### Description

The Mathematical Generalizing Performance task introduces students to the steps for developing proof-related competencies with a variety of mathematical areas.

This task requires students to think and operate within the constraints of mathematical reasoning and proof, and to develop cogent arguments within the context of mathematical representations (algebraic, graphical, geometric, and tabular). These are non-trivial tasks and require students to think in sophisticated ways about what does and does not constitute an accurate proof, and the distinction between using empirical examples to provide evidence that a claim is true and the production of an argument that shows the claim is true in all cases.

### Content Areas

- Math

## Explore Mathematical Generalizing

**What is the Mathematical Generalizing?**

Develop a clear enough understanding of the characteristics of mathematical generalizing to be able to explain your understanding to others.

### Common Core Standards

- CCSS.MP.4

### Time To Complete

## Explore The Validity Of A Mathematical Claim Through Empirical Experimentation

**Does the information presented support the mathematical claim?**

Use your knowledge of mathematics to discover whether the claim is supported by the information provided.

### Common Core Standards

- CCSS.MP.7
- CCSS.MP.8

### Time To Complete

## Detect And Articulate Patterns

**What can I infer about the relationship among the members of the set? **

Find the similarities and extend them to other cases.

### Common Core Standards

- CCSS.MP.6
- CCSS.MP.7
- CCSS.MP.8

### Time To Complete

## Conjecture About The Validity Of The Claim

**Does it always work?**

Take a stance about whether the claim is true or not?

### Common Core Standards

- CCSS.MP.3

### Time To Complete

## Modify Or “Tinker” With The Claim To Make It Valid

**What would make my claim valid?**

Use a variety of tools and strategies to figure out if a mathematical claim can be made valid.

### Common Core Standards

- CCSS.MP.6
- CCSS.MP.1

### Time To Complete

## Model Using Mathematical Representations

**What are various ways to represent numerical data?**

Develop an appropriate mathematical representation that accurately reflects the patterns that you noticed.

### Common Core Standards

- CCSS.MP.6
- CCSS.MP.4
- CCSS.MP.2

### Time To Complete

## Develop A Convincing Mathematical Argument

**How do I know it works and how do I convince others?**

Provide evidence and reasoning to convince others that your claim is valid.

### Common Core Standards

- CCSS.MP.6
- CCSS.MP.3

### Time To Complete

## Give and Receive Feedback (Mathematical Generalizing)

**How can I improve my work?**

Strengthen your work by giving and receiving feedback from a peer or teacher.

### Common Core Standards

- CCSS.MP.6
- CCSS.MP.3

### Time To Complete

## Revise (Mathematical Generalizing)

**How can I improve my draft?**

Using feedback from a peer and/or teacher, strengthen your draft by ensuring your facts and details are relevant, your organization is clear, and your use of voice is strong and appropriate to the audience.

### Common Core Standards

- CCSS.MP.6
- CCSS.MP.3

### Time To Complete

## Edit (Mathematical Generalizing)

**How can I improve my draft?**

Using feedback from a peer and/or teacher, strengthen your writing with a focus on conventions such as grammar and professional language.

### Common Core Standards

- CCSS.MP.5
- CCSS.MP.6