Math 3-6

Number Sense

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Factor Connections

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

How Number Sense connects to...

Number Sense includes both the conceptual understanding of whole and rational numbers and their magnitude, and the ability to represent and operate with these numbers. Students with good Number Sense can readily transition between representations of quantity in the real world and mathematical expressions, and therefore can easily access and use their number knowledge to inform their math problem solving.

Main Ideas

Number Sense includes multiple skills that begin to develop in the early years (see the Math PK-2 model) and continue to be foundational to successful math learning and performance:

  • Symbolic Number: An understanding of how a quantity maps onto the symbols - or numerals - that represent it and the ability to combine those numerals;
  • Decomposition: An understanding of how to break numbers into smaller parts;
  • Place Value: An understanding of the base-10 system and the value of individual numerals in a multi-digit number; and
  • Estimation: The ability to give a rough approximation of the magnitude of a number or value of a calculation.

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Research-Based Strategies For This Factor

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.

Creating Visual Representations

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

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 common problem structures 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 mathematical thinking and intentionally tackle problems.

Error Analysis

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

Math Games

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

Multiple Representations: Visual Representations

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

Real-world Math

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

Rich Resources: Children's Literature

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

Student-generated Problems

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

Untimed Tests

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

Worked Examples

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

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