Read and Write Equations

Read and Write Equations

I can

• Write an equation from a verbal sentence.

• Translate an equation into a verbal sentence.

• Determine if an equation is true by substituting values from a set into the equation.

Standards

• 6.AF.5 Solve equations of the form x + p = q, x - p = q, px = q, and x/p = q fluently for cases in which p, q and x are all nonnegative rational numbers. Represent real-world problems using equations of these forms and solve such problems.

• 6.AF.4 Understand that solving an equation or inequality is the process of answering the following question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Write this as an algebraic expression:

The quotient of 14 and a number less 27

Open Ended

Write this as an algebraic expression:

The quotient of 14 and a number less 27

What was your answer?

Real world example

• I needed 100 feet of fencing for my side yard. What could the measurements be for the length and width of my yard?

• 2x +2y = 100

Key Ideas

• An expression is a mathematical phrase. Therefore, verbal phrases are translated into expressions. For instance, the verbal phrase “a number increased by 4” can be translated into the expression n + 4.

Key Ideas

• An equation is a mathematical sentence. Verbal sentences containing words or phrases that describe equality, such as is, equals, is equal to, and is the same as can be translated into equations. For example, the verbal sentence “A number increased by 4 is 10” can be written as the equation n + 4 = 10.

Open Ended

Write an equation to model this verbal sentence:

A number decreased by 10 is 14.

A number decreased by 10 is 14.

• is means  $=$  

• "a number decreased 10" by tells us that a number we don't know should be subtracted by 10

•  $x-10\ =$  

• The words after the word is, tells us what should be on the right side of the equation. So 14 should be on the right side of the equation. 

•  $x-10=14$  

Open Ended

Write an equation to model the verbal sentence:

Two more than 3 times a number is the same as the number divided by 5.

Two more than 3 times a number is the same as the number divided by 5.

• "is the same as" - =

• The phrase to the left of is the same as describes the expression to the left of the equal sign.

• Two more than 3 times a number = 2 more than 3 times a number means 3 times a variable, such as n, plus 2

• 3n +2 =

Two more than 3 times a number is the same as the number divided by 5.

• 3n +2 =

• The phrase to the right of is the same as, describes the expression on the right side of the equation.

• the number divided by 5 means a variable (n) divided by 5

•  $\frac{n}{5}$  

• SO -  $3n+2=\frac{n}{5}$  

Poll

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• What is algebra?