Developing Mathematical Thinking: Enhancing Number Sense and Fluency

November 06, 2024

Building students' math fluency is a critical endeavor that lays the foundation for students to become confident problem-solvers. Whether you're an experienced teacher or just beginning your teaching journey, empowering students with strong number sense is crucial to their success in tackling complex math concepts. From early elementary to secondary classrooms, establishing a solid foundation in fluency allows students to think critically and confidently about approaching math challenges, both in and out of the classroom.

At Fishtank Learning, we are committed to helping teachers cultivate these essential skills through our guiding principles embedded in our curriculum. Our curriculum is designed to help all students become confident and competent mathematicians. We achieve this by providing standards-aligned, content-rich tasks that engage students in deep learning, fostering opportunities to communicate their mathematical thinking, and valuing the learning process. By offering research-backed strategies, our curriculum empowers teachers to make the best instructional decisions for their students while continuously monitoring student progress to drive meaningful learning outcomes.

 

Why Focus on Fluency?  

Mathematical fluency goes beyond rote memorization; it is the foundation for a deeper understanding of mathematics and problem-solving skills. Research indicates that a strong grasp of math fluency is essential for students to succeed in higher-level problem-solving tasks. This type of fluency allows students to process numbers more efficiently, creating more cognitive space for handling complex problem-solving. Fishtank Learning is committed to nurturing fluency in students from an early stage and maintaining it consistently. By placing emphasis on fluency, students can make a smooth transition from concrete operations to abstract thinking, which ultimately prepares them for long-term success.

 

Three Activities to Foster Math Fluency

At Fishtank, we aim to give teachers the resources to drive student success. As part of that, we've created a dedicated library of fun, standards-aligned fluency activities accessible with a Fishtank Plus account. To help you get started with a focus on fluency, we're sharing 3 of our favorite fluency activities with you below: 

 

1. Number Talks:

''Number Talks'' are powerful tools for developing fluency and mathematical reasoning. In a Number Talk, students mentally solve a math problem and then discuss their solutions with their peers. This activity encourages students to articulate their thought processes and understand multiple approaches to problem-solving. 

By engaging in Number Talks, students build the ability to manipulate numbers mentally and develop a deeper understanding of numbers. Number Talks are incredibly versatile and can be used as a warm-up activity, during transitions, or even as a brain break to refocus during a lesson. For more information on using Number Talks to boost engagement, check out our blog post, Building Procedural Fluency with Number Talks

Download the activity here.

 

2. Find the Missing Number:

In "Find the Missing Number," students use their understanding of number relationships to solve equations by identifying the missing value. This helps students develop fluency in addition and subtraction while reinforcing critical algebraic thinking. The game involves two players, each trying to find an equation on their game board where the number on a drawn card completes the equation. If a match is found, the player fills in the blank and keeps the card.

Players take turns drawing cards and attempting to complete their equations. The goal is to find all the missing numbers in their column. This hands-on activity promotes student engagement, fluency, and a deeper understanding of number relationships, making it an excellent tool for introducing algebraic concepts early in the learning process.

Download the activity here.

 

3. High or Low: 

In ''High or Low?'', students use estimation reasoning to compare the values of given expressions without evaluating them. For example, when presented with an expression like 468 + 235, students determine if the sum is higher or lower than related expressions such as 400 + 200 or 500 + 300. This helps develop estimation skills and a better understanding of number relationships. Teachers can guide discussions by asking questions like, "How do you know?" or "How did you estimate?" to encourage critical thinking.

The activity can be adapted to various mathematical operations, including estimating sums, differences, products, and quotients of multi-digit numbers or decimals. It can also be modified for individual or partner play, where students practice comparing expressions with rounded values. This flexible exercise builds estimation proficiency and supports overall number sense, making it suitable for whole-class or small-group instruction.

Download the activity here.

 

Supporting Your Classroom

Interested in creating an engaging, rigorous, and relevant math learning experiences for your students? Sign up for a free Fishtank Learning account to stay updated on blog posts and gain access to our free 3rd-8th grade, Algebra 1, Algebra 2, and Geometry curriculum. With a Fishtank Plus account, you can access fluency-building activities such as Number Talks, 'Find the Missing Number,' and 'High or Low,' along with other fluency resources. See how Fishtank Plus can benefit your teaching.

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