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Statistical Reasoning involves thinking about and understanding uncertainty and building mental models to capture key aspects of real world phenomena. As they reason with this uncertainty, students should be able to formulate questions about data and determine what data they need to answer these questions. They then gather, organize, analyze, and display this data to describe and make inferences to help them answer their questions.

Statistical Reasoning involves an integrated conceptual understanding of statistics and probability:

**Statistical thinking**includes using critical thinking to organize, represent, analyze, and interpret data; understanding how to use the appropriate statistical tools; explaining statistical processes; and connecting statistical concepts.**Probabilistic thinking**includes calculating the likelihood of future events, including what kinds of distributions of chance events may be expected and how rare or common a particular outcome will be.

Key concepts involved in developing statistical and probabilistic thinking are:

**Center:**The average value of the data, typically measured by the mean or median;**Distribution**: A collection of all the values in the set of data presented in an organized manner such as a table or graph (e.g., a bell curve representing the frequency of each value);**Spread or Variability:**How similar or different the set of values is from the center (e.g., range) in a distribution; and**Randomness:**The lack of a pattern in a set of events.

Competency in statistical and probabilistic thinking enables students to reason about and discuss what data means, including the ability to use models that quantify important aspects of data that can have uncertainty, noise, and error.

Both statistical and probabilistic thinking can be influenced by the context in which the data or events occur. Further, students' prior knowledge, beliefs, and any misconceptions about chance or uncertain situations may influence the quality of their Statistical Reasoning.

Providing math tasks with high cognitive demand conveys high expectations for all students by challenging them to engage in higher-order thinking.

Students activate more cognitive processes by exploring and representing their understandings in visual form.

Continual use of foundational skills with different problems reinforces a conceptual understanding of math skills.

Daily review strengthens previous learning and can lead to fluent recall.

Thinking of and about patterns encourages learners to look for and understand the rules and relationships that are critical components of mathematical reasoning.

Discussing strategies for solving mathematics problems after initially letting students attempt to problem solve on their own helps them understand how to organize their mathematical thinking and intentionally tackle problems.

Analyzing incorrect worked examples is especially beneficial for helping students develop a conceptual understanding of mathematical processes.

When students explain their thinking process aloud with guidance in response to questions or prompts, they recognize the strategies they use and solidify their understanding.

Adding motions to complement learning activates more cognitive processes for recall and understanding.

In guided inquiry, teachers help students use their own language for constructing knowledge by active listening and questioning.

Spending time with new content helps move concepts and ideas into Long-term Memory.

Math centers support learner interests and promote the development of more complex math skills and social interactions.

Rhyming, alliteration, and other sound devices reinforce math skills development by activating the mental processes that promote memory.

By talking through their thinking at each step of a process, teachers can model what learning looks like.

Visualizing how ideas fit together helps students construct meaning and strengthens recall.

Providing physical and virtual representations of numbers and math concepts helps activate mental processes.

Visual representations help students understand what a number represents as well as recognize relationships between numbers.

Having students teach their knowledge, skills, and understanding to their classmates strengthens learning.

When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.

Math games and manipulatives for vision differences support math development for learners with visual needs.

When students create their own number and word problems, they connect math concepts to their background knowledge and lived experiences.

Analyzing and discussing solved problems helps students develop a deeper understanding of abstract mathematical processes.

Writing that encourages students to articulate their understanding of math concepts or explain math ideas helps deepen students' mathematical understanding.

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