Reaso n i n g an d Co m m u n i cat i n g
- Reason abstractly and quantitatively.
As a strong math thinker and problem solver, you are able to make sense o f quantities in problem
situations. You can both represent a problem situation using symbols or equations and explain w h a t
the symbols or equations represent in relationship to the problem situation. As you represent a situation
symbolically or mathematically, you can explain the meaning o f the quantities.
- Construct viable argum ents and critique the reasoning o f others.
You are able to communicate clearly and convincingly about your solutions to problems. You can build
sound mathematical arguments, drawing on definitions, assumptions, or established solutions. You
can develop and explore conjectures about m athem atical situations. You make use o f examples and
counterexamples to support your arguments and ju stify your conclusions. You respond clearly and
logically to the positions and conclusions o f your classmates, and are able to compare tw o arguments,
identifying any flaw s in logic or reasoning th a t the argum ents may contain. You can ask useful questions
to clarify or improve the argument of a classmate.
Rep r esen t i n g an d Co n n ect i n g
- Model w ith mathematics.
As a strong math thinker, you are able to use m athematics to represent a problem situation and can
make connections betw een a real-w orld problem situation and mathematics. You see the applicability
o f mathematics to everyday problems. You can explain h ow geom etry can be used to solve a carpentry
problem or algebra to solve a proportional relationship problem. You can define and map relationships
among quantities in a problem, using appropriate tools to do so. You are able to analyze the
relationships and draw conclusions.
- Use ap p ro p riate tools strategically.
As you develop models to match a given problem situation, you are able to strategize about w hich
tools w ould be most helpful to use to solve the problem. You consider all tools, from paper and
pencil to protractors and rulers, to calculators and softw are applications. You can articulate the
appropriateness o f d ifferent tools and recognize w hich w ould best serve your needs fo r a given
problem. You are especially insightful about technology tools and use them in ways th a t deepen or
extend your understanding o f concepts. You also make use o f mental tools, such as estim ation, to
determine the reasonableness of a solution.
Se e i n g St r u c t u r e a n d Ge n e r a l i z i n g
- Look fo r and m ake use o f structure.
You are able to go beyond simply solving problems, to see the structure of the m athematics in
these problems, and to generalize m athem atical principles from this structure. You are able to see
complicated expressions or equations as single objects, or a being composed of many parts.
- Look fo r and express reg u larity in repeated reasoning.
You notice w hen calculations are repeated and can uncover both general methods and shortcuts for
solving similar problems. You continually evaluate the reasonableness o f your solutions as you solve
problems arising in daily life.
Using Your Book f or Success xix