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Title
Word Problems Strategies
Lesson Objective
Students will demonstrate their ability to solve problems in mathematics by selecting and correctly applying appropriate problem
solving strategies to a given problem and explaining why the strategies are appropriate.
Background Information for Teacher
N/A
Student Prior Knowledge
Students should have a basic level of proficiency with addition and subtraction with/without regrouping, multiplication and division.
Materials:
list of problem solving process and strategies (included in Step 2)
chart paper or whiteboard
markers
paper
pencil
Step-by-Step Guided Lesson
Step 1: Start Video
(Tips: Interact with the video by pausing, to ask questions or discuss information viewed with student.)
Step 2: Teach Lesson
Discuss problems students have had and the ways they solved them. Ask students these kinds of questions:
a. Have you ever forgotten your lunch? What did you do?
b. Have you ever been unable to do your homework because you didn't understand it? What did you do?
c. Have you ever been in a fight with somebody? How did you work it out?
Talk about the strategies scientists, engineers, and mathematicians use when solving problems. How are their strategies similar to
those of the students? Below is a list of a few different types of problem solving strategies.
Use guess and check. When a problem calls for a numerical answer, a student may make a random guess and then
check the guess with the facts and information given within the problem. If the guess is incorrect, the student may
make and check a new guess. Each subsequent guess should provide more insight into the problem and lead to a
more appropriate guess. In some instances the guess and check strategy may also be used with problems for which
the answer is non-numerical.
Draw a picture or a diagram/use a graph or number line. A picture or graph may illustrate relationships between
given facts and information that are not as easily seen in word or numerical form.
Use manipulatives or a model/act it out. When a problem requires that elements be moved or rearranged, a
physical model can be used to illustrate the solution.
Make a list or table. A list or table may be helpful to organize the given information. It may be possible to make an
orderly list or table of all possible solutions and then to choose the solution that best fits the given facts and
information from this list. In some problems, the answer to the problem is a list or table of all possible solutions.
Eliminate possibilities. When there is more than one possible solution to a problem, each possibility must be
examined. Potential solutions that do not work are discarded from the list of possible solutions until an appropriate
answer is determined.
Look for a pattern. Patterns are useful in many problem-solving situations. This strategy will be especially useful in
solving many real-world problems. “Patterns are a way for young students to recognize order and to organize their
world” (NCTM, 2000, p. 91).
Choose the operation/write a formula or number sentence. Some problems are easily solved with the application
of a known formula or number sentence. The difficulty often lies in choosing the appropriate formula or operation.
Work the problem backward. If the problem involves a sequence of steps that can be reversed, it may be useful to
work the problem backward. Children at the early childhood level may already have some experience in working
backward. In solving many mazes and puzzles, it is sometimes easier to begin at the end than to begin at the
beginning.
Ask the student the following questions: When does diagramming or drawing pictures come in handy? When do students or their
parents make lists to help them solve problems? How does discussing a problem or situation help solve it? Why is it important to
think clearly and be organized when solving a problem?
Brainstorm some home-based problems with the student, (such as taking out the trash, noise, incorporating healthier foods in meal
planning, the need for more computer time or devices). Choosing one, discuss with the student how they might go about solving it.
What are some possible solutions to this problem? How would you test the solutions? Who would you talk with to discuss possible
solutions? Would a diagram or drawing help you solve this problem? Do you need math to solve this problem? What would you say
to make people understand your solution?
Demonstrate drawing a line down the center of a piece of paper. Draw an example of a problem on one side of the paper, such as
planning lunch or difficulty building a model airplane. On the other side of the divided paper, draw a solution to the problem, perhaps
asking for help, or a child drawing a diagram of the model airplane.
Distribute drawing paper and have the student divide their paper in half and write or draw a problem on one side and the solution on
the other side. Once the student has completed their drawing, have them share and explain their drawing and how the arrived to their
solution.
Now it is time for the student to solve a couple of word problems. Complete the two problem with the student using the steps in the
video in Step 1. Have the student decide which strategy they would like to use to solve each problem. Encourage different strategies.
Problem One
Mrs. Mason has just returned from a day trip to Washington D.C. She looked in her wallet and found that all she had left were two
one dollar bills, a twenty dollar bill, a five dollar bill, three quarters, a nickel, a dime and three pennies. She remembered that she only
spent money twice during the trip. She spent $15.07 on gasoline and some money on food. When she counted the amount of money
in her wallet, she realized that it was exactly half of the amount of money she left home with in the morning. How much money did
she spend on food during her trip? Which strategy or strategies did you choose? Explain why you think you chose the best strategy
for solving this problem?
First we need to count /add to find out exactly how much is left in the wallet. We know that the amount spent on food would be the
difference between double the money she has left now and money she has now plus money spent on gasoline… (The student might
proceed to solve it that way, or may discover that since they asked to find out how much was spent on food, they could simply say
change-gas money=food money. Check the student’s plan and provide feedback as needed. Have the student solve the problem
individually based on their plan. Discuss the solution process once the student has solved the problem. If the student solved the
problem incorrectly, give students an opportunity to try again if needed.
Answer: She spent $12.86 on food.
Problem Two
Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?
Answer: She spent $6.80.
Finally, have the student complete the worksheet from Step 3. Encourage the student to select a strategy to solve each problem.
Step 3: Complete the worksheet attached below.
Worksheets for extra practice with answer key
Step 4: Review. Start the next lesson with the game or activity attached below for review so the student can demonstrate
understanding of this lesson before moving forward.
Multi-Step Word Problems (online practice) with answers