* ***The Foundation Pieces**

The importance of building good number sense cannot be overstated. The ability to reason, think flexibly, and understand relationships—these and other characteristics of number sense are the foundational pieces needed for everything from simple arithmetic to more complex math. Without a strong grounding in number sense, it becomes difficult to do basic everyday activities from finding the best price online or at the store, to buying furniture that fits into your home, to borrowing, saving or investing for vacations, college or retirement. For us as educators, building strong number sense ensures our students are ready for next gen assessments, algebra, and eventually college and career—not to mention every-day adult living.

**Common Core Connections**

The central role of focus and coherence in the Common Core Content underlines the importance the designers place on developing number sense. For example, when learning addition and subtraction, students initially spend time just understanding numbers, their meanings and their properties relative to the operations. This deep, fundamental preparation soon leads to mastery of the content as students achieve fluency, develop strategies and master algorithms. Interwoven content then builds on itself in a careful, logical progression—from addition and subtraction to multiplication and division and from whole numbers to fractions and decimals—enabling students to fully master core topics in preparation for algebra.

The Common Core Mathematical Practices reflect how students should interact with math content to master skills and their underlying concepts. Building on the NCTM’s Process Standards and National Research Council’s Strands of Mathematical Proficiency. The Common Core Standards for Mathematical Practice call upon students to speculate, reason, defend and debate their thinking and solve problems in more than one way. These important “processes and proficiencies” support students’ development of number sense as well as more complex math.

**Classroom Ideas**

*Real World Experiences
*Ensure that students see mathematics as relevant by presenting problems related to students’ everyday experiences both inside and outside the classroom. Because number sense develops over time, your students need regular opportunities to reason with numbers, hear others’ thoughts and opinions and crystalize their own thinking.

**Primary Activity: After figuring out who is absent, ask students to calculate how many children are in class that day. Another day, ask whether every child will have a partner if the class lines up in pairs or have students figure out how much money a year’s worth of school lunches costs for one student.**

Intermediate Activity: Have students think about comparison shopping. For example, show students two product packages with different amounts and different price points. Ask them which is the better deal. Extend this activity by exploring grocery store circulars—asking them which store offers the best deal on a particular product. After talking about some possible ways to approach the problems, have students write individual papers describing their reasoning.

Explore additional activities to build number sense in this article by Marilyn Burns:

How I Boost My Students’ Number Sense, Marilyn Burns

During class discussions, use questions such as the following to help students focus on numerical reasoning skills and routines:

- Why do you think that?
- Why does your answer make sense?
- How do you know when you have an answer?
- Is there only one solution? How do you know?
- Will your strategy work with every number? Every similar situation? Why do you think so?
- Did anyone think about this differently? Enriching Your Math Curriculum Grade 5 by Lainie Schuster, Math Solutions Publications

**Guiding Principles**

Drawing upon academic work and our own classroom-grounded research and experience, Math Solutions has identified the following four instructional needs as absolutely essential to improving instruction and student outcomes:

**• Robust Content Knowledge**

** • Understanding of How Students Learn**

**• Insight into Individual Learners through Formative Assessment**

**• Effective Instructional Strategies**

These four instructional needs drive the design of all Math Solutions courses, consulting and coaching. We consider them our guiding principles and strive to ensure that all educators:

**Know the math they need to teach**—know it deeply and flexibly enough to understand various solution paths and students’ reasoning.

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**Understand the conditions necessary for learning,** what they need to provide, and what students must make sense of for themselves.

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**Recognize each student’s strengths and weaknesses,** content knowledge, reasoning strategies, and misconceptions.

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**Have the expertise to make math accessible for all students**, to ask

questions that reveal and build understanding, and help students make sense

of and solve problems.

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