Podcast
Questions and Answers
What is Josie's total jogging time in week six?
What is Josie's total jogging time in week six?
- 96 minutes
- 132 minutes
- 108 minutes
- 120 minutes (correct)
How many minutes does Josie increase her jogging time each week?
How many minutes does Josie increase her jogging time each week?
- 6 minutes
- 10 minutes
- 8 minutes
- 12 minutes (correct)
If Josie were to continue her routine for another week, what would her total minutes jogged in week seven be?
If Josie were to continue her routine for another week, what would her total minutes jogged in week seven be?
- 144 minutes
- 128 minutes
- 140 minutes
- 132 minutes (correct)
In the triangular arrangement of tennis balls, how many balls are in a triangle with 3 rows?
In the triangular arrangement of tennis balls, how many balls are in a triangle with 3 rows?
What method can be used to find the number of balls in a triangle with 'n' rows?
What method can be used to find the number of balls in a triangle with 'n' rows?
If each row has increasing numbers of balls with a pattern, how many balls would a triangle with 5 rows have?
If each row has increasing numbers of balls with a pattern, how many balls would a triangle with 5 rows have?
What is the total formula for Josie's weekly jogging total if she maintains her schedule for five weeks?
What is the total formula for Josie's weekly jogging total if she maintains her schedule for five weeks?
What patterns can be observed in Josie's weekly jogging schedule?
What patterns can be observed in Josie's weekly jogging schedule?
What is the first step when using the strategy of solving a similar but simpler problem?
What is the first step when using the strategy of solving a similar but simpler problem?
Which of the following methods is NOT considered a strategy for problem-solving?
Which of the following methods is NOT considered a strategy for problem-solving?
When creating a table to look for a pattern, which of these is the most direct benefit?
When creating a table to look for a pattern, which of these is the most direct benefit?
How many unit squares are found in a 3 unit by 3 unit square picture?
How many unit squares are found in a 3 unit by 3 unit square picture?
What is the probability of rolling a sum of 7 with two six-sided dice?
What is the probability of rolling a sum of 7 with two six-sided dice?
Which statement best describes the process of 'working backwards' in problem-solving?
Which statement best describes the process of 'working backwards' in problem-solving?
In solving a problem, what is the purpose of guessing and checking?
In solving a problem, what is the purpose of guessing and checking?
When are diagrams particularly useful in problem-solving?
When are diagrams particularly useful in problem-solving?
What is the total number of balls in a triangle arrangement with 5 rows?
What is the total number of balls in a triangle arrangement with 5 rows?
How do you determine the number of balls in a new triangle based on the old triangle?
How do you determine the number of balls in a new triangle based on the old triangle?
Which of the following correctly describes the pattern for calculating the number of balls?
Which of the following correctly describes the pattern for calculating the number of balls?
If there are 28 balls in a triangle with 7 rows, how many balls will there be in a triangle with 8 rows?
If there are 28 balls in a triangle with 7 rows, how many balls will there be in a triangle with 8 rows?
What mathematical operation is used to find the total number of balls when adding a new row to the triangle?
What mathematical operation is used to find the total number of balls when adding a new row to the triangle?
In the context of the problem involving Paul and his piggy bank, what is the main strategy used to find the amount he started with?
In the context of the problem involving Paul and his piggy bank, what is the main strategy used to find the amount he started with?
When creating a table to represent the number of balls in the triangle, what should be included?
When creating a table to represent the number of balls in the triangle, what should be included?
What is the mathematical result of adding the numbers in the first 8 rows together?
What is the mathematical result of adding the numbers in the first 8 rows together?
Flashcards
Josie's jogging time
Josie's jogging time
Josie increases her jogging time by two minutes per day, jogging six days per week. This results in a 12-minute increase per week.
Weekly jogging time calculation
Weekly jogging time calculation
Starting with a base of 60 minutes per week, Josie's jogging time increases by 12 minutes each week for five weeks. Adding together these increases gives the total jogging time.
Triangular arrangement of tennis balls
Triangular arrangement of tennis balls
Tennis balls are arranged in the shape of triangles.
Rows in a triangular pattern
Rows in a triangular pattern
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One-row triangle
One-row triangle
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Two-row triangle
Two-row triangle
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Three-row triangle
Three-row triangle
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Example 2
Example 2
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Solving a simpler problem
Solving a simpler problem
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Strategy: Table/Pattern
Strategy: Table/Pattern
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Strategy: Work Backwards
Strategy: Work Backwards
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Strategy: Guess and Check
Strategy: Guess and Check
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Strategy: Diagram
Strategy: Diagram
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Example: Counting Squares
Example: Counting Squares
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Example Probability
Example Probability
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Probability Calculation
Probability Calculation
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What is the pattern?
What is the pattern?
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Total balls in triangle
Total balls in triangle
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Working Backwards
Working Backwards
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Paul's Money
Paul's Money
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What's the 'Reverse' Step?
What's the 'Reverse' Step?
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Undoing the Transactions
Undoing the Transactions
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Initial Amount
Initial Amount
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Final Amount
Final Amount
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Study Notes
Mindfulness Moment
- A moment of focused reflection and awareness.
Prayer for Typhoon Relief
- Acknowledges the challenges of a typhoon.
- Expresses thanks for technology connecting the group remotely.
- Provides comfort and support for those affected by the storm.
- Recognizes the efforts of responders and caregivers.
- Emphasizes resilience, gratitude, hope and determination.
Problem-Solving: Polya's Approach
- Focused on heuristic strategies for problem-solving.
- Highlights the importance of a practical approach often involving educated guesses, trial and error.
Intended Learning Outcomes
- Students will recognize different heuristic strategies (e.g., working backward, guess and check).
- Students will understand the heuristic approach and its importance in problem-solving.
- Students will apply Polya's four-step process in mathematical and real-life problems (Understand the problem, Devise a plan, Carry out the plan, and Look back).
What is Heuristics
- Heuristics are experience-based techniques for problem-solving, learning, and discovery.
- Solutions are not guaranteed to be optimal.
Polya's Steps in Problem Solving
- Understand the problem
- Devise a plan
- Carry out the plan
- Look back
Polya's Steps in Problem Solving Elaboration
- Understand all the words
- Restate in own words
- Find what you need to find
- Diagram
- Is enough information provided?
Strategies: Heuristic Approach
- Guess and check
- Solve similar but simpler problems
- Make an organized list
- Make a table and look for a pattern
- Work backwards
- Draw a diagram
Strategies: Devising a Plan
- Solve a similar but simpler problem
- Make a table and look for a pattern
- Work backwards
- Guess and check
Solve a Similar but Simpler Problem
- Break the problem into parts.
- Simplify the problem.
- Solve the simplified problem.
- Use answers to solve original problem.
Example 1: Squares
- To determine the number of squares.
- Count squares with sides of 1 unit
- Count squares with sides of 2 units
- Count squares with sides of 3 unit
- Add the results.
Example 2: Probability of Rolling a Sum of 7
- To find the probability of rolling a sum of 7 when two six-sided dice are rolled.
- Simplify the problem by first trying for a sum of 4.
- List all possible outcomes (pairs) that sum to 4.
- Divide the number of favorable outcomes (sum to 4) by the total number of outcomes for two dice (6*6 = 36).
- Apply the simplified probability to the original problem.
Example 3: Solving an Exponential Equation
- To solve for x in 32x = 81
- Simplify by writing 81 as a power of 3.
- Set exponents equal and solve for x.
Make a Table and Look for a Pattern
- This method involves systematically organizing data in columns and rows to spot patterns.
Example 1: Josie's Jogging Time
- Given Josie's increasing jogging time each week.
- The total jogging time in week six is calculated using tabulated week-by-week increase in time and multiplied by six days that Josie jogs.
Example 2: Tennis Balls in Triangular Arrangement
- To solve for the number of balls in a triangle with 8 rows.
- Create a simple table to track number of rows.
- Determine the pattern.
- Add the numbers in each row to find the total number of balls.
Work Backwards
- A problem-solving strategy.
- Solving a problem by beginning at the end point.
- Then doing the reversal steps from the end to get to the beginning
Example: Paul's Piggy Bank
- Paul's original amount of money in his piggy bank is calculated by reversing the transactions:
- Calculate the final total minus the amount for birthday and calculate the remaining money.
- Next calculate the remaining amount minus the amount spent on ice-cream.
- The last calculation is the original amount saved.
Example 2: Solving for a Variable
- A problem involving a variable is simplified into a simpler equation.
- The simpler equation is solved for the variable.
- The variable is calculated back using the solution to the simplified equation.
Guess and Check
- A trial-and-error strategy for problems.
- Begin by making an educated guess.
- Check the result against the given problem condition.
- If result is not correct, adjust your next guess based on your previous answer
Example 1: I am a 2-digit Number
- Using the clues, make educated guesses to determine the number.
- Narrow the possibilities until the correct answer is found.
Example 2: Nadia's Ribbon
- A problem about dividing a ribbon into pieces using numbers.
- Devise a guess-and-check strategy by guessing different values for the lengths of the pieces.
- Continue to adjust the guesses until correct answer is found.
- Using the information on lengths to get the appropriate sizes.
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Description
This quiz focuses on understanding Polya's problem-solving strategies and their application. Students will explore heuristic methods and the importance of practical approaches to solving mathematical and real-life problems. Participants will learn to recognize various strategies and actively apply them in different contexts.
