Revision:
When solving practical problems, the general procedures are:
Step 1: Understand the problem and use a variable (e.g. x) to represent one of the
unknown quantities.
Step 2: Set up an equation in x and y according to the information given in the
question.
Step 3: Choose the most appropriate algebraic or graphical method to solve the listed
equation.
Step 4: Check the solution to see if the steps are acceptable and reject those which are
unreasonable.
Step 5: Write down clearly the answer(s) to the problem in a complete sentence.
The word problem:
The total cost of 4 apples and 3 oranges is $23, while the total cost of 7 apples and 4
oranges is $34. How much does each apple and orange cost?
Teacher’s scaffolding for students in a probing dialogue
T: When we are solving a word problem, what should we do at the beginning?
S: Let the unknown be x
T: What is the unknown in this question? / What do we need to find in this question?
S: apple and orange cost
T: So that means we have 2 unknowns. If x represents the total cost of each apple,
what should represent the total cost of each orange?
S: y
T: Should we have a unit?
S: Yes
T: So what’s the unit?
S: dollar
T: So…Step 1 is “Let the cost of each apple be $x and the cost of each orange be $y”
T: Then how do we set up the equation?
S……
T: Maybe, let’s read the question carefully and underline the key words first.
S: OK.
T: So what are the key words e?
S: total cost
T: Any more?
S: apples and oranges
T: any more?
S: no
T: How do we find the total cost? The total cost depends on…
S: The total cost of 4 apples
T: And also…?
S: The total cost of 3 oranges
T: That means it depends on two things - one is the total cost of apples and the other is
the total cost of oranges
T: How do we calculate the total cost of apples?
S: Number of apples times the cost of apple
T: Exactly! The number of apples times the cost of “each” apple
T: Is it the same for the total cost of oranges?
S: Yes.
T: Now express it by using mathematical symbols
T: For the first piece of information, what is the number of apples?
S: Four
T: And for the oranges?
S: Three
T: What is the total cost of 4 apples?
S: 4x
T: How about the 3 oranges?
S: 3y
T: OK!!! So who can put all that together and tell me the equation?
S: Me!!! 4x + 3y = 23
T: How about the second piece of information?
S: 7x + 4y = 34
…..