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Hover to see how factors connect to Arithmetic Fact Retrieval. Then click connected factors to explore strategies related to multiple factors.

Arithmetic Fact Retrieval requires efficiently, accurately, and flexibly drawing basic number combinations from Long-term Memory to use in performing more complex calculations. Though arithmetic facts and number combinations are typically in place by the end of elementary school, fluent and flexible fact retrieval continues to scaffold math learning and outcomes through high school.

More recently, the term arithmetic or number **combinations** is often used in place of "fact retrieval" because basic arithmetic problems can be solved in a variety of ways and are not always retrieved as "facts."

There are three key components to Arithmetic Fact Retrieval:

**Efficiency:**Retrieval of arithmetic combinations should be fluent and use the most directly applicable strategy;**Accuracy:**Arithmetic combinations stored in Long-term Memory should be correct; and**Flexibility:**Combinations allow students to access and use their connected number networks for arithmetic problem solving.

Before students are able to use fact retrieval with efficiency, accuracy, and flexibility, they need to have experience working with number combinations using modeling and counting strategies. This experience provides opportunities for students to develop a network of connections that supports understanding. This network, in turn, allows students to use fact retrieval strategies that are less subject to interference and errors. For example, to figure 7 x 8, a student with a connected network of understanding might retrieve the fact 8 x 8 = 64 and relate it to 7 x 8 by subtracting 8: 7 x 8 = 8 x 8 - 8 or 64 - 8.

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 math facts sets the foundation for learning new concepts.

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

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.

Practicing until achieving several error-free attempts is critical for retention.

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

Math games allow students to practice many math skills in a fun, applied context.

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

When students have meaningful conversations about math and use math vocabulary, they develop the thinking, questioning, and explanation skills needed to master mathematical concepts.

Mnemonic devices help students remember mathematical concepts and steps of math and classroom processes.

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.

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.

Connecting information to music and dance moves enhances Short-term and Long-term Memory by drawing on auditory processes and the cognitive benefits of physical activity.

When teachers connect math to the students' world, students see how math is relevant and applicable to 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 create their own number and word problems, they connect math concepts to their background knowledge and lived experiences.

Students deepen their math understanding as they use and hear others use specific math language in informal ways.

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

Having students verbally repeat information such as instructions ensures they have heard and supports remembering.

Wait time, or think time, of three or more seconds after posing a question increases how many students volunteer and the length and accuracy of their responses.

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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