## 8 Mathematical Practices

One of the most exciting elements of the Common Core State Standards in Mathematics is the identification and development of the 8 Mathematical Practices for Kindergarten through 12th grade. These practices refute the myths surrounding math instruction and demystify what it means to think like a mathematician. No longer can students (and parents) say that they don't have the "math gene" and that they have always struggled to do math. What researchers found is that successful mathematicians have developed certain habits of mind that lend themselves to being a productive mathematician. Through practice and specific learning opportunities,* all* students can develop these math practices and increase their mathematical efficacy. Here you will see a summary of the practices. If you want to know how you can help your child develop these habits of mind, click

**here to access some questions**you might ask to help develop their mathematical thinking. For those of you who would like to listen to an explanation of these math practices with some examples, click

**AUDIO**to access that resource.

1. Make Sense of Problems and Perservere in Solving Them

- Make meaning of the problem and look for a starting point.
- Plan a solution pathway instead of just looking for a solution
- Analyze what is given, relationships between elements of the problem and the goal
- Relate current situation to concepts or skills previously learned and connect mathematical ideas to one another
- Monitor and evaluate progress and change course if necessary
- Continually ask if this solution or strategy makes sense

2. Reason Abstractly and Quantitatively

- Makes of quantities and their relationships
- Represent symbolically (create equations, expressions)
- Create a logical representation of the problem
- Think about the meanings of quantities, not just how to compute them

3. Construct Viable Arguments and Critique the Reasoning of Others

- Understand and use definitions when constructing mathematical arguments (arguing for your answer)
- Justify conclusions with mathematical ideas
- Listen to the arguments of others and ask useful questions to determine if their argument makes sense
- Ask clarifying questions or suggest ideas to improve/revise the argument
- Compare two arguments and determine correct or flawed logic
- Communicate and defend mathematical reasoning using objects, drawings, diagrams, actions, verbal and written communication

4. Model with Math

- Solve math problems arising in everyday life
- Apply assumptions and approximations to simplify complicated tasks
- Use tools such as diagrams, two-way tables, graphs, or concrete manipulatives to simplyfy tasks
- Analyze relationships mathematically to draw conclusions
- Reflect on whether the results make sense, possibly improving/revising the model

5. Use Appropriate Tools Strategically

- Decide which tools will be the most helpful (i.e. ruler, calculator, protractor)
- Use technological tools to explore and deepen understanding of concepts
- Use estimation and other mathematical knowledge to detect possible errors

6. Attend to Precision

- Communicate precisely with others and try to use clear mathematical language
- Understand the meanings of symbols and use them consistently and appropriately
- Calculate efficiently and accurately

7. Look For and Make Use of Structure

- Look closely to see if there is a pattern or structure to help solve the problem
- Step back for an overview and shift perspective
- See complicated things as being composed of single objects or several smaller objects

8. Look for and Express Regularity in Repeated Reasoning

- See repeated calculations and loof for generalizations or shortcuts
- See the overall process of the problem and still attend to the details
- Understand the broader application of patterns and see the structure in similar situations
- Continually evaluate the reasonableness of their immediate results

## Problem of the Month Process

## Family Math Night

October 15th was a great success, with 54 families coming into the MPR to learn about Common Core Mathematics Instruction and how teachers at QR work to build the 8 Mathematical Practices into our classrooms. Mrs. Alamillo, Ms. Sun, Mrs. Cooke, Mrs. Tapia and Mrs. Tricaso guided our families through a condensed Problem of the Month, allowing students and their families to have rich mathematical discussions, as they worked to discover and justify their answers. After all of that group problem solving, we all had the opportunity to see and evaluate the work of other teams solving the same problems. It was an exciting night with lots of laughter and math learning. For those unable to attend, or those who want to look back at the presentation, you may click on **Power Point**.

Handouts from the night can also be downloaded and printed.