Solving Problems Involving the GMDAS Rules

Lesson Overview and Competencies

• Unit 2: Operations and GMDAS Rules.

• Lesson 2: Solving Problems Involving the GMDAS Rules.

• Learning Competency: At the end of this lesson, the learners should be able to perform three or more different operations by applying the GMDAS rules.

• Learning Targets:

  • Analyze real-world problems and determine the appropriate mathematical operations needed.

  • Apply the GMDAS (Grouping, Multiplication, Division, Addition, Subtraction) rules to solve multi-step word problems.

  • Evaluate the accuracy of solutions and explain the reasoning behind the steps.

The GMDAS Rule Definition

• Interpretation of the Rule: The acronym stands for Grouping, Multiplication and Division, and Addition and Subtraction.

• Purpose: It dictates the specific order in which operations should be performed to correctly solve mathematical expressions.

• Example Expression: Consider the expression $5 + (3 \times 2) - 4$.

  • First, perform the operation inside the grouping: multiply $3$ and $2$ to get $6$.

  • Next, perform the addition: $5 + 6 = 11$.

  • Finally, subtract $4$ to find the result: $11 - 4 = 7$.

  • Complete string of operations: $5 + 6 - 4 = 7$.\n

Solving Word Problems Involving GMDAS

• Process: This task involves reading and interpreting word problems to identify the necessary mathematical operations, then applying the GMDAS rules to find the correct solution.

• Introductory Example (Book and Pen Purchase):

  • Scenario: You have $₱1,000$ and buy 3 books at $₱150$ each and 2 pens at $₱50$ each.

  • Goal: Determine the total cost and the remaining amount.

  • Step 1: Calculate Total Cost: $(3 \times 150) + (2 \times 50) = 450 + 100 = 550$.

  • Step 2: Calculate Remaining Amount: $1,000 - 550 = ₱450$.

Detailed Practice: Budgeting Money

• Problem Statement: You have $₱200$. You buy 2 notebooks for $₱30$ each and a pen for $₱20$. How much money will you have left?

• Systematic Solution:

  • Step 1 (Data Extraction):

    • Cost of 2 notebooks: $2 \times 30$

    • Cost of a pen: $20$

    • Budget: $200$

  • Step 2 (Expression for Total Expenses): $(2 \times 30) + 20$

  • Step 3 (Expression for Remaining Amount): $200 - [(2 \times 30) + 20]$

  • Step 4 (Simplification):

    • $200 - [(2 \times 30) + 20]$

    • $200 - (60 + 20)$

    • $200 - 80 = 120$

  • Conclusion: You will have $₱120$ pesos left.

Detailed Practice: Market Shopping (Ana)

• Problem Statement: Ana goes to a local market to buy ingredients for her small food stall. She buys 30 kilograms of vegetables. Each kilogram of vegetables costs twice as much as a kilogram of rice. After purchasing the vegetables and rice, she spends $₱150$ on spices. At the end of her shopping, she picks up fruits for an additional $₱200$. If one kilogram of rice costs $₱40$, how much did Ana spend in all?

• Systematic Solution:

  • Step 1 (Data Extraction):

    • Cost of one kilogram of rice: $40$

    • Cost of vegetables: 30 kilograms at twice the rice price: $30 \times (2 \times 40)$

    • Cost of spices: $150$

    • Cost of fruits: $200$

  • Step 2 (Total Expenses Expression): $[30 \times (2 \times 40)] + 150 + 200$

  • Step 3 (Simplification Processes):

    • Step 3.1: Evaluate the innermost grouping (Price of vegetables per kg): $2 \times 40 = 80$

    • Step 3.2: Evaluate the cost of all vegetables: $30 \times 80 = 2,400$

    • Step 3.3: Sum the totals: $2,400 + 150 + 200 = 2,750$

  • Conclusion: Ana spent $₱2,750$.

Individual and Group Exercises

• Individual Task (Money Remaining): You have $₱500$. You buy 3 books for $₱80$ each and a pencil case for $₱50$. Calculate the remaining money.

• Individual Task (Palawan Tour Guide Income):

  • A tour guide offers a group rate for up to 10 people at $₱1,500$ per pax.

  • Any additional person (above 10) pays only half the group rate ($₱1,500 \div 2$).

  • If a group of 15 people books a tour, and the guide has expenses of $₱2,000$ for transport and meals, what is the total income after expenses?

• Group Task (Company Salary Calculation):

  • A company has 12 employees.

  • 4 employees receive a salary of $₱700$ per day.

  • The remaining employees ($12 - 4 = 8$) receive $₱500$ per day.

  • There are 5 working days in a week.

  • Calculate how much the company spends on salaries per week.

Key Points and Summary

• Ordering Rule: Use GMDAS to ensure the correct order: Perform operations inside grouping symbols first, followed by multiplication and division (from left to right), and then addition and subtraction (from left to right).

• Operational Method: Solving real-world problems involves breaking down complex scenarios into manageable steps and applying the rules systematically.

Attribution and References

• Images and layouts sourced via freepik.

• "GEMDAS ORDER OF OPERATIONS" onlinemath4all.com.

• "Order Of Operations – Definition, Steps, FAQs, Examples" SplashLearn.

• Stapel, Elizabeth. “The Order of Operations: PEMDAS.” Purplemath.