Math 7-9

Systems Change
Math 7-9 > Strategies

Math 7-9

Select one or more factors to see the strategies that support your chosen factor(s). For each strategy, we provide ideas for classroom and product application, videos, and further resources.



Algebraic Thinking
Geometric Reasoning
Math Communication
Mathematical Flexibility
Proportional Reasoning
Statistical Reasoning


Cognitive Flexibility
Long-term Memory
Short-term Memory
Spatial Skills
Speed of Processing
Visual Processing
Working Memory

Social and Emotional Learning

Math Mindset
Sense of Belonging
Social Awareness & Relationship Skills
Stereotype Threat

Student Background

Adverse Experiences
Math Learning Environment
Physical Well-being
Social Supports
Socioeconomic Status


Accessible Vocabulary & Syntax

Teachers support language development by using and providing vocabulary and syntax that is appropriately leveled (e.g., using simple sentences when introducing complex concepts).

Brief Instruction Steps

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

Building Trusting Relationships

Building positive and trusting relationships with learners allows them to feel safe, a Sense of Belonging, and that their academic, cognitive, and social and emotional needs are supported.

Cognitively Demanding Tasks

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

Collaborative Problem Solving

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

Concrete-Representational-Abstract (CRA)

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

Creating Visual Representations

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

Cumulative Review

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

Daily Review

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

Dim or Natural Lighting

Dim or natural lighting provides a calming environment.

Direct Instruction: Patterning

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

Direct Instruction: Problem Structures

Teaching students to recognize the structures of algebraic representations helps them transfer solution methods from familiar to unfamiliar problems.

Direct Instruction: Problem-solving Strategies

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

Encourage Student Self-advocacy

Overtly encouraging all students to seek support and ask questions creates a safe space for risk-taking and skill development.

Error Analysis

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

Explaining Their Thinking

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.

Expressive Writing

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.

Family Engagement

Students are more likely to come to school when families feel like a valued part of the community.

Flipped Classroom

The flipped classroom has two parts: cooperative group activities in class and digitally-based individual instruction out of class.

Foster Growth Mindset

Teachers can help students understand that learning involves effort, mistakes, and reflection by teaching them about their malleable brain and modeling their own learning process.

Gallery Walk

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


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

Goal Setting & Monitoring

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.

Growth Mindset Feedback

Providing feedback that focuses on the process of developing skills conveys the importance of effort and motivates students to persist when learning.

Guided Inquiry

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

Guided Practice

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

Incorporate Students' Cultural Practices

Learning about students' cultures and connecting them to instructional practices helps all students feel like valued members of the community.

Individual Deliberate Practice

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

Individual Spaces

Having space where students can go supports Self-regulation and individual deliberate practice.


As students work with and process information by discussing, organizing, and sharing it together, they deepen their understanding.

Math Centers

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

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

Math Songs

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

Math Talks

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

Mindfulness Activities

Through short but regular mindfulness activities, students develop their awareness and ability to focus.

Mindfulness Breaks

Short breaks that include mindfulness quiet the brain to allow for improved thinking and emotional regulation.

Mnemonic Device

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

Mobility & Flexibility

Multiple tables and chairs on wheels allow for setting up the classroom to support the desired learning outcomes of each activity.

Model Assignment or Skill

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

Model Positive Connections to Math

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

Movement Breaks

Brain breaks that include movement allow learners to refresh their thinking and focus on learning new information.

Multimodal Instruction

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.

Multiple Display Boards/Screens

Multiple display spaces help develop oral language skills as well as Social Awareness & Relationship Skills by allowing groups to share information easily as they work.

Multiple Representations: Graphic Organizer

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

Multiple Representations: Manipulatives

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

Multiple Representations: Visual Representations

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

Multiple Writing Surfaces

Multiple writing surfaces promote collaboration by allowing groups to share information easily as they work.

Music & Dance

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

Peer Teaching

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

Positive Self-talk

When students reframe negative thoughts and tell themselves kind self-statements, they practice positive self-talk.

Predictability: Environment & Structure

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

Quiet Environment/Pockets of Quiet

Decreasing extra audio input provides a focused learning environment.

Real-world Math

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

Reciprocal Teaching

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

Reflect on Learning

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

Response Devices

Response devices boost engagement by encouraging all students to answer every question.

Rich Resources: Audio & Braille

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

Rich Resources: Children's Literature

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

Rich Resources: Diversity

Multicultural resources, such as posters with different types of people and word problems based in different settings, allow all students to see themselves in their math work, supporting their identity development and Sense of Beloning.


When students engage in a dialogue with themselves, they are able to orient, organize, and focus their thinking.


When students monitor their comprehension, behavior, or use of strategies, they build their Metacognition.

Sensory Stimulation

Incorporating multiple senses with strategies like chewing gum, using a fidget, and sitting on a ball chair supports focus and Attention.

Sentence Frames

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

Sound Level

Providing ways for students to adjust sound level supports individual auditory needs.

Sound-blocking Devices

Using earplugs or headphones can increase focus and comfort.

Student Choice

Providing students a voice in their learning is critical for making learning meaningful.

Student-generated Problems

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


Providing ways for students to meet their individual temperature needs supports focus and Self-regulation.

Text-to-speech Software

Transforming written text into audio activates different parts of the brain to support learning.


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

Uncluttered Environment

Spaces that are structured, organized, and clean provide increased room for collaboration and active learning.

Untimed Tests

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

Verbal Repetition

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


Providing visuals to introduce, support, or review instruction activates more cognitive processes to support learning.

Visual Reading Aids

Visual supports, like text magnification, colored overlays, and guided reading strip, help students focus and properly track as they read.

Wait Time

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.

Word Walls

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

Worked Examples

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

Writing to Learn Math

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