Math Background

Lesson: Writing and Solving Equations
Developing the Concept

Once students practice isolating the specific words in a sentence that indicate operations and expressions, they are ready to write and solve equations.

Materials: overhead projector or chalkboard

Preparation: Write the word problem on the overhead projector or chalkboard.

Prerequisite Skills and Concepts: Students should be familiar with words that indicate operations as well as numbers and should understand that addition and subtraction are inverse operations. They will also need to simplify and evaluate expressions.

Write or project this word problem.

“Tina gave four CDs to her friend Dan. He put them in with his collection that he was donating to a local charity. His CD player was broken and he didn't listen to that kind of music anymore. But Dan's sister asked if she could take three of Tina's CDs. He told her she could, without remembering he had promised to donate at least ten CDs. He checked the box and there were still ten inside. How many CDs were in Dan's collection at the start?”

  • Say: Let's read through this word problem and see if we can create an equation that will solve it.
    Have students read the problem aloud. Then review the problem word by word, sentence by sentence, trying to locate the words that will become part of an equation.
  • Ask: What words in the first sentence could be part of an expression or an equation?
    You want the students to focus on “four” but “Tina” is also important because “Tina” and “four” go together.

    Write 4 on the board or the overhead.

  • Ask: What word in the second sentence tells us something about 4?
    The idea of these 4 CDs being “put in with” should suggest addition. The rest of the sentence is less important. But point out the word collection because this is what the 4 is put in with and it will be important later.
  • Say: “Put in with” means “combine” or “add to.” This indicates addition. Let's put a plus sign on the board.

    Write + on the board or overhead to the right of the 4, but leave room in between.

  • Say: Now let's look at the next sentence. You will notice that it doesn't mention any numbers, values, or words that show us an operation to use in an equation. This sentence has nothing to do with our equation. But the sentence after this gives us two more pieces to our equation.
    Go through the fourth sentence to isolate “take” and “three” from the sentence. Emphasize that “Dan's sister” is also important because it goes with “three” and “take.”
  • Ask: What operation does “take” suggest?
    Students should realize that “take” or “take away” refers to subtraction. In this case, we will need to take 3 from 4.

    Write − 3 to the right of 4 and the left of +.

  • Say: 4 − 3 is an expression that describes the number of CDs Tina gave and Dan's sister took away. Let's put parentheses around it to show this operation needs to be done first.

    Write (4 − 3) + .
    Remind students that they haven't written an equation yet. They are still gathering information.

  • Say: Let's look at the next two sentences. The word “ten” appears twice. This will be part of our equation. Notice also the word “collection.” We saw this earlier. Tina put her CDs in with Dan's collection. But these two sentences don't tell us how many CDs Dan had in his collection—just that there were 10 CDs in the box.
    Help students to realize that Dan's collection of CDs and Tina's CDs make up a total of 10.

    Write = 10 to the right of (4 − 3) +.

  • Ask: Does (4 − 3) + c = 10 make sense? What part is missing from this equation?
    Remind students that Tina's CDs are represented by (4 − 3) and this number was added to Dan's collection. Students should realize that they don't know a number for Dan's collection of CDs.
  • Say: Let's look at the last sentence to see what it tells us about our equation. Notice that it is a question. It's asking us to find the number of CDs in Dan's collection. An unknown number can be represented by a variable. Let's use c for “collection.”

    Write: (4 − 3) + c = 10.

    Guide students through the solution, recording the steps on the board or overhead.

    (4 − 3) + c = 10  
    (1) + c = 10 red left arrow simpify what is in the parentheses first
    c = 10 − 1 red left arrow use the inverse of addition, so subtract 1 from both sides of the equation
    c = 9  
  • Say: Now solve the equation by simplifying the expression and using inverse operations.
    Dan had 9 CDs in his collection at the start because there was only one left after Dan's sister took 3 of Tina's 4 CDs.
    Have students check that c = 9 by substituting it back into the equation.

Wrap-Up and Assessment Hints
Assign other word problems and have students practice going through the words and sentences, step by step to create an equation. Remind them that different words are used to indicate operations, expressions, and variables.

Houghton Mifflin Math Grade 5