Writing Equations
Math A (Grade 9)

Materials: 
Calculator, worksheets, pencils, guided notes, chalk, chalkboard 

Lesson Overview:  
Students will develop a clear understanding of how to create algebraic equations from verbal sentences and also how to create sentences from algebraic equations.

Lesson Objectives:  
J	Students will be able to execute the Four-Step Problem Solving Plan when solving word problems.
J	Students will be able to translate sentences into algebraic equations.
J	Students will be able to translate equations into sentences.

NYS Standards:
J	Key Idea 3:  Operations
		~Use addition, subtraction, multiplication, division, and exponentiation 			  with real numbers and algebraic expressions (3A)
J	Key Idea 4:  Modeling/Multiple Representation  
		~Represent problem situations symbolically by using algebraic expressions 		  (4A)

Anticipatory Set: (time 5 minutes)
Pass out the Let’s Get Started worksheet out to the students.  The students will be required to write an algebraic expression based on a sentence, and also a sentence based on an algebraic expression.  (This was introduced in the very first lesson taught.)

		Answer:  37 less than 5 times the square of a number

	A pair of shoes costs x dollars.  What would the algebraic expression be to show the cost of 10 pairs of shoes?
		Answer:  10x
Go over the answers as a class.

Developmental Activity:
	1.)  Pass out Guided Notes for Writing Equations worksheet.
	2.)  Fill in the blanks with the students.
	3.)  Work through the examples as a class as they appear in the notes on the board. 	Be sure to give more examples if the students are struggling.

Closure:	
Students will work in pairs on Write it Out worksheet.  I will circulate around as the students are working to make sure that they are on task and know how to complete the questions.  Once the students are finished I will go over the answers on the chalk board with the students.  If students are struggling or still have questions go back and review problem areas.

Assessment:
Students will be given a homework worksheet that will be collected next class.  During the next class students’ questions that they had on the homework should be addressed.

Name:									Date:

Let’s Get Started!!

Name:					Teacher Copy			Date:

Guided Notes for Writing Equations 

An equation is an algebraic expression that is set equal to something.

	Examples of other expressions that imply the equals sign:
		is, is equal to, is as much as, equals, is the same as, is identical to

Recall, variables are used to represent the unspecified values in a sentence or problem.

Translate a sentence into an equation, example:
	Two times a number n decreased by eight is equal to seventy.
		2n-8=70

Example:  Five times the sum of x and y is the same as seven times x.
			5(x+y)=7x

Now let us try it the other way!
Translate and equation into a sentence:
	3(ab)=3a
	Three times the product of a and b is the same as three times a.

Example:  20(d-f)=18d
	Twenty times the difference between d and f equals eighteen times d.

The four-step problem-solving plan can help you solve any word problem!!

Step 1:  Explore the problem
		~Identify what info is given and what you are suppose to find
Step 2:  Plan the solution
		~Write an equation
Step 3:  Solve the problem
Step 4:  Examine the solution
		~Does the answer make sense?

Example:  Use the Four-Step Plan.  The population of the United States in 2001 was about 284,000,000 and the land area of the United States is about 3,500,000 square miles.  Find the average number of people per square mile in the United States.

Explore:  You know there are 284,000,000 people.  You want to find out the number of 	 	    people per square mile.
Plan:  Write equation-let p be the number of people per square mile
	3,500,000 x p=284,000,000

Solve:  p is approximately 81.14.  Therefore there are about 81 people per square mile.

Examine:  81 x 3,500,000=283,500,000 which is about 284,000,000

Name:										Date:

Guided Notes for Writing Equations 

An _____________    is an algebraic expression that is set ______________to something.

	Examples of other expressions that imply the equals sign:
		______, ______________, ____________, __________, ___________, 			_______________

Recall, ___________ are used to represent the unspecified values in a sentence or problem.

Translate a sentence into an equation, example:
	Two times a number n decreased by eight is equal to seventy.

Example:  Five times the sum of x and y is the same as seven times x.

Now let us try it the other way!
Translate and equation into a sentence:
	3(ab)=3a

Example:  20(d-f)=18d

The __________________________________ can help you solve any word problem!!

Step 1:  ___________ the problem
		~Identify what info is given and what you are suppose to _________.
Step 2:  Plan the _____________  
		~Write an _____________
Step 3:  __________ the problem
Step 4:  Examine the _____________
		~Does the answer make sense?

Example:  Use the Four-Step Plan.  The population of the United States in 2001 was about 284,000,000 and the land area of the United States is about 3,500,000 square miles.  Find the average number of people per square mile in the United States.

Explore:  

Plan:  

Solve:

Examine:  

Name:										Date:

Write it Out

Translate the sentence into an equation:

One-third of the sum of m and n is 72.

Translate the equation into a sentence:

Use the following information to answer the next two questions:

Matthew is training for to prepare for a wrestling tournament.  He weighs 170 pounds now.  He wants to lose weight so that he can start the tournament at 160 pounds.

If t represents the number of pounds he wants to lose, write an equation to represent the situation.

How many pounds does Matthew need to lose to reach his goal?

Name:									Date:

Homework

Mrs. Smith is planning to place a fence around her garden.  The fencing costs $2.25 per yard.  She buys f  yards of fencing and pays $5.55 in tax.  If the total cost of the fencing is $52.80, write an equation to represent the situation.

Translate into a sentence: