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Join for free resources →Have you ever wondered how to teach your 6th or 7th grade students writing algebraic expressions from word problems?

In this lesson plan, students will learn how to write expressions, translate verbal phrases into algebraic expressions and work with expressions that include exponents. This artistic lesson plan includes guided notes (interactive sketch notes), check for understanding questions, and practice with a maze activity as well as a doodle and color by number activity to build understanding.

The lesson culminates with a real-life application where students learn how algebraic expressions help them to model a lemonade stand to make the most profit.

- Duration: 2 Hours
- Type: Lesson Plans
- Standard: CCSS 6.EE.A.2.a
- Topic: Expressions
- Grades: 6th Grade, 7th Grade

After this lesson, students will be able to:

Write algebraic expressions to represent real-life situations

Translate verbal phrases into algebraic expressions

Work with expressions that include exponents

Understand how algebraic expressions can be used in a real-world application (e.g. to model costs, revenue, and profit in a lemonade stand business)

Before this lesson, students should be familiar with:

Basic math operations (addition, subtraction, multiplication, and division)

Understanding of variables and their use in equations

Basic understanding of exponents (optional, but helpful)

Materials:

Pencils

Colored pencils or markers

Writing Algebraic Expressions Guided Notes

Algebraic expressions

Sum, Difference, Product, Quotient (and more keywords specific to each operations!)

Verbal phrases

Exponents

Costs, revenue, and profit

As a hook, ask about whether they’ve ever started a business like a lemonade stand? What were the costs in the business, and how do they know if they’re making money? Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the first page of the guided notes to introduce writing expressions, specifically key words associated with each of the four operations. Then have students practice translating verbal phrases to expressions and expressions back to verbal phrases. Refer to the FAQ below for ideas on how to respond to common student questions.

**Check for Understanding.**Have students walk through the “You Try!” section. Call on students to talk through their answers. Based on student responses, reteach concepts that students need extra help with.

Use the second page of the guided notes to introduce translating between verbal phrase and expressions. Refer to the FAQ below for ideas on how to respond to common student questions.

**Check for Understanding.**Have students walk through the “Practice” section. Call on students to talk through their answers. Based on student responses, reteach concepts that students need extra help with.

Use the guided notes to introduce expressions with exponents. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

**Check for Understanding.**Have students walk through the “You Try!” and “Putting It all Together” sections. Call on students to talk through their answers, potentially on the whiteboard or projector. Based on student responses, reteach concepts that students need extra help with.

If your class has a wide range of proficiency levels in the various checks for understanding, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

Have students practice writing algebraic expressions from verbal phrases and key words using the maze activity included in the lesson plan. Walk around to answer student questions.

Fast finishers can dive into the doodle math activity for extra practice. You can assign it as homework for the remainder of the class.

Bring the class back together, and introduce the concept of running a lemonade stand as a real-life application that requires the use of algebraic expressions. Students will learn how to use algebraic expressions to model costs, revenue, and profit in a lemonade stand business. Refer to the FAQ for more ideas on how to teach it!

A fun, no-prep way to practice writing algebraic expressions is Doodle Math — it's a fresh take on color by number or color by code. It includes a vocabulary sheet, 3 levels of practice, and comes with a nature theme perfect for a review day or sub plan any time of year.

Algebraic expressions are mathematical statements that involve variables, constants, and arithmetic operations such as addition, subtraction, multiplication, and division. They are used to represent real-world situations and can be manipulated and simplified using algebraic rules and properties.

Algebraic expressions are mathematical statements that use numbers, variables, and arithmetic operations (such as addition, subtraction, multiplication, and division) to represent real-world situations. Being familiar with common key words associated with addition, subtraction, multiplication, and division will be immensely helpful. They can be manipulated and simplified using algebraic rules and properties.

Exponents are a mathematical notation used to indicate that a number should be multiplied by itself a certain number of times. For example, if you have the expression "2^3", this means that you should multiply 2 by itself three times: 2 x 2 x 2 = 8. The number 3 in this expression is the exponent.

Verbal phrases in algebraic expressions are words or phrases that describe a mathematical operation or relationship. Here are some examples:

"Three times a number": 3x

"The sum of 5 and a number": x + 5

"The difference between a number and 8": x - 8

"The product of 7 and a number": 7x

"The quotient of a number and 2": x/2

"The square of a number": x^2

"The cube of a number": x^3

Translating verbal phrases into algebraic expressions is an important skill in solving real-world problems using mathematical equations.

To translate a verbal phrase into an algebraic expression, you need to identify the key words and phrases that indicate mathematical operations. This is covered in the Writing Algebraic Expressions Guided Notes.

For example, the phrase "twice a number increased by 5" can be translated to the expression "2x + 5", where "x" represents the unknown number. The word "twice" indicates multiplication by 2, and the phrase "increased by" indicates addition.

If your students need a visual example, I find this Khan Academy video to be helpful:

By breaking down the verbal phrase into its mathematical components, you can create an algebraic expression that represents the situation.

When working with expressions that include exponents, it's important to remember that the exponent indicates how many times the base number should be multiplied by itself. For example, if you have the expression 2^3, this means that you should multiply 2 by itself three times: 2 x 2 x 2 = 8. You can simplify expressions with exponents using rules such as the power of a power rule, power of a product rule, and power of a quotient rule.

Algebraic expressions are highly applicable in various fields, here are some specific examples:

**Finance:**Algebraic expressions can be used to calculate costs, revenue, and profit in a business. For example, a business owner can use algebraic expressions to determine the cost of producing goods or services, the revenue from sales, and the profit margin.**Engineering:**Engineers use algebraic expressions to design and analyze structures such as bridges and skyscrapers. For instance, they can use algebraic expressions to calculate the load capacity of a bridge and ensure its stability.**Physics:**Algebraic expressions are commonly used in physics to model and solve problems related to motion, energy, and forces. For example, algebraic expressions can be used to calculate the velocity of an object, the amount of work done on an object, and the force exerted on an object.**Computer Science:**Computer scientists use algebraic expressions to write algorithms and perform various computations. For instance, they can use algebraic expressions to calculate the running time of an algorithm or to represent data structures such as arrays and matrices.**Statistics:**Algebraic expressions are used in statistics to analyze data and make predictions. For example, algebraic expressions can be used to calculate the mean, median, and mode of a set of data, as well as to calculate probabilities and make predictions based on statistical models.

Algebraic expressions can be used to model costs, revenue, and profit in a business, such as a lemonade stand. Here are some example equations:

**Costs:**The cost of producing lemonade can be represented by the equation`C = f + v`

, where`f`

is the fixed cost (e.g. the cost of buying a pitcher and cups) and`v`

is the variable cost (e.g. the cost of lemons, sugar, and water).**Revenue:**The revenue from selling lemonade can be represented by the equation`R = p * s`

, where`p`

is the price per cup and`s`

is the number of cups sold.**Profit:**The profit from selling lemonade can be represented by the equation`P = R - C`

, where`R`

is the revenue and`C`

is the cost.

By using algebraic expressions to model costs, revenue, and profit, a lemonade stand owner can make informed decisions about pricing, production, and marketing strategies. For example, they can determine the optimal price per cup to maximize profit, or decide whether to increase production to meet demand.

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