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Hover to see how Factors connect to Operations. Then click connected Factors to explore strategies related to multiple Factors.

Operations involve manipulating and calculating with numbers. There are four basic arithmetic operations: **addition**, **subtraction**, **multiplication**, and **division**.

Operational fluency, a key component for math success, is when students are able to perform simple arithmetic and also learn standard procedures or invented strategies for solving more complex multi-digit problems.

Students reach operational proficiency when they have conceptual understandings of the properties of each of the Operations types and can perform these Operations fluently.

As students solve problems in a group, they learn new strategies and practice communicating their mathematical thinking.

CRA is a sequential instructional approach during which students move from working with concrete materials to creating representational drawings to using abstract symbols.

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.

10 minutes in each math session devoted to building fluent retrieval of basic arithmetic facts sets the foundation for learning new concepts.

In explicit number naming, the structure of the number name labels the number in Place Value order and clearly states the quantity.

Knowing the language of math is critical because students must use this language to understand math concepts and determine calculations needed.

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

Teaching students to recognize common problem structures helps them transfer solution methods from familiar to unfamiliar problems.

Discussing strategies for solving mathematics problems helps students understand how to organize their mathematical thinking and intentionally tackle problems.

Dot cards build number sense and promote early math skills, particularly Spatial Skills and Non-symbolic Number knowledge.

With this interactive technique, teachers help students use their own language for constructing knowledge by active listening and questioning.

Math centers with math games, manipulatives, and activities support learner interests and promote the development of more complex math skills and social interactions.

Math games use numbers and Spatial Skills, allowing students to practice many math skills in a fun, applied context.

A math trail provides students with the opportunity to discover and tackle math concepts outside the classroom and in their communities.

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

Easy access to seeing the relationships between numbers promotes number sense as students see these connections repeatedly.

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

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

Students deepen their understanding and gain confidence in their learning when they explain to and receive feedback from others.

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

Children's literature can be a welcoming way to help students learn math vocabulary and concepts.

When students explain their thinking process aloud, they recognize the strategies they use and solidify their procedural understanding.

Students develop their skills by listening to and speaking with others in informal ways.

Three-phase lesson format is a problem-solving structure to promote meaningful math learning by activating prior knowledge, letting students explore mathematical thinking, and promoting a math community of learners.

Timed practice drills help students achieve automaticity, a critical aspect of Estimation and mental calculations.

Untimed tests provide students the opportunity to flexibly and productively work with numbers, further developing their problem-solving abilities.

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