Solving Expressions in Word Problems
Students will be able to solve multi-step word problems by writing and solving expressions with the order of operations.
- Review PEMDAS (or GEMDAS). Hand out the Expressions & Word Problems worksheet and display its top section using a document camera. With student input, put the operations in order.
- Remind students that this specific order is called the order of operations and it is important because it is a universal set of rules for how to solve multi-step problems.
- Point out that multiplication and division are part of the same step. This means that these two operations are done during the same step, from left to right. The same is true for addition and subtraction.
- Write the acronym (PEMDAS or GEMDAS) on the board in large letters and tell students that they can use it as a reminder throughout the lesson.
- Explain that today students will practice using the order of operations and written statements to solve multi-step word problems.
Explicit Instruction/Teacher modeling(10 minutes)
- Review the definition of the key terms expression (a numerical phrase with numbers and operations) and equation (two expressions that are equal to one another, separated by an equal sign). Provide examples for each term (e.g., 2 + 4 vs. 2 + 4 = 11 – 5) or ask students to suggest examples. Explain that today students will be working with expressions.
- Write an expression on the board, like 2 + 3 x 5. Demonstrate how to solve the expression using the order of operations.
- Ask students to consider what would happen if you tried to solve the expression without using the order of operations. Call on students to suggest ideas. Then, show students how the outcome is different if you solve left to right instead of using the order of operations.
- Emphasize that, in order to get the correct answer, we must always use the order of operations.
- Direct students' attention to the second section of the Expressions & Word Problems worksheet and model how to solve two expressions using the order of operations.
- As you solve each expression, model how to say and write it in word form (e.g., (7 x 2) + 3 is "three more than double seven").
- For the remaining three expressions, instruct students to work in pairs to solve each expression.
- Call on students to share their answers, then model how to write each expression in word form (e.g., "the difference between eleven and seven times five squared").
- Remind students of key terms and common math vocabulary if needed. Write key terms, like "quotient," "sum," and "product" on the board for student reference.
Guided Practice(15 minutes)
- Direct students' attention to the third section of the Expressions & Word Problems worksheet. Complete one multiple choice question as an example.
- Instruct students to work in pairs or small groups to discuss and solve the remaining four problems in the section.
- Call on students to share their answers and correct misconceptions as needed.
- Display the first word problem in section four and read it aloud. Identify keywords and phrases that suggest operations or expressions. Highlight each word or phrase as you model your thinking.
- Support students in writing an expression based on the word problem. Then, have students solve the expression with a partner.
- Invite a student to share their work with the class and correct misconceptions as needed.
Independent working time(10 minutes)
- Instruct students to solve the remaining two word problems independently. Remind them to look for key terms before writing an expression.
- Circulate and offer support as needed.
- When students are finished, call on volunteers to share the key terms they identified and the expressions they wrote. Then, invite them to share their solution.
- Review key math terms in a mini pre-lesson.
- Strategically form partnerships during guided practice so that struggling students are paired with grade level or advanced peers.
- Have students work in pairs to develop their own word problems using the phrases they saw during the lesson. Then, have partners swap their word problems with another pair of students and solve.
- Have students work in groups to create posters with key math terminology, example expressions, and phrases. Allow each group to present their poster to the class.
- Write a word problem on the board (e.g., "Kim picked three times as many lemons as Joe. Joe picked two less than a dozen. How many lemons did Kim pick?"). If needed, remind students that "a dozen" is equal to 12.
- Have students talk in groups to identify key statements and phrases in the word problem. Listen to groups to gauge understanding.
- Hand out an index card to each student. Instruct them to independently write an expression for the word problem and solve it using the order of operations.
- Collect student work as an exit card.
Review and closing(5 minutes)
- Lead the class in a brief closing discussion:
- What is challenging about solving word problems?
- What strategies did you use to solve word problems today?
- Remind students that not all word problems will have the exact phrases that they saw in the lesson today. A single expression can be written in many different ways. Provide an example (e.g., "two times three," "double three").
- Then ask follow-up questions:
- How can we use what we learned today as we solve other word problems in the future?
- What can we do if we see word problems with unfamiliar phrases?