Formative

Agree & Disagree Statements (A&D Statements), allow students to analyze a statement that may be true or false. Students indicate whether they agree, disagree, depends on, or are unsure of the validity of the statement, and then are expected to provide their thoughts on their answer. Finally students describe a method on how they could prove the statement is true or false. It is important when designing these exercises that you include a statement for every possible answer (agree, disagree, depends on, and unsure), to ensure students are critically thinking.
 * A & D Statements (Adele, Alisa, Andrew) **
 * Description:**

This method promotes meta-cognition, providing opportunity to think about their own understanding. Group explorations create a common experience for discussion. FACTS used are intended to expose common misconceptions thus providing opportunity for critical thinking. It allows the teacher the opportunity to assess the students understanding.
 * Benefit**:


 * Specific Example: A&D Statement Example**


 * Always, Sometimes, Never True (Caroline, Christine, Bryan) **


 * Commit & Toss (Denise, Diana, Inga) **




 * Concept Card Mapping (Jacob, Jason, Joe Anne) **


 * Create Problem (Justin, Katie, Keith) **

The 'Create the Problem' method is a form of reverse problem solving. Using this allows you to give students the computation and solution and create and example of a real world problem.
 * Description:**

This method allows students to use a higher level of thinking to try and determine the purpose for performing certain computations. This method promotes engagement through creativity and allows the students to connect mathematical concepts to real world applications. This encourages students to use their own intuition and life experience to better their understanding of mathematics. Some of the areas that this would best apply to are:
 * Benefit**:
 * Modelling linear and exponential functions
 * Ratios
 * Percents
 * Data and graphs
 * Probability
 * Statistics
 * Logic Problems
 * Exponents

Ask students to create a real world problem that may have been solved using the given equations: 1.y = 2x + 25 2.5x + 10y = 120
 * Specific Example**:


 * Fact First Questioning (Kelly, KV, Lauren) **

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 * Description: **
 * This technique is used to have students tap into their deeper thinking processes by stating the fact first and asking students to explain or elaborate on it
 * Fact First Questioning takes a “what is” question and turns it into a “how” or “why” questions
 * Students are given time to think about the answer and other possible examples or facts that relate to the subject
 * Allows the teacher to see if the students can recall prior knowledge
 * Benefit ** :
 * Students are required to tap into their deeper thinking processes
 * Through deeper thinking processes, students are able to elaborate on concepts as well as gain a better understanding of important concepts
 * Can open the door to providing valuable information to teachers (i.e. can students understand conceptual ideas, are students able to recall previous information)
 * Teachers can determine if their lessons have incorporated too much definitions and memorization and if the understanding of concepts needs to be emphasized
 * Specific Example ** :
 * This is the quadratic formula.Why do we use the quadratic formula?
 * This is the quadratic formula. How do you get the quadratic formula?
 * y=2x+5 is an equation of a line. Why is this an equation of a line?
 * This is an exponential function:y = 2^x. Why is this an exponential function?


 * Think-Puzzle-Explore (Lukasz, Nabgha, Peter) **


 * Justified True False (Sean, Shima, Stefan) **

Students pair up with a partner and discuss their ideas about a new topic being addressed. Pairs are asked to summarize their partner’s views and thoughts and then present to the class.
 * Partner Speaks (Stephanie, Sylvia, Taylor) **
 * Description:**


 * Benefit**:
 * Helps students develop careful listening and paraphrasing skills
 * Provides an opportunity for shy, less confident students to have their ideas be heard
 * Allows overconfident students to accept ideas of others
 * Lets teachers know what their students’ ideas are, and where they are at in their learning so that future lessons can be planned accordingly.

__Finding the Roots of a Quadratic Equation__
 * Specific Example**:
 * Teacher asks: How can we go about finding the roots of x^2+6x+9?
 * 1st Partner
 * Use the quadratic equation. Plug in the a b and c values (1, 6, and 9) to find the roots.
 * 2 nd Partner
 * Factor it. Look through the different ways we have learned to factor (simple trinomial, complex trinomial, difference of squares, common factoring, grouping) and find the roots.


 * Term Inventory (Ted, Tiffany, Warren) **