Opening Math Routines

Opening Routines are short, quick opportunities that support productive mathematical thinking and encourage student discourse. These routines develop number sense, give all students opportunities to think creatively, build a community of mathematical thinkers, activate prior knowledge of skills and content, and provide access to all students.

strategies to support facilitation

Predictability: Environment & Structure

Math 7-10

Maintaining consistent classroom routines and schedules ensures that students are able to trust and predict what will happen next.

Brief Instruction Steps

Math 7-10

Content that is provided in clear, short chunks can support students' Working Memory.

Wait Time

Math 7-10

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.

Model Positive Connections to Math

Math 7-10

Teachers sharing math-to-self, math-to-math, and math-to-world connections model math schema building.

Math Talks

Math 7-10

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

Guided Inquiry

Math 7-10

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

Multiple Representations: Visual Representations

Math 7-10

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

Multimodal Instruction

Math 7-10

Instruction in multiple formats allows students to activate different cognitive skills to understand and remember the steps they are to take in their math work.

Word Walls

Math 7-10

A word wall helps build the Math Communication and vocabulary skills that are necessary for problem solving.

Sentence Frames

Math 7-10

Sentence frames or stems can serve as language support to enrich students' participation in academic discussions.

strategies to support student thinking

Error Analysis

Math 7-10

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

Think-Pair-Share

Math 7-10

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

Explaining Their Thinking

Math 7-10

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.

Worked Examples

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

Multiple Representations: Manipulatives

Math 7-10

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

Multiple Representations: Graphic Organizer

Math 7-10

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

Creating Visual Representations

Math 7-10

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

Gallery Walk
Math 7-10

As students walk through stations working in small groups, the social and physical nature of the learning supports deeper understanding.

Strategies to support student ownership

Expressive Writing

Math 7-10

Writing freely about one's emotions about a specific activity, such as taking a test, can help students cope with negative Emotion, such as math anxiety.

Incorporate Students' Cultural Practices

Math 7-10

Learning about students' cultures and connecting them to instructional practices helps foster a Sense of Belonging and mitigate Stereotype Threat.

Collaborative Problem Solving

Math 7-10

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

Reflect on Learning

Math 7-10

Providing space and time for students to reflect is critical for moving what they have learned into Long-term Memory.

Peer Teaching

Math 7-10

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

Goal Setting & Monitoring

Math 7-10

Setting overall goals, as well as smaller goals as steps to reaching them, encourages consistent, achievable progress and helps students feel confident in their skills and abilities.

factors to consider for building mathematical thinking

Math 7-10

Speed of Processing is the rate at which we perceive and process information and formulate an appropriate response.

Math 7-10

Cognitive Flexibility, a component of executive functioning, is the ability to effectively adapt our behavior as we face changing environmental and task demands.

Math 7-10

Working Memory, a component of executive functioning, allows a person to temporarily hold and manipulate information to apply in other processes.

Math 7-10

A Sense of Belonging allows us to feel included, respected, and supported in school.

Math 7-10

Motivation is the desire and energy that guides behavior.

Math 7-10

Math Mindset includes learners' self-concept and self-efficacy beliefs as well as their mindset toward failure, all of which shape their willingness to get involved with mathematics.

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In our society, there are many stereotypes that exist about the academic abilities of learners based on characteristics such as their race, gender, disability, and socioeconomic status.

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Operations specify how quantities can be combined and transformed.

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Proportional Reasoning involves an understanding of ratio and the relationships between ratios.

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Mathematical Flexibility is the ability to maintain and shift among multiple representations of numbers and between problem-solving strategies in an adaptive manner.