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# The 8 Standards for Mathematical Practice

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## Diane Trantham

on 4 August 2014

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#### Transcript of The 8 Standards for Mathematical Practice

The 8 Standards for Mathematical Practice
Computation
the action of mathematical calculation
the act or process of computing or calculating something
Mathematics
the study of the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations
Can you match the standard to its partial definition?
Standards for Mathematical Practice
#7, 8
Standards for Mathematical Practice #4, 5, 6
To Sum it Up
What Can You Expect?
By the end of this presentation you will:
* Gain knowledge of something you can use in your classroom today!
* Be thinking about math instruction in a way you have not in the past
Math: No Spectators Allowed!
SMP #6 I can be precise when solving problems and clear when communicating my ideas
Mathematicians communicate with others using....
math vocabulary with clear definitions
symbols that have meaning
context labels
units of measure
calculations that are accurate and efficient
Example:

48 inches = 4 feet

How is this an example of precision?
Focus on Mathematics
In short, mathematics is problem solving, and what is problem solving?

the process of finding solutions to difficult or complex issues.
What is Mathematics?
Ask this question to your class and these may be some of the responses you get:
*subtracting!
*multiplying!
*dividing!
*HARD!
*Others?
And I am sure there are many others. But now ask yourself:

SMP #1: Make sense of problems and PERSEVERE in solving them.
What tools do we have to help us with computation?
What tools do we have to help us with mathematics?

Problem solving is what you do when
you don't know what to do!

*Enter...the SMPs
Standards for Mathematical Practice #1, 2, 3
CCSS.MP1 Make sense of problems and persevere in solving them.

CCSS.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize and contextualize.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples.
CCSS.MP4 Model with mathematics.

CCSS.MP5 Use appropriate tools strategically

CCSS.MP6 Attend to precision

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately.
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation.
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.
CCSS.MP7 Look for and make use of structure

CCSS.MP8 Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property.
The Standards for Mathematical Practice are at the very heart of ensuring our students become expert problem solvers...which translates to:
EXPERT MATHEMATICIANS!!

Math instruction should focus on these 8 standards, using our content standards to practice them!
Get your posters for all 8 standards at http://elemmath.jordandistrict.org/mathematical-practices-by-standard/
http://www.npr.org/blogs/health/2012/11/12/164793058/struggle-for-smarts-how-eastern-and-western-cultures-tackle-learning
Embrace the Struggle!
SMP #6
Attend to Precision
How would you describe this In-N-Out Cheeseburger?
How would you compare these two In-N-Out Cheeseburgers?
So, what is Mathematics?
SMP #1: Make sense of problems and PERSEVERE in solving them.
Embrace the Struggle!
http://www.npr.org/blogs/health/2012/11/12/164793058/struggle-for-smarts-how-eastern-and-western-cultures-tackle-learning
http://robertkaplinsky.com/how-old-is-the-shepherd/

diane.trantham@carrollcountyschools.com