Incorporating Standards for Mathematical Practice Into Lessons and Observations

Grade Levels
K - 2nd, Homeschool, Staff
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  • Supporting Document
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  1. The Standards for Mathematical Practice provide the foundation for teaching all math standards--from kindergarten up. These kindergarten-specific posters, along with the K-2 training video, will help you to implement these standards easily and effectively in your classroom.Please also consider my Ki
    Save $3.30
  2. The Standards for Mathematical Practice provide the foundation for teaching all math concepts and skills. These first grade-specific posters, along with the K-2 training video, will help you to implement these standards easily and effectively in your classroom.Please also consider my companion video
    Save $3.30
  3. The Standards for Mathematical Practice provide the foundation for teaching all math concepts and skills. These second grade-specific posters, along with the K-2 training video, will help you to implement these standards easily and effectively in your classroom.Please also consider my companion vide
    Save $3.30
Supporting document
This is an additional download that supports the video.


This video will help you to gain a deeper understanding of the CCSS Standards for Mathematical Practice. You'll also learn how standards relate to your grade level, along with simple, practical ideas for incorporating them into your daily lessons.

Here is a detailed table of contents for this presentation:

0:00 Introduction

1:30 Finding the Standards for Mathematical Practice

1:51 The “Big Picture:” The “5 P’s” for incorporating all standards into outstanding math lessons and observations, along with an explanation for the order of this presentation

3:21 MP 1: Make sense of problems and persevere in solving them – Introduction

4:50 Questions about making sense of problems

5:28 “I can” statements

5:49 Rubrics

8:21 Formative vs. summative assessments

10:42 Questions for consideration

11:12 MP5: Use appropriate tools strategically – Introduction

12:31 Questions

13:02 “I can” statements

13:19 Rubric

13:24 Questions for consideration

13:51 MP4: Model with mathematics – Introduction

15:10 Questions

15:44 “I can” statements

15:48 Rubric

16:01 Questions for consideration

16:19 MP2: Reason abstractly and quantitatively – Introduction

16:50 Questions

17:25 “I can” statements (See this packet for rubrics.)

17:31 Questions for consideration

18:57 MP3: Construct viable arguments and critique the reasoning of others – Introduction

19:22 Questions

19:44 “I can” statements

19:59 Rubric

20:45 MP6: Attend to precision – Introduction

20:54 Questions, “I can” statements, and rubric

21:25 Questions for consideration

21:33 MP7: Look for and make use of structure – Introduction

22:22 Questions, “I can” statements, and rubric

21:25 Questions for consideration

22:50 MP8: Look for and express regularity in repeated reasoning – Introduction

23:13 Questions, “I can” statements, and rubric

21:25 Review in terms of “The Big Picture”

25:25 Thank you/Credits

These posters are also great tools for teaching the standards for mathematical practice--aligned to your grade level!

Kindergarten Standards for Mathematical Practice Posters

1st Grade Standards for Mathematical Practice Posters

2nd Grade Standards for Mathematical Practice Posters

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to see state-specific standards (only available in the US).
Make sense of problems and persevere in solving them. 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. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Reason abstractly and quantitatively. 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-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
Construct viable arguments and critique the reasoning of others. 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. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
Model with mathematics. 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. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
Use appropriate tools strategically. 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. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.


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