Transcript Focus on Common Core

Lessons that inspire critical reasoning and problem
solving in mathematics
What’s the difference, really?
Linear and Exponential Relationships
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
1. graph
Represent
of f(x)=mx +and
b. solve equations and inequalities graphically
3. 2. Write,
use, and solve linear
equations and
using
graphical
and symbolic
methods with
Understand
the concept
of ainequalities
function
and
use function
notation
one or two variables. Represent solutions on a coordinate graph or number line.
3.
Interpret
functions
that graphically
arise in applications
in terms
of aofcontext
4. Solve
systems of two
linear equations
and algebraically, and
solve systems
two linear
graphically.
4.inequalities
Analyze
functions using different representations
5. Given a quadratic or exponential function, identify or determine a corresponding table or graph.
5. Build a function that models a relationship between two quantities
6. Given a table or graph that represents a quadratic or exponential function, extend the pattern to
6.make
Build
new functions from existing functions
predictions.
7. 7. Compare
the characteristics
of and distinguish
linear, quadratic,
and exponential
functions
Construct
and compare
linear, among
quadratic,
and exponential
models
that are expressed in a table of values, a sequence, a context, algebraically, and/or graphically, and
and solve
interpret the domain and range of each as it applies to a given context.
Interpret
for functions
in analyze
termsthe
ofrelationship
the situation
8. 8.Given
a quadraticexpressions
or exponential function,
interpret and
betweenthey
the
independent
model 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?
 http://www.ted.com/talks/dan_meyer_math_curricul
um_makeover.html
What’s the difference, really?
Use of
multimedia
1.1. Lack
initiative
2.2. Lack
of perseverance
Encourage
student intuition
3. Lack of retention
3. Ask the shortest question you can
4. Aversion to word problems
Let the students
5.4. Eagerness
for formulabuild 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)
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
Marty Wilder ([email protected])