The 8 Standards for Mathematical Practice within the Common Core

Kate Cave

BCPS

The 8 Standards for Mathematical Practice within the Common Core

Maryland Common Core State Standards

The 8 Standards for Mathematical Practice

What do the 8 Standards for Mathematical Practice actually look like?

Standard 1: Make Sense of Problems and Persevere in Solving Them
[Mathematical Practice # 1] (Note: The link above and those in brackets in each of the following cells comes from Michelle Flaming of ESSDACK: ) / Standard 2:Reason Abstractly and Quantitatively
[Mathematical Practice # 2] / Standard 3:Construct Viable Arguments and Critique the Reasoning of Others
[Mathematical Practice #3] / Standard 4: Model with Mathematics
[Mathematical Practice #4]
Standard 5: Use Appropriate Tools Strategically
[Mathematical Practice #5] / Standard 6: Attend to Precision
[Mathematical Practice #6] / Standard 7: Look for and Make Use of Structure
[Mathematical #7] / Standard 8: Look for and Express Regularity in Repeated Reasoning
[Mathematical Practice #8]


The 8 Standards for Mathematical Practice within the Common Core

I.  Make sense of problems and persevere in solving them

Make meaning of a problem and look for entry points to its solution: mind mapping

Analyze givens, constraints, relationships, and goals: Thinking creatively when you don’t know what to think

Make conjectures about the meaning of the solution

Develop a plan: Calculation Nation- Dirt Dash (If you get an error page, click on the main link for Calculation Nation and enter as a Guest or create an account.)

Monitor and evaluate progress and change course if necessary: Calculation Nation - Square Off (Great for whiteboards and team play! If you get an error page, click on the main link for Calculation Nation and enter as a Guest or create an account.)

Check answers to problems and determine if the answer makes sense


The 8 Standards for Mathematical Practice within the Common Core Reasoning and Communication

II.  Reason abstractly and quantitatively

Make sense of quantities and their relationships: Teaching Number Bases

Represent symbolically (ie: Equations, expressions): Solve and Represent Equations, Inequalities, and Systems (scroll halfway down to see helpful tabs)

Manipulate equations (attends to the meaning of the quantities, not just computes them) InterActivate (In the search box, type “manipulate” and several interactive activities to manipulate equations come up. Click the tabs for more differentiation options. )

Understand and use different properties and operations: Free Equation Editor

The 8 Standards for Mathematical Practice within the Common Core Reasoning and Communication

III.  Construct viable arguments and critique the reasoning of others

Understand and use definitions in previously established results when justifying results

Attempt to prove or disprove conjectures through examples and counterexamples

Communicate and defend mathematical reasoning using objects, drawings, diagrams, actions, verbal and written communication:

Communicate about Math Using Games (For examples of how to talk about math)

Communication about Math among Students (for discussion on how to help students “talk in numbers” to others)

The 8 Standards for Mathematical Practice within the Common Core Representation and Connections

Model with mathematics

Solve math problems arising in everyday life:

Middle and High School: Real World Math (using Google Earth) Elementary: Plane Math

Apply assumptions and approximations to simplify complicated tasks

Use tools such as diagrams, two-way tables, graphs, flowcharts and formulas to simplify tasks

Analyze relationships mathematically to draw conclusions

Interpret results to determine whether they make sense: Authentic Assessment Toolbox


The 8 Standards for Mathematical Practice within the Common Core Representation

IV.  Use appropriate tools strategically

Decide which tools will be most helpful (ie: ruler, calculator, protractor): How to introduce tools to students

Detect possible errors by strategically using estimation and other mathematical knowledge

Make models that enable visualization of the results and compare predictions with data: Probability and Geometry

Use technological tools to explore and deepen understanding of concepts: Visual thinking

The 8 Standards for Mathematical Practice within the Common Core Reasoning and Communication

V.  Attend to precision


Communicate precisely to others: Using Math Vocabulary

Use clear definitions in discussion with others

State the meaning of the symbols consistently and appropriately

Calculate accurately and efficiently: Order of Operations Bingo

Accurately label axes and measures in a problem


The 8 Standards for Mathematical Practice within the Common Core Problem Solving

VI.  Look for and make use of structure

Look closely to determine a pattern or structure: Dynamic Paper

Step back for an overview and shift perspective

See complicated things as being composed of single objects or several smaller objects


The 8 Standards for Mathematical Practice within the Common Core Problem Solving

VII. Look for and express regularity in repeated reasoning

Identify calculations that repeat

Look both for general methods and for shortcuts: Cool Math Tricks

Maintain oversight of the process, while attending to the details

Continually evaluate the reasonableness of results


The 8 Standards for Mathematical Practice within the Common Core

General Sites:

Videos and Explanations of the Common Core

Open-Source Assistive Technology Software for UDL

National Council of Teachers of Mathematics Virtual Manipulatives (including daily puzzles)

National Library of Virtual Manipulatives

The Ugly Pages

If one of the links above doesn’t work, you can copy its URL below into your browser.

From Opening Page:

1.  Maryland Common Core Standards: http://mdk12.org/instruction/curriculum/mathematics/index.html
2.  Maryland 8 Standards of Mathematical Practice: http://mdk12.org/instruction/academies/resources/Mathematics/MathD1/Standards_for_Mathematical%20_Practice.pdf
3.  Standard 1: http://michellef.essdack.org/?q=node/156
4.  Standard 2: http://michellef.essdack.org/?q=node/157 / 5.  Standard 3: http://michellef.essdack.org/?q=node/158
6.  Standard 4: http://michellef.essdack.org/?q=node/161
7.  Standard 5: http://michellef.essdack.org/?q=node/162
8.  Standard 6: http://michellef.essdack.org/?q=node/165
9.  Standard 7: http://michellef.essdack.org/?q=node/166
10. Standard 8: http://michellef.essdack.org/node/167

From Standard I Page:

1.  Mind Mapping: http://www.youtube.com/watch?v=wLWV0XN7K1g&feature=fvwrel

2.  Thinking Creatively: http://members.optusnet.com.au/~charles57/Creative/Techniques/index.html

3.  Calculation Nation: http://calculationnation.nctm.org/Login.aspx?ReturnUrl=%2fGames%2fGame.aspx%3fGameId%3dCA10F335-7BA3-444B-B02A-50F151D106CA&GameId=CA10F335-7BA3-444B-B02A-50F151D106CA (choose Guest Pass button)

From Standard II:

1.  Teaching Number Bases: http://nlvm.usu.edu/en/nav/frames_asid_152_g_3_t_1.html

2.  Equations and Inequalities: http://www.scimathmn.org/stemtc/frameworks/824b-solve-represent-equations-inequalities-systems

3.  Manipulate Equations (InterActivate): http://www.shodor.org/interactivate/activities/

4.  Online Equation Editor: http://www.homeschoolmath.net/worksheets/equation_editor.php

From Standard III:

1.  Communicate about Math Using Games: http://www.nctm.org/standards/content.aspx?id=24608

2.  Communicate about Math among Students: http://www.nctm.org/standards/content.aspx?id=24604

From Standard IV:

1.  Real-life Math: http://www.realworldmath.org/Real_World_Math/Lessons.html

2.  Plane Math: http://planemath.com/planemathmain.html

3.  Authentic Assessment Toolbox: http://jfmueller.faculty.noctrl.edu/toolbox/examples/tasks_middle_math.htm

From Standard V:

1.  Introducing Math Tools: http://jfmueller.faculty.noctrl.edu/toolbox/examples/tasks_middle_math.htm

2.  Make Models (Spinners): http://nlvm.usu.edu/en/nav/frames_asid_186_g_2_t_5.html?open=activities&from=category_g_2_t_5.html

3.  Make Models (Polygons): http://www.nctm.org/standards/content.aspx?id=25008

4.  Visual Thinking: http://www.nctm.org/standards/content.aspx?id=25008

From Standard VI:

1.  Using Math Vocabulary: http://michellef.essdack.org/?q=node/164

2.  Calculate Accurately (Operations BINGO): http://illuminations.nctm.org/LessonDetail.aspx?id=L730

From Standard VII:

1.  Determine Patterns and Structure (Use Dynamic Paper): http://illuminations.nctm.org/ActivityDetail.aspx?ID=205

From Standard VIII:

1.  General Methods and Shortcuts: http://coolmathtricks.com/

General Sites:

1.  Videos and Explanations of Common Core: http://www.insidemathematics.org/index.php/common-core-standards

2.  NCTM Virtual Manipulatives: http://illuminations.nctm.org/

3.  National Library of Virtual Manipulatives: http://nlvm.usu.edu/

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Kathleen Cave