The Problem Solvers
(SMP 1 & 2)
(SMP 1 & 2)
This first practice asks students to make sense of problems and not give up, or to "persevere" in doing this.
What is solving them?
SMP 6 requires students to communicate with this, which involves using clear definitions and state symbols correctly.
What is precision?
SMP 4 focuses on using mathematics to solve problems arising in this "real" place.
What is everyday life (or the real world)?
SMP 7 suggests students look closely to discern a pattern or one of these.
What is a structure?
To satisfy SMP 1, students should check their answers using a different one of these.
What is a method (or strategy)?
According to SMP 3, students should not only build their own arguments but also do this to the reasoning of others.
What is critique?
SMP 5 states that students should use "appropriate" tools, but more importantly, they should use them this way.
What is strategically?
In SMP 8, students notice if calculations do this, leading them to find a general formula or shortcut.
What is repeat?
Under SMP 2, students do this when they transition from a real-world scenario to mathematical symbols.
What is decontextualizing?
Students practicing SMP 3 often use these logical statements that start with "if" and end with "then."
What are conjectures?
A flow chart, a formula, or a graph used to describe a real-world situation is an example of one of these.
What is a mathematical model?
Seeing 7 x 8 as the same as 7 x (5 + 3) is an example of using this practice.
What is Practice 7 (Look for and make use of structure)?
This "abstract" practice involves two complementary abilities: "decontextualizing" and this, which means putting the math back into context.
What is contextualizing?
When "attending to precision," students must be careful to specify these, such as "inches" or "grams."
What are units of measure?
In SMP 5, this digital tool is often cited as helpful for visualizing functions or data sets.
What is a graphing calculator (or dynamic software)?
SMP 8 asks students to maintain oversight of the process while attending to these small components.
What are details?
In SMP 1, proficient students look for these rather than just jumping into calculations.
What are correspondences (or constraints/goals)?
This SMP involves justifying conclusions with mathematical proofs or specific examples to "construct viable" these.
What are arguments?
Modeling includes this step, where a student decides if their mathematical results actually make sense in the original situation.
What is interpreting (or validating)?
This term in SMP 8 describes the type of "regularity" students should look for in repeated reasoning.
What is repeated regularity?