Numerical Expression, Algebraic Expressions… What’s the difference?

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SWBAT demonstrate their ability to understand the significance of the different parts of a mathematical expression.

Big Idea

Express Your Self! The many different ways that a quantity can be expressed mathematically.

Curriculum Reinforcer

10 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students' minds so that the knowledge of these concepts become a part of students' long-term memories.


10 minutes

Today, I will open up today’s lesson with a discussion using the following question: In what ways do we use mathematics to express the value of a number?

Using this question, I am hoping that my students will realize that we express the value of numbers using mathematical expressions (which, at this point they would probably know this concept as a number sentence). To demonstrate this link between a number's value and a numerical expression, I will ask my students to express the number 9 mathematically. Hopefully this will prompt someone to give me an answer such as 3+6. Once I get one student to express 9 in a mathematical way, I will ask the rest of my students to give me other ways to express 9 mathematically.

After getting several answers, as far as, how to express the number 9, to make a connection that I hope will stay with my students, I will ten ask them the following:

"In what way can we as human beings express ourselves?" I should receive resonpnses such as happy, sad, mad, silly... etc.

I will then ask, "Does expressing ourselves in all these different ways change who we are? In other words, am I the same person when I am angry as when I am happy? Do I become someone else when I spressmyself in differnet ways? I should get the anser "no."

And once I get that student or students who say no, I will say, "Exactly!" I am still me whether I am happy, mad, sad... etc. 

I will then go on to explain that the same is true for the number 9, or any other number we can think of, for that matter. No matter how we express it, it is still the number 9. This is why we call these sets of numbers and symbols that represent a quantity, an expression. Because these sets of numbers and symbols express a particular quantity... In this case, the number 9.


Instruction & Teacher Modeling

10 minutes

In today’s instructional piece, I will be teaching my students the significance of the following vocabulary terms:

  • Numerical expression
  • Algebraic expression
  • Term
  • Operation
  • Variable
  • Constant
  • Coefficient
  • Exponent
  • Base

During this instruction, I will provide my students with a thorough explanation of each of these vocabulary terms as well as a visual demonstration as to their meaning. While I am presenting the vocabulary, my students will be taking notes using an organizer that will help them to decipher the meaning of each word.

After I have gone over these terms, I will then segue into teaching my students about algebraic expressions and how they differ from numerical expressions. Once again, students should be taking notes using the provided organizer.

Today's lesson focuses on the unit vocabulary, as these are words and phrases that the students have not yet been exposed to. For this reason, it is vital that a good amount of time is spent just understanding the language of this unit, as it is the foundation of the language that will be used for subsequent units, as well as subsequent mathematical content presented in higher grade levels.

Try It Out

5 minutes

To guide my students through this lesson, I will have them fill in a graphic organizer that will illustrate the similarities and differences between numerical expressions and algebraic expressions. This graphic organizer will also highlight the characteristics of each kind of expression while providing an example that students will be required to label. The students should be using this organizer during the instructional piece as a method of taking notes and making sense of the concepts being presented.


The numerical expression that I will use in the organizer is, (3*2) + 7^3 - 4. The algebraic expression that I will use in this organizer is, 3x + y^3 - 4.


Using these expressions, I will have the students demonstrate that they understand all of the vocabulary terms and their significance.



Independent Exploration

20 minutes

To demonstrate that they understand what was taught during today’s lesson, I will have my students label the different parts of eight different expressions using a color code. Each item will be assigned a color. For example, exponents will be red while base numbers will be blue, and terms will have to be circled in green, while coefficients are underlined in orange. I will have the students place a purple box around any constants, and they will have to identify the expression as numerical or algebraic. Furthermore, students will have to write the meaning of each part of a mathematical expression in their own words. All of this will be presented on the worksheet attached to this section of this lesson


After completing this activity, the students will complete a second task for which they will write a brief essay on all that they have learned today about numerical and algebraic expressions. Students will need to ensure that they highlight the similarities and more importantly the differences between numerical expressions and algebraic expressions.

Closing Summary

15 minutes

To close out today's lesson, selected students will present their completed assignments. I will choose eight students. Each student will present one problem and one definition written in their own words. The rest of my students will listen attentively while ensuring that they are ready to answer questions, make comments, and or critique their presenting peers.

Then, I will choose two other students to share what they wrote concerning what they learned during today's lesson. Once again, the rest of my students need to listen attentively while being ready to answer questions, make comments, and or critique their presenting peers.