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Multi-Step Word Problems
Students will be able to use problem-solving thought processes to help solve multi-step word problems.
- Write the following problem on the board and ask students to solve the problem in pairs on scrap paper: "Alexis lines up his jelly beans so that he creates an array with 4 jelly beans vertically and 6 jelly beans horizontally. Then, he adds 10 more to the total amount of jelly beans. How many jelly beans does he have in total?"
- Choose students to share their answers and how they solved the problem. Highlight the question they answered, the equations they used, and the important information and keywords as you jot down notes on the board from their explanations.
- Have students discuss what they had to do first in the problem (i.e., 4 x 6) and then the next step (i.e., 24 + 10). Choose students that have drawings that represent their answers. Have them show their work and explain their drawings.
- Tell students today they'll review how to solve multi-step word problems by rephrasing the question, drawing a picture, and labeling important information for each question.
Explicit Instruction/Teacher modeling(10 minutes)
- Model finding the correct answer to the problem from the introduction by restating the problem, listing the two steps, and then circling important information (e.g., "array," "4 up and 6 across," "10 more," "total," etc.).
- Write the following word problem on the board: "The class is having a party and students brought desserts. Alejandro brought in 11 cookies less than double the recipe. One recipe should make 24 cookies. How many cookies did Alejandro bring in total?" Read the problem three times. The first time you read, underline the question and restate the situation without any numbers (e.g., "Alejandro is bringing cookies to the party and he makes more than the normal batch, but he does not take all the cookies.").
- Read the question a second time and circle the numbers or key terms that suggest a mathematical operation (e.g., "double," "24 cookies," "11 less," etc.).
- Read the question a third time and think aloud how to solve the problem. For example, say, "I know he made double, or two times, the normal recipe of cookies and the normal recipe of cookies is 24 total. So, I need to do 24 x 2. He should have had 48 total cookies, but he had 11 less than the double batch. So, the next step is 48 − 11Because "less" means to subtract. Alejandro brought a total of 37 cookies to class."
- Write a checklist on the board for solving the multi-step word problem:
- Read the question one time and restate the situation without using numbers.
- Read the question again and circle key information.
- Read the question a third time and think about possible solutions. What expression can you make? What is the second expression?
Guided practise(20 minutes)
- Ask a student to summarize for the class how you were able to find out how many cookies Alejandro brought to the class. Then, ask another student to restate the steps you listed on the board to help them solve the word problem.
- Distribute the first page of the Can You Afford It? worksheet and scrap paper and ask students to follow the steps on the board to answer each of the questions. Allow students to complete the problems in partners, following the steps listed on the board. Have them brainstorm their processes together but make sure each partner completes every problem on their own paper.
- Stop in the middle of their work and review how to calculate the percentage of a whole number (i.e., the fourth problem from the top on the Can You Afford It? worksheet). See if students can walk you through the process before reviewing the steps yourself. Then, allow another student to show how to subtract using the decimals.
- Allow students to finish the worksheet page in partners. Review all the answers as a whole class to make sure all students have the correct answers before continuing to the independent practise section.
Independent working time(10 minutes)
- Distribute the second page of the Can You Afford It? worksheet. Have students complete the problems on their own.
- Allow students to review their answers with their partners and correct their own responses as necessary.
- Observe students and take note of any particular problem that many are struggling with. Review the problem with the whole class if necessary.
- Pre-teach key terms surrounding all mathematical operations, such as "earned," "taxes," "percentage," etc., and their significance or meaning in word problems.
- Allow students to complete less problems and compare answers with partners. Ask them to explain their process to their partner to show understanding.
- Pair students with a sympathetic partner that can explain how to solve a problem.
- Allow students to explain their process to the class and answer student questions about the word problems.
- Ask students to create their own multi-step word problems with different operations and values (e.g., some with decimals, fractions, or whole numbers). Allow students to solve each other's problems.
- Write the following word problem on the board: "Caren is collecting fallen leaves. She finds seven while waiting for the bus in the morning and eight when she gets to school. On the way home, she collects six times what she found earlier in the day. How many leaves did she collect in total?" Distribute a sheet of paper to each student.
- Ask students to solve the problem following the same steps from the board.
Review and closing(5 minutes)
- Choose volunteers to share their assessment answer aloud (i.e., (7 +6) x 6 = 90) and tell them to try to convince the class that it's the right answer. Allow students to ask follow-up questions, or challenge the presenter.
- Ask students to discuss in partners if the checklist was helpful or not in understanding the problem and helping them solve it. Use their answers to guide future word problem lessons.