Writing Equations

Writing Equations Using Symbols

First: our goals for Module 4

• I can use my knowledge of proportional relationships to compare situations that have constant rates and find missing information in problems by solving linear equations.

• I can solve linear equations in one and two variables

• I can interpret the unit rate as the slope of a linear equation

In 6th and 7th grade:

• 6.EE.B.7 - Solve real-world and mathematical problems by writing and solving equations of the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞

• 7.EE.B.4 - Solve word problems leading to equations of the form 𝑝𝑥 + 𝑞 = 𝑟 and 𝑝(𝑥 + 𝑞) = 𝑟.

Paulo has a certain amount of money. If he spends $6.00, then he has 1/4 of the original amount left. 

• We can express this statement symbolically with math:

•  $x-6=\frac{1}{4}x$  

• Are there other ways we an represent this statement symbolically?

Some background:

• People started using letters to represent numbers in mathematical statements in the 1600s, introduced by René Descartes

• Before, people used words and sentences to describe mathematical situations

• Using letters expanded the possibilities of math and also saved time and work

• Writing in symbols is simpler than writing in words, as long as everyone involved is clear about what the symbols mean. 

How to write statements with symbols

• Define your variables. State clearly what you want each symbol to represent.

• Break complicated problems into smaller parts.

• Statements can be represented as more than one correct symbolic equation.

Shauna is reading a book. On Monday, she was one-third done. On Tuesday, she reads 46 more pages and finishes the book.

• How do we write this symbolically?

• We can use x to represent the number of pages in the entire book

•  $\frac{1}{3}x+46=x$  

A whole number has the property that when the square of half the number is subtracted from five times the number, we get the number itself. 

• How do we write this symbolically?

•  $5x-\left(\frac{x}{2}\right)^2=x$ 

The sum of three consecutive integers is 372. 

• How do we express this symbolically?

•  $x+\left(x+1\right)+\left(x+2\right)=372$  

The sum of three consecutive odd integers is 93

• How do we express this symbolically?

•  $x+\left(x+2\right)+\left(x+4\right)=93$  

To summarize: how to write statements with symbols

• Define your variables. State clearly what you want each symbol to represent.

• Break complicated problems into smaller parts.

• Statements can be represented as more than one correct symbolic equation.