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Massachusetts Department of Education

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The Strand Number Sense

Number Sense is the foundation of numeracy. Sound number sense enables us to interpret and represent the world in which we live. It is evident in all we do, whether in complex examples such as the Gross National Product, basic issues such as the family budget, or as personal as a blood pressure reading. Mathematical intuition grows with a strong basic understanding of numbers and, with that, our ability to do mathematical problem solving.

To be efficient workers or consumers in today's world, adults must have a strongly developed conceptual understanding of arithmetic operations, as well as the procedural knowledge of computation and number facts. They must be able to perceive the idea of place value and be able to read, write, and represent numbers and numerical relationships in a wide variety of ways. Simple paper-and-pencil computation skills are not enough. Adults must be able to make decisions regarding the best method of computation (mental math, paper-and-pencil, or calculator/computer) to use for a particular situation. Knowledge of numbers, operations and computation must include both a well-developed number sense and the ability to use basic mathematics-related technologies.
Number sense promotes accuracy in estimation and flexibility and efficiency in mental math. While calculators and computers are used to do most of the complex computations in today’s world, the ability to estimate is critical for lifelong learners. Adults use informal measurements in life skill activities such as cooking, shopping, buying clothes, or estimating the time required for daily tasks. Estimation is a valuable skill for checking the reasonableness of computation or accuracy in problem solving, and is an aid in timed-test situations such as the GED. It builds on adult experience and knowledge. Good estimators use a variety of strategies and techniques for computational estimation that can be explored and shared by learners.

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to:

  • Standard N-1. Represent and use numbers in a variety of equivalent forms in contextual situations,

  • Standard N-2. Understand meanings of operations and how they relate to one another, and in

  • Standard N-3. Compute fluently and make reasonable estimates.

The Strand Patterns, Functions, and Algebra

Mathematics has been defined as the study of patterns. Learning to recognize, analyze, describe, and represent patterns and number relationships connects math to the world and helps us to appreciate fully the intrinsic value of such pleasures as poetry, art, music, and science. Math concepts formerly taught only in basic algebra courses are increasingly part of the culture and vocabulary of modern life. Headlines and news reports speak of exponential growth of the national debt, a variable rate mortgage, or a balanced budget, while medical literature uses terms like “HIV-positive,” or “RH-negative.”

Being able to see and use patterns has been identified as a fundamental skill needed for developing mathematical understanding. The Patterns, Functions, and Algebra strand is positioned after the Number Sense strand because of the importance of building pre-number skills such as patterning which, in turn, enable adult learners to learn multiplication tables and number relationships necessary for efficient and fluent computation skills. The strand also encompasses skills that are necessary for developing concepts in the Data and Geometry and Measurement strands.
Algebra serves as a bridge between arithmetic and more broadly generalized mathematical situations. These generalizations can be expressed in words, tables and charts, the notation of formulas, and graphs. Life experience has afforded adult basic education learners with a broad base of real-world ties that can be readily linked to the concepts of equation, function, variable, and graph. From baby formulas to chemical formulas, algebra offers a succinct way to define real-world situations that can aid adults in the home and in the workplace.
Algebra impacts the competency of workers, parents and citizens, and algebraic thinking skills are crucial if adults are to compete in the global economy. Workplace skills requiring competencies in “information,” “systems,” and “technology” stress the need for organizing, interpreting and communicating information and employing computers as a tool for those tasks, as well as the ability to “discover a rule or principle underlying the relationship between two or more objects and apply it in solving a problem.” Identifying and expressing pattern, relation and function are the algebraic skills imbedded within these competencies.

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to:

  • Standard P-1. Explore, identify, analyze, and extend patterns in mathematical and adult contextual situations,

  • Standard P-2. Articulate and represent number and data relationships using words, tables, graphs, rules, and equations,

  • Standard P-3. Recognize and use algebraic symbols to model mathematical and contextual situations, and

  • Standard P-4. Analyze change in various contexts.

The Strand Statistics and Probability

The Statistics and Probability strand links numeracy and literacy learning. Numbers, logical reasoning, and texts interweave to describe phenomena visually, numerically and verbally in what we term data, which is the heart of this strand.

Data is a wide-ranging topic that touches on many areas of academic study and tells us much about our world. For instance, we learn about preferences, predilections and group characteristics when we read and interpret data. We learn about the power of evidence as we develop the skills to make statements and evaluate arguments based on data. We learn the power of the question and the framer of the question when we collect and represent data, and we learn that sometimes true, sometimes false, pictures are created when we compress data into statistics. Data is a powerful descriptive tool.
So powerful is data that agencies of authority often use it to generate, promote and, sometimes, evaluate decisions. Citizens, therefore, must understand the ways of data in order to exercise their collective and individual intelligence by responding to the expanding presence of this dense expression of information.
The learning standards in the Statistics and Probability strand provide adult learners with the tools for dealing with data.

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to:

  • Standard S-1. Collect, organize and represent data,

  • Standard S-2. Read and interpret data representations,

  • Standard S-3. Describe data using numerical descriptions, statistics and trend terminology,

  • Standard S-4. Make and evaluate arguments or statements by applying knowledge of data analysis, bias factors, graph distortions and context, and

  • Standard S-5. Know and apply basic probability concepts

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