Lesson 93: PEMDAS Word Problems

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson teaches students to tackle word problems that require multiple operations, reinforcing the use of PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to determine the correct solution order.

Learning Objectives

• Identify operations in a word problem and determine the correct order of operations.
• Translate word problems into mathematical expressions.
• Solve multi-step problems accurately using PEMDAS.

Topics Covered

• Translating word problems into mathematical expressions
• Applying PEMDAS in multi-step calculations
• Checking answers for reasonableness in context

Key Terms

• PEMDAS: The order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
• Expression: A combination of numbers, operations, and sometimes variables without an equals sign.
• Word Problem: A math problem written in a narrative form requiring translation into a numerical expression.

Lesson Examples

Example 1: Grocery Calculation

1. Problem: Sarah bought 3 packs of pencils at $2 each and a notebook for $5. How much did she spend in total?
2. Step 1: Multiply the number of pencil packs by the cost: 3 × 2 = 6
3. Step 2: Add the notebook: 6 + 5 = 11
4. Answer: Sarah spent $11 in total.

Example 2: Classroom Supplies

1. Problem: A teacher buys 4 boxes of markers, each with 12 markers. She also buys 5 packs of erasers, 3 erasers per pack. How many total items did she buy?
2. Step 1: Multiply markers: 4 × 12 = 48
3. Step 2: Multiply erasers: 5 × 3 = 15
4. Step 3: Add total items: 48 + 15 = 63
5. Answer: She bought 63 items in total.

Practice Problems

1. John bought 2 shirts for $15 each and 3 hats for $5 each. How much did he spend?
2. A gardener planted 5 rows of flowers, 8 flowers per row, and 3 trees. How many plants did she plant in total?
3. Emily reads 3 pages each morning and 2 pages each evening for 7 days. How many pages did she read in total?
4. A baker made 4 batches of cookies, 12 cookies each, and sold 10 cookies. How many cookies remain?

Tips & Common Mistakes

• Read the problem carefully and underline key numbers and operations.
• Write the expression before calculating to avoid skipping steps.
• Follow PEMDAS strictly, especially when parentheses are involved.

Summary

Word problems require careful translation into mathematical expressions. Using PEMDAS ensures accurate calculation of multi-step problems. Checking your answer in the context of the problem helps prevent mistakes and confirms reasonableness.

Challenge Problems

1. A store sells 5 pencils for $2 each and 3 notebooks for $4 each. If a customer buys 2 sets of these items, how much does he spend?
2. Mike has 3 boxes of chocolates with 10 pieces each and buys 2 more boxes with 12 pieces each. He gives 15 pieces to his friends. How many chocolates remain?
3. During a sale, a shopper buys 2 shirts at $18 each, 3 hats at $5 each, and a jacket for $25. Calculate the total cost.