DISCUSIÓN Y CONCLUSIONES 1 Discusión

Objective: in addition to the above mentioned objectives, students are expected to:

- Modify a solution to a situation when a certain given data is varied - Vary the question to a given problem situation

- Make up extension problems to a given situation - Check the validity of the questions they pose

Class discussion

- Stress on important factors that helped in solving the problem or hindered the solution. - Encourage students to reflect on the importance of each given provided in the problem. - Ask the following questions:

1- What if the trip needed 12 hours?

2- What if ship averaged 20 kilometers/hour or 30 kilometers/hour? 3- What if the ship reduced its speed to 15 instead of 16 km/hr

- Ask students to pose 3 extension problems to be added to the above problem wich may be solved with the given data, or additional given data, to be submitted in an assigned time. Ask them to solve their problems as well.

131 Lesson Plan 9

Durations: 2 sessions (50 minutes each).

Objective: This problem can be solved using inequalities however the chapter hasn’t been explained yet at this stage. Students are expected to:

- organize the given data in an effective way

- identify the conditions that are necessary to solve the problem - use an appropriate representation that will facilitate the solution - translate given data into mathematical expressions

- restate the situation in their own words

- To communicate appropriately a meaningful solution

Solutions: the least number of DVDs which makes offer A better is 4 DVDs Phase I: solving

Stage 1: introducing the task (5 minutes) - the following problem is given:

“A DVD rental shop offers its customers the following packages: Package A: a monthly fee of 15$ and then 2$ for each rented DVD. Package B: 7$ for each rented DVD.

What is the minimum number of DVDs that you should rent so that Package A suits you best?”

- Discuss the different elements of the problem. Stage 2: classwork (20 minutes)

- Ask students to explain the problem in their own words or by a representation of their choice.

- Discuss their explanations/representations.

- Allow students to work individually on solving the problem. - Rotate to offer guidance.

Stage 3: class discussion (15 minutes)

- Ask some students to present their solutions and discuss the strategies used. - Stress on the given that allowed us to solve the problem.

Phase II : posing

Objective: in addition to the above mentioned objectives, students are expected to: - Modify a problem situation when a certain given data is changed

132 - Identify what types of problems requires the use of equations.

- Make up a similar problem to the original given situation - Stage 1: varying the given (10 minutes)

- Ask for suggestions on how we can change the problem: for example how can we change the variable? How will this affect the questions asked at the end? If we don’t know the monthly fee, how would we modify the question?(we will need the number of DVDs to be rented). How can we make it an equation problem?

Stage 2: posing a problem (20 minutes)

- Ask students to pose a similar problem: they can choose their own setting, and own variable.

- Encourage them to check if their problems can be solved. Stage 3: class discussion (30 minutes)

133

Lesson Plan 10: Duration: 2 sessions (50 minutes each)

Objective: this problem requires knowledge of formulating and solving simple equations,

evaluating numerical expressions, and knowledge of divisibility rules. Students are expected to:

- Organize given data in an effective method

- Translate given data into mathematical expressions and equations

- Make use of some given conditions to reduce the variables in the problem - Use logic, numerical reasoning as well as knowledge of divisibility rules - Check the validity of their answer

- Present a meaninful solution

Solution: he bought 10 pigs, 24 goats and 66 sheep. Phase I: solving Stage 1: introduce the problem (5 minutes)

“Mr. Melhim bought some pigs, goats and sheep. Altogether he bought 100 animals and spent $600. Mr. Melhim paid $21 for each pig, $8 for each goat and $3 for each sheep. There was an even number of pigs. How many of each of the animals did he buy?”

Stage 2: students’ individual work (15 minutes)

- Encourage students to interpret the given data using a representation that best helps them to understand the problem.

- Allow students some time to work on the above problem. - Rotate among students to offer guidance.

Stage 3: class discussion (20 minutes)

- Ask some students to discuss their solution strategies with the class.

- Stress on important factors that helped in solving the problem or hindered the solution. - Encourage students to reflect on the importance of each given provided in the problem.

Phase 2: posing

Objective: in addition to the above mentioned objectives, students are expected to:

- Replace a given data with another and then track the changes that would happen to the situation at hand

- Make up their own problem similar to the original given one.

134 - Ask the following questions:

1- Why is the even number of pigs important?

2- What if the number of pigs was odd? What would change?

3- If the total of $600 was removed. What given might be added that would enable you to solve this problem? Would the question change and how?

- Assign the following homework to be submitted on a following assigned session:

“Make up 3 versions of this problem, each having a certain condition removed or added. Offer them some examples such as: omit the price for a pig, and encourage them to see how would this problem be modified so that it remains solvable?”

- Students’ assignment should be collected and analyzed.

- Choose interesting problems to be discussed in the following session. The chosen problems may or may not be solved.

Stage 2: posing questions (20 minutes)

- Ask students to swap their posed problems with a friend and to try and solve them. - Encourage students to modify a problem if it seems unsolvable.

- Rotate among students to offer guidance when needed.

Stage 3: class discussion (30 minutes)

- Ask some students to present their problems to be discussed in class.

- Put emphasis on important factors which helped in solving or hindered it, as well as interesting solution strategies used.

135

Appendix D