E7,+Constructing+Different+Questions+with+Same+Data+and+Answer

__Name of PEEL Procedure: E7, Constructing Different Questions with Same Data and Answer __

**1) Summary of Procedure: ** Students are given an answer and a set of data and asked to come up with a set of questions that fit the data and the answer. Students work backwards from the solution to come up with the questions they produce. (Peel Publications, 2009)

**2) Strengths and weaknesses of Procedure: ** (Peel Publications, 2009)
 * **Strengths ** || **Weaknesses ** ||
 * Students must think through the algorithms to work backward through the problem || May be challenging for some students to think about how to approach the problem ||
 * Students think about what their answers could mean and how numbers can be manipulated || May be challenging for the teacher to come up with many examples ||
 * Can be applied to any grade level with examples ranging from easy to difficult || Misconceptions could be interpreted if student does not have a good grasp of mathematical reasoning ||

**3) Explanation why this is beneficial to student learning: ** This procedure forces students to deconstruct and analyse algorithms. A variety of questions can be found for the same answer given. Students of different levels of mathematics within the classroom can be given different answers and data to challenge them at their individual level.

**4) 3 examples of the procedure: ** <span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">a. MCT4C (Grade 12 Mathematics for College Technology). Students are given a coordinate as a point of intersection and are asked to write 3 pairs of exponential equations that would have this point of intersection.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">b. MDM4U (Grade 12 Mathematics of Data Management). Students are told that they must explain three ways to get the probability ¾ using a bag filled with a mixture of math manipulatives of different colours and shapes. Each explanation must be different.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">c. MEL3E (Grade 11 Mathematics for Work and Everyday Life). Students are given a scenario where they have a certain amount of money and are told that they must travel from Toronto to Florida. Students are to find two ways to make the journey, each within their budget.

**<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">5) Curricular expectation for each example: ** <span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">a. MCT4C, A1.3 determine, through investigation using graphing technology, the point of intersection of the graphs of two exponential functions, recognize the x-coordinate of this point to be the solution to the corresponding exponential equation, and solve exponential equations graphically

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">b. MDM4U, B1.7 solve problems involving probability distributions, including problems arising from real-world applications

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">c. MEL3E, C3.4 solve problems involving the comparison of information concerning transportation by airplane, train, bus, and automobile in terms of various factors (Ontario Ministry of Education, 2007)

**<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">6) How each example is related to student’s lives: ** <span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">a. If students enter into a college program that looks at energy uses of devices such as an HVAC program, they may need to know different exponential growths and how to interpret what an intersection means on a graph.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">b. This shows students the differences between real probability and forced probability and may have them thinking about statistics they see in the media.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">c. Whether they go into the workforce or to further their education, students will need to budget and use schedules to plan trips and use transportation in the future.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; line-height: 23px;">Written by Amy Kelland

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 22px;">Works Cited ** =

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">Ontario Ministry of Education. (2007). The Ontario Curriculum Grades 11 and 12 Mathematics. Queen's Printer for <span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;"> Ontario.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">Peel Publications. (2009). PEEL in Practice. Retrieved December 2010, from PEEL Project for Enhancing Effective Learning: <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;">[]