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Students will be able to identify, compare, and contrast different mathematical approaches, representations, and concepts to solve problems, developing their meta-awareness of mathematical thinking.

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• Compare at least two different solution methods for a problem
• Explain similarities and differences between approaches
• Justify which method might be more efficient in different situations
• Use appropriate mathematical language to describe connections

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How can different approaches to solving a mathematical problem help us understand the concept better?

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Students examine three different ways to solve the equation 2x + 5 = 13:
• Algebraic method
• Number line approach
• Balance scale model
Discuss: What makes each method unique? Which do you prefer and why?

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Using Padlet's collaboration feature, groups will post different solutions to the problem: 'Find 25% of 80.' Methods might include:
• Converting to decimal
• Using fractions
• Breaking down into smaller percentages
Groups will comment on each other's approaches.

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Watch this video on different ways to multiply two-digit numbers. Take notes on the various methods shown.

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Multiply Two Digit Numbers - Visualizing Algebra

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Create a comparison chart for solving proportions:
• Cross multiplication
• Unit rate method
• Scale factor approach
Identify when each method might be most useful.

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Challenge: Create your own problem that can be solved in at least three different ways. Share on the class Padlet wall and explain why each method works.

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Throughout the lesson, monitor student discussions and written work using these prompts:
• What patterns do you notice between different methods?
• How do you know these approaches are equivalent?
• Which method would you use and why?

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Students will be given a problem and three different solution methods. They must:
1. Explain each method
2. Identify similarities and differences
3. Recommend which method works best for specific scenarios

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This page failed to load. Our development team has been informed of the issue.

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With a partner, discuss:
• What new method did you learn today?
• How has seeing different approaches changed your understanding?
• Which method challenges you the most and why?

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Complete this statement:<br>'Today I learned that there are different ways to solve [specific type of problem]. The method I find most helpful is ___ because ___. One thing I'm still wondering about is ___.'

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Solve each problem using at least two different methods. Explain which method you prefer and why:
1. Find 30% of 150
2. Solve 3x - 7 = 14
3. Find the ratio of 15:45 in simplest form

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Complete the online practice exercises focusing on multiple solution strategies.

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Systems of equations with substitution (practice) | Khan Academy

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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

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Create a mini-portfolio showing three different problems solved in multiple ways. Include your reflections on each method's strengths and challenges.