Lesson: Writing and Solving Equations
Introducing the Concept
Translating expressions and equations from numbers and symbols to words is the first step in writing equations. A more challenging aspect is having students analyze a word problem and generate expressions and equations from words or word phrases themselves. Students may have difficulty with the variety of information presented in a word problem. Work with the class to isolate the specific information needed to write an expression.
Materials: overhead projector or chalkboard
Preparation: none
Prerequisite Skills and Concepts: Students should be familiar with words that indicate operations as well as numbers. They should also have a working knowledge of the use of parentheses in an expression as well as the process of simplifying.
Write “3 more flowers than” and “the total amount” and “the difference between” and “what is left” on the board or overhead.
- Ask: Can anyone tell the class what operations are described by these words?
You are trying to have the students represent words by using mathematical symbols or operations. “More than” and “total” indicate addition. “Difference” and “left” indicate subtraction.Write or project the following on the board or overhead: “Three boys went to the movies with five dollars each in their pockets.”
- Ask: How could we write an expression that would show the money the boys have?
Try to keep the students from rushing ahead and adding the money for a fifteen-dollar total. Draw attention to each separate five-dollar amount. Students should suggest 5 + 5 + 5. If students suggest 3 x 5, tell them you want them to work with addition. - Ask: Which words told us the amount of money each boy had?
Students should point out the words “three,” “five dollars,” and “each.” - Say: “Three” is the number of boys. There will be three addends in the expression. “Five dollars” is the amount each boy has. These will be the addends. And “each” tells us that all three boys had the same amount.
Review how the expression was generated by walking through each of these statements.Write
++ for the three boys and three addends.
Then write 5 in each blank space. Note that the amount is the same for each boy.Write: “At the movies, the boys gave their money to the cashier, who combined it in an envelope with one hundred dollars.”
- Ask: What should be added to our original expression to show what the cashier did?
Keep the 5 + 5 + 5 expression in front of the class. Students should suggest adding “+ 100” to this expression. - Ask: Which words told us the amount of money the cashier had and what she did with it?
Students should point out the words, “one hundred dollars” and “combined it … with.” - Say: “One hundred” is the cashier's money. This is another addend for the expression. “Combined it … with” tells us it is added to the boys' money.
Review how this addend was included in the expression by walking through these statements. - Write on the board or overhead
5 + 5 + 5 + .
Then add 100 in the last blank.
Note that the amount of the cashier's money combined with the boys' money differs. - Ask: How could I group the addends to show the boys' money and the cashier's money?
Students should suggest placing parentheses around 5 + 5 + 5.Write (5 + 5 + 5) + 100.
- Say: If we total the amount inside the parentheses, we know how much all three boys spent at the movies.
If necessary, show the addition of 5 + 5 + 5 separately to produce a total of 15.Rewrite the expression as 15 + 100. Students should note that now this expression tells how much the cashier had in the envelope. Further simplify the expression by adding. The result is 115.
Repeat this process by using different problems and stressing the proper construction of an expression as well as the placement of parentheses. Different words can be used to indicate different operations.