Math 306 Chapter 6 – Problem Solving, Study notes of Acting

Problem solve by acting it out and making a drawing or diagram. 4. List and apply Polya's four-step plan to problem solving.

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Guided Notes p. 78
Math 306
Chapter 6Problem Solving
Student objectives/focus questions for this lesson:
1. Students should be able to contrast problem solving to practicing exercises.
2. Students should be able describe factors for success in problem solving.
3. Problem solve by acting it out and making a drawing or diagram.
4. List and apply Polya’s four-step plan to problem solving.
1. a) Act out the following: There are five people in a group and each shakes
hands with every other person. How many handshakes take place in a group? ________
b) Draw/diagram what took place and write down what each part of your diagrams represents.
2. a) Solve the following problem in your head:
Amy’s exercise rout is running on a circular track. There are six cones evenly spaced around
the track. It takes her 1 min to go from the first cone to the third cone. How long would it
take for her to travel around the entire track? Explain to a classmate how you came-up with
your solution. And record the key elements of your explanation.
b. Diagram the following problem and use that to check your answer.
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Math 306

Chapter 6 – Problem Solving

Student objectives/focus questions for this lesson:

  1. Students should be able to contrast problem solving to practicing exercises.
  2. Students should be able describe factors for success in problem solving.
  3. Problem solve by acting it out and making a drawing or diagram.
  4. List and apply Polya’s four-step plan to problem solving.
  5. a) Act out the following: There are five people in a group and each shakes hands with every other person. How many handshakes take place in a group? ________

b) Draw/diagram what took place and write down what each part of your diagrams represents.

  1. a) Solve the following problem in your head: Amy’s exercise rout is running on a circular track. There are six cones evenly spaced around the track. It takes her 1 min to go from the first cone to the third cone. How long would it take for her to travel around the entire track? Explain to a classmate how you came-up with your solution. And record the key elements of your explanation.

b. Diagram the following problem and use that to check your answer.

  1. Problem Solving-Start with a situation that provides a context for thinking about number sentences involving several variables.

Ex. Ricardo has 7 pet mice. He keeps them in two cages that are connected so that the mice can go back and forth between cages. One of the cages is large and the other is small (but it can hold all the mice). List all the ways that the 7 mice can be divide among the two cages.

List all the possible arrangements.

How many possibilities would there be if there were 10 mice? …

How many possibilities would there be if there were n mice?

Explain the difference between problem solving and practicing exercises.


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Give an example of each of the three “signposts” that you would use to guide you in the teaching of Mathematics mentioned on pp.123-124.


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