Missing Information
In some problems, information needs to be found before the problem can be solved. Sometimes students may need to find the number of feet in a yard, the number of days in the month of January, the number of minutes in an hour, or the number of ounces in a pound, before they can solve the problem. For example:
Serena buys milk every school day for lunch. How many containers of milk does she buy in a week?
I know there are 7 days in a week. There are 5 school days in a week. If she buys one container every school day, she will buy 5 containers in a week.
Multiple Operations
Some problems have multiple steps involving multiple operations. Model how to solve these problems, thinking aloud to make your thoughts visible. Have students read the problems carefully and think aloud or take notes to record their thinking. For example:
Olivia has 6 baseball cards. Owen has 2 more cards than Olivia. Oscar has twice as many cards as Owen. How many baseball cards do they have in all?
You might think aloud saying something such as:
"The problem says "how many in all," so I probably have to add. First I have to find how many cards each person has. I know Olivia has 6 cards. I'll write that down.
Olivia, 6 cards
Two more cards would be 6 + 2 = 8, so Owen has 8 cards.
Owen, 8 cards
"Twice as many" means 2 times the number. So, 8 times 2. Or I could add 8 two times. 8 + 8 = 16.
Oscar, 16 cards
Now I have to find the number of cards in all, so I'll add the cards together.
6 + 8 + 16 = 30 cards
Number Sentences
Some students may find it easier to translate word problems directly into number sentences, for example:
Word Problem
Katie pays with a $10.00 bill and receives $2.57 in change. How much did she spend?
Number Sentence
Money Katie paid with - cost of what she bought = change
Fill in the sentence with numbers and then find the missing amount to solve the number sentence.
$10.00 - cost of what she bought = $2.57
To find how much change, I need to subtract.
$10.00 - $2.57 = $7.43Check Your Answer
Read the problem again to be sure the question was answered.
Katie pays with a $10.00 bill and receives $2.57 in change. How much did she spend?
I found how much she spent, so I answered the question.Check the math to be sure it is correct.
$10.00 - $2.57 = $7.43, and $7.43 + $2.57 = $10.00
Determine if the best strategy was chosen for this problem, or if there was a better way to solve the problem.
I used the correct information and subtracted to find the change. I chose the correct operation to find the answer.
Explain the Answer
Students should be able to explain their answer and the process they went through to solve a problem using words first, and then learn to use conventional mathematical symbols or their own forms of representations to convey their thinking. It is important for students to talk or write about their thinking. Give students frequent opportunities to explain their problem-solving strategies and solutions and to seek general methods that apply to many problems.
Guided Practice
Have students try solving the following problem, choosing the correct operation and focusing on important information.
There are 6 turkey sandwiches and 24 cans of soda. Each sandwich costs $5.85, and is cut in half. If 3 people eat 3 halves each, how many sandwiches will be left?
Have students work in pairs, groups, or individually to solve this problem. They should be able to tell or write about how they found the answer and justify their reasoning.
How Can You Stretch This Strategy?
Math problems can be simple, with few criteria needed to solve them, or they can be complex, requiring several steps to find the answer. As students become proficient in solving word problems, increase the difficulty of the problems you present to extend students' thinking and challenge their problem-solving skills. For example, consider these problems:
"Manuel has fourteen books. He gets three books for his birthday. How many books does he have now?"
"Manuel has fourteen books and loses two books, then gives away three books. How many books does he have left?"
"Manuel is buying two books. If one book costs $14.95 and another costs $4.50, how much change will he get back if he pays with $30.00?"
