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.html2. 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