paper around the classroom. Each paper will be labeled with one of the four operations. I will then split my students up into 4 groups. Each group will be given a different color marker so that it is apparent which group wrote what words. I will have each of the four group of students stand by the chart paper that I assign as their starting point. And then, I will provide them with 45 seconds to write down at least one word that means that they should do the operation indicated on the chart paper that they are assigned to. 

After the 45 seconds has expired, the students will rotate clockwise to the next chart paper and we will repeat the process. We will do this until every group has been to every sheet of chart paper.

Attached to this section of this lesson is a great example of the types of words that should be present on each piece of chart paper.

Curriculum Reinforcer

10 minutes

For today’s warm up, my students will complete 3 problems  that will help them to review concepts that they learned during units 1 and 2. This section of my lessons will allow my students to keep previously learned concepts fresh in their minds throughout the school year, helping them to retain more information.

Instruction & Teacher Modeling

10 minutes

The instructional piece of today’s lesson will use what the students did during the opening activity.  After the students complete the carousel activity, the class will come together and discuss what is on each list as well as what could be added to the papers and/or what should be taken away. 

The focus of this instruction is for my students to understand mathematical language which, speaks directly to practice standard 1, Make sense of problems and persevere in solving them. To place emphasis on this focus, I will introduce students to the multiple ways that mathematical expressions can be expressed in words. I will do this using the lists that my students created during the carousel activity.

Using this carousel activity, I will then segue into demonstrating how mathematical expressions (both numerical and algebraic) can be written and words. I will also demonstrate how mathematical phrases can be written as mathematical expressions.

Examples that I will start with are:

  • 7(2+3) - Translates to... The sum of 2 and 3 multiplied by 7
  • 5 + (8/4) - Translates to... The quotient of 8 and 4 increased by 5
  • 9 less than the sum of 12 and a number - Translates to... (12+n) - 9
  • the product of 6 and 7 increased by 1 - Translates to... (6*7) + 1

*** PLEASE NOTE: There are more than one way to translate some of the mathematical expressions and mathematical phrases.

After going over this, I will then transition to facilitating understanding of algebraic expressions in a real-world context. 

During this portion of the lesson, students will learn how to define a variable and write an expression based upon how the mathematical situation is presented.

Examples that I will use to demonstrate this concept are as follows:

  • California has three times as many airports as Georgia.
    • Express the number of airports California has as an algebraic expression.
    • Express the number of airports Georgia has as an algebraic expression.
  • Write each phrase as an algebraic expression
    • Eight dollars more than Ryan earned
    • Ten dollars less than the original price
    • Four times the number of gallons

Using the above examples I should be able to get my students to understand how mathematical phrases and situations relate to mathematical expressions.


Try It Out

5 minutes

To try out the concepts presented in this lesson, my students will translate the following mathematical expressions and phrases. Afterward, we will go over the answers as a class to determine whether or not the students are ready to move on to solving problems on their own.

The mathematical expressions and phrases that the students will translate are as follows:

  1. (6-3)/5
  2. 8 - (9*s)
  3. The sum of 4 and 5 times 8
  4. The quotient of 9 and a number less than 15
  5. Write the phrase 5 less than 3 times the number of points scored as an algebraic expressions.
  6. Write the phrase $3 more than four times the cost of a pretzel as an algebraic expression.
  7. Terri bought a magazine for $5 and 2 bottles of nail polish. Write an expression to represent the total amount she spent.
  8. What if we knew that each bottle of nail polish costs $3, how much would Terri have spent in total?

To complete these problems successfully, I am looking for my students to demonstrate that they can define the variable and determine the operations necessary to represent each mathematical situation. Also, I am looking for my students to be able to translate a mathematical expression into words, using precise mathematical language. 

Please click on PowerPoint attached to this section of this lesson to digitally project these problems.


Independent Exploration

20 minutes

During the independent exploration portion of this lesson my students will practice writing algebraic expressions given a mathematical phrase or situation. They will do this by completing the worksheet attached to this section, independently for 15 minutes. After 15 minutes, they can consult with a peer for 5 minutes. They will discuss misconceptions, compare and contrast their solutions, and ultimately debate, critique, and discuss the concept of translating mathematical phrases and situations.

Each set of partners will be required to create a bulleted list of what they have learned as well as the ideas that they may still be struggling with.

Closing Summary

15 minutes

To close out today’s lesson we will participate in a whole group discussion where students will share what they learned today from me and from their partnered discussions. Each set of partners will come up and place their bulleted list on the board. We will use these lists to guide our discussion. We will also compare and contrast the different items presented on the different lists. Through this discussion, I am hoping to provide my students with a deeper understanding by addressing those questions that they presented on their list as well as those questions that they may not have thought of that are presented on other student lists. By displaying and discussing everyone's understandings and misunderstandings we will cover the content of this lesson in a more comprehensive fashion that allows for a deeper understanding of the concept.