Lessons that inspire critical reasoning and problem solving in mathematics

1.Given a linear function, interpret and analyze the relationship between the independent and dependent variables. 2.Solve for x given f(x) or solve for f(x) given x. Analyze how changing the parameters transforms the graph of f(x)=mx + b. 3.Write, use, and solve linear equations and inequalities using graphical and symbolic methods with one or two variables. Represent solutions on a coordinate graph or number line. 4.Solve systems of two linear equations graphically and algebraically, and solve systems of two linear inequalities graphically. 5.Given a quadratic or exponential function, identify or determine a corresponding table or graph. 6.Given a table or graph that represents a quadratic or exponential function, extend the pattern to make predictions. 7.Compare the characteristics of and distinguish among linear, quadratic, and exponential functions that are expressed in a table of values, a sequence, a context, algebraically, and/or graphically, and interpret the domain and range of each as it applies to a given context. 8.Given a quadratic or exponential function, interpret and analyze the relationship between the independent and dependent variables, and evaluate the function for specific values of the domain. 9.Given a quadratic equation of the form x²+ bx + c = 0 with integral roots, determine and interpret the roots, the vertex of the parabola that is the graph of y = x² + bx +c, and an equation of its axis of symmetry graphically and algebraically. What’s the difference, really? 1. Represent and solve equations and inequalities graphically 2. Understand the concept of a function and use function notation 3. Interpret functions that arise in applications in terms of a context 4. Analyze functions using different representations 5. Build a function that models a relationship between two quantities 6. Build new functions from existing functions 7. Construct and compare linear, quadratic, and exponential models and solve 8. Interpret expressions for functions in terms of the situation they model Linear and Exponential Relationships

What’s the difference, really? um_makeover.html um_makeover.html

What’s the difference, really? 1. Lack of initiative 2. Lack of perseverance 3. Lack of retention 4. Aversion to word problems 5. Eagerness for formula 1.Use multimedia 2.Encourage student intuition 3.Ask the shortest question you can 4.Let the students build the problem 5.Be less helpful

Exercise New Habits Get comfortable with discomfort Focus on the destination and allow many paths Ask questions about the inside, let the students address the outside Let’s play a game

Exercise New Habits Designing “juicy” math problems Work backwards from goals or outcomes Come up with the basic question Encourage perseverance, trials and creativity Support students in providing explanations Review methods as a class (formulate) Give opportunities for practice Evaluate comprehension (not specific skills)

Marty Wilder Most teachers waste their time by asking questions which are intended to discover what a pupil does not know, whereas the true art of questioning has for its purpose to discover what the pupil knows or is capable of knowing. - Albert Einstein