Problem Solving

Getting Started

In this discussion, you will use problem-solving skills to solve a problem based on the first letter of your last name. Review the problem-solving resources below. Understanding how to approach problems using these techniques will help you solve many types of problems.

Upon successful completion of the course material, you will be able to:

• Communicate      quantitative problems and their solutions clearly and correctly in written      or oral form.
• Utilize critical      thinking skills to evaluate quantitative information in everyday life.
• Formulate a plan      based on the mathematical concepts that apply to a problem.
• Analyze the      mathematical relationships and patterns that confront the modern world.

Background Information

First letter of your Last name

Solve the problem
  Show and explain the steps you take to solve the problem; post your work and   the solution.

A – D

A toll collector on a highway receives $3 for cars and $4 for   buses. At the end of a 1-hour period, she collected $60. How many cars and   buses passed through the toll booth during that period? List all possible   solutions.

E – K

Two cars, 360 kilometers apart, begin driving toward each   other on a long, straight highway. One car travels 80 km per hour and the   other 100 km per hour. At the same time, a canary, starting on one car, flies   back and forth between two cars as they approach each other. If the canary   flies 120 km per hour and spends no time to turn around at each car, how far   has it flown when the cars collide?

L – R

Suppose you are designing a rectangular garden and you have 22   meters of fencing with which to enclose the garden. Explain how a garden 7   meters long and 4 meters wide can be enclosed with the available fencing.   What is the area of a garden with these dimensions? Using the 22 meters of   fencing, what dimensions would provide the largest area for a garden?

S – Z

Consider the case in which each of two piles initially   contains fifteen marbles, where one pile contains fifteen white marbles and   the other pile contains fifteen black marbles. Suppose that on the first   transfer, three black marbles are moved to the white pile. On the second   transfer, any three marbles are taken from the white pile and put into the   black pile. Demonstrate, with diagrams and words that you will always end up   with as many white marbles in the black pile as black marbles in the white   pile. List all possible solutions.

Instructions

1. Review the      rubric to make sure you understand the criteria for earning your grade.
2. Make sure to      read the following on Problem Solving: 
   1. Read: Secret to Solving Math Word Problems. Hint: It’s Not about       Math
   2. Read: A Guide to Problem Solving
3. Review the      rubric to make sure you understand the criteria for earning your grade.
4. In the 1.2 Discussion forum respond by      solving one of the problems above based upon the First letter      of your Last name (W). You must show your work, not just      give the answers.
5. Your initial      posting needs to thoroughly answer the discussion question, using critical      thinking and thoughtful reasoning.
6. Your initial      post is due by the end of the fourth day of the workshop.
7. For your second      post, choose one of your classmates’ initial posts and respond by stating      whether you agree or disagree with their explanation and solution(s) and      why.
8. For your third      post, choose one of the following tasks: 
   1. Respond to a       classmate who reviewed your post.  The response should show evidence       of critical thinking and quantitative reasoning.
   2. Choose another       classmate’s initial post and respond by stating whether you agree or       disagree with their explanation and solution(s) and why.
9. Read and respond      as well to any follow-up instructor questions directed to you, by the end      of the workshop.
10. Your postings      should also: 
11. Be well        developed by providing clear answers with evidence of critical thinking.
12. Add greater        depth to the discussion by introducing new ideas.
13. Provide        clarification to classmates’ questions and provide insight into the        discussion.
14. A response of        ‘Good job,’ or a similar comment is not acceptable.
15. Your two      follow-up responses need to be clearly collaborative by taking the      initiative to respond to classmates’ questions, providing clarification      and insight on issues in the discussion.

https://mindprintlearning.com/blog/solving-word-problems/

https://nrich.maths.org/10218