6th Grade Math: Solving Problem 2 On Page 21

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6th Grade Math: Solving Problem 2 on Page 21

Hey guys! Let's break down problem 2 from page 21 of your 6th-grade math book. Math problems can sometimes seem intimidating, but with a step-by-step approach, even the trickiest questions become manageable. We'll go through a general strategy for tackling math problems and then apply it specifically to this question. Whether you're struggling with homework or just want to brush up on your skills, this guide will help you understand the problem and how to solve it effectively. Remember, practice makes perfect, so don't be discouraged if it takes a few tries to get it right! Keep at it, and you'll become a math whiz in no time. Understanding the core concepts is super important. Make sure you grasp the underlying principles behind each step we take. This will not only help you solve this particular problem but also equip you with the knowledge to tackle similar problems in the future. Math isn't just about memorizing formulas; it's about understanding why those formulas work.

General Problem-Solving Strategy

Before diving into the specifics of problem 2, let’s outline a general strategy that you can use for pretty much any math problem:

  1. Read Carefully: The first and most crucial step is to read the problem very carefully. Understand what is being asked. Identify the knowns (the information given) and the unknowns (what you need to find).
  2. Identify Key Information: What are the important numbers, units, and relationships in the problem? Underline or highlight these details to keep them in focus.
  3. Choose the Right Operation: Decide which mathematical operation(s) are needed to solve the problem. This could be addition, subtraction, multiplication, division, or a combination of these.
  4. Set Up the Equation: Write out the equation or formula you will use to solve the problem. Make sure you understand why that particular equation applies to the problem.
  5. Solve the Equation: Perform the calculations carefully, showing your work step by step. This makes it easier to check for errors and helps you understand the process.
  6. Check Your Answer: Once you have an answer, check if it makes sense in the context of the problem. Does it seem reasonable? If possible, plug your answer back into the original equation to verify that it works.
  7. Write the Final Answer: Clearly state your final answer with the correct units.

Applying the Strategy to Problem 2 (Page 21)

Since I don't have the textbook in front of me, I need you to provide the exact text of problem 2 from page 21. However, I can show you how to apply the general strategy once you provide the problem. Let's assume, for example, that problem 2 is something like this:

Problem Example: A bakery sells cupcakes for $3 each and cookies for $2 each. If Sarah buys 5 cupcakes and 8 cookies, how much does she spend in total?

Now, let’s apply our problem-solving strategy:

  1. Read Carefully: Sarah buys 5 cupcakes at $3 each and 8 cookies at $2 each. We need to find the total amount she spends.
  2. Identify Key Information:
    • Cupcakes cost $3 each.
    • Cookies cost $2 each.
    • Sarah buys 5 cupcakes.
    • Sarah buys 8 cookies.
  3. Choose the Right Operation: We need to use multiplication to find the cost of the cupcakes and cookies separately, and then addition to find the total cost.
  4. Set Up the Equation:
    • Cost of cupcakes = Number of cupcakes × Price per cupcake
    • Cost of cookies = Number of cookies × Price per cookie
    • Total cost = Cost of cupcakes + Cost of cookies
  5. Solve the Equation:
    • Cost of cupcakes = 5 × $3 = $15
    • Cost of cookies = 8 × $2 = $16
    • Total cost = $15 + $16 = $31
  6. Check Your Answer: The answer seems reasonable. Buying a few cupcakes and cookies should cost around $30, so $31 is a plausible answer.
  7. Write the Final Answer: Sarah spends $31 in total.

Dealing with Word Problems

Word problems can be tricky because they require you to translate real-world scenarios into mathematical equations. Here are some tips for tackling word problems:

  • Read Actively: Don’t just passively read the problem. Engage with it by underlining key information and writing down what you know and what you need to find.
  • Draw Diagrams: Visual aids can be incredibly helpful. Draw a picture or diagram to represent the problem. This can help you see the relationships between the different elements.
  • Break It Down: Divide the problem into smaller, more manageable parts. Solve each part separately and then combine the results.
  • Use Variables: If you're not sure how to represent a quantity, use a variable (like x or y) to stand for the unknown value. This can help you set up an equation.
  • Look for Keywords: Certain words often indicate specific mathematical operations. For example:
    • Sum, total, increase, more than usually indicate addition.
    • Difference, less than, decrease, fewer usually indicate subtraction.
    • Product, times, multiplied by usually indicate multiplication.
    • Quotient, divided by, shared equally usually indicate division.

Practice Makes Perfect

The key to mastering math is practice. The more problems you solve, the better you will become at recognizing patterns, applying formulas, and understanding the underlying concepts. Here are some ways to get more practice:

  • Do Your Homework: Make sure you complete all your assigned homework problems. This is a great way to reinforce what you have learned in class.
  • Use Online Resources: There are many websites and apps that offer practice problems and tutorials on various math topics. Khan Academy, for example, is a fantastic resource.
  • Work with a Study Group: Studying with friends can make learning more fun and help you understand the material better. You can quiz each other, explain concepts, and work through problems together.
  • Ask for Help: Don’t be afraid to ask your teacher or a tutor for help if you are struggling with a particular concept or problem. They can provide additional explanations and guidance.

Specific Example Scenarios

Let’s consider some more example scenarios to illustrate how to approach different types of math problems.

Scenario 1: Geometry

Problem: A rectangle has a length of 12 cm and a width of 8 cm. What is the area of the rectangle?

  1. Read Carefully: We need to find the area of a rectangle given its length and width.
  2. Identify Key Information: Length = 12 cm, Width = 8 cm.
  3. Choose the Right Operation: We need to use the formula for the area of a rectangle: Area = Length × Width.
  4. Set Up the Equation: Area = 12 cm × 8 cm.
  5. Solve the Equation: Area = 96 cm².
  6. Check Your Answer: The answer seems reasonable for the dimensions given.
  7. Write the Final Answer: The area of the rectangle is 96 cm².

Scenario 2: Fractions

Problem: John has 3/4 of a pizza. He eats 1/2 of what he has. How much of the whole pizza did he eat?

  1. Read Carefully: John eats a fraction of a fraction of the pizza.
  2. Identify Key Information: John has 3/4 of the pizza, and he eats 1/2 of that amount.
  3. Choose the Right Operation: We need to multiply the two fractions: (1/2) × (3/4).
  4. Set Up the Equation: Amount eaten = (1/2) × (3/4).
  5. Solve the Equation: Amount eaten = 3/8.
  6. Check Your Answer: Eating half of 3/4 makes sense to be 3/8, which is less than half the whole pizza.
  7. Write the Final Answer: John ate 3/8 of the whole pizza.

Scenario 3: Percentages

Problem: A store is having a 20% off sale. If an item originally costs $50, what is the sale price?

  1. Read Carefully: We need to find the sale price after a percentage discount.
  2. Identify Key Information: Original price = $50, Discount = 20%.
  3. Choose the Right Operation: First, calculate the discount amount: Discount amount = Original price × Discount percentage. Then, subtract the discount amount from the original price to find the sale price.
  4. Set Up the Equation: Discount amount = $50 × 0.20, Sale price = Original price - Discount amount.
  5. Solve the Equation: Discount amount = $10, Sale price = $50 - $10 = $40.
  6. Check Your Answer: A 20% discount on $50 seems reasonable to be $10 off, making the final price $40.
  7. Write the Final Answer: The sale price is $40.

By practicing these strategies and examples, you'll become much more confident in your ability to tackle any math problem that comes your way! Keep practicing and don't give up!

Remember to provide the actual text of problem 2 from page 21 so I can give you a more specific solution. Good luck, and keep up the great work! Math can be challenging, but with the right approach and a bit of persistence, you can conquer it. You've got this! Don't hesitate to ask for help whenever you need it. Your teachers, classmates, and online resources are all there to support you. So, keep learning, keep practicing, and most importantly, keep believing in yourself. You're on your way to becoming a math superstar!