# NUMBERS Professional Development

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## Built to Meet the Expectations of More Rigorous Standards

NUMBERS is an interactive, hands-on mathematics professional development offering for elementary and middle school math teachers. Integrating findings from the most current research, NUMBERS incorporates numerous strategies and best practices that meet the expectations of rigorous state standards. The modules provide opportunities for teachers to strengthen their own math knowledge, which will result in improved student outcomes.

## Webinar Presentation

Presented by Author John Woodward, Ph.D.

## Number Sense (K-5)

A sense of numbers begins shortly after birth. This module begins with a review of important preschool developmental milestones learning about numbers and concludes with division and the concept of remainders. The major strands are:

• Number meaning— focus on counting strategies
• Number relationships— spatial patterns, number combinations, place value
• Operations on numbers—fact fluency, estimation, traditional and alternative algorithms
• Problem solving— type and structure of problems

## Geometry and Measurement (K-5)

At times, measurement and geometry clearly overlap. At others, they call for separate skills such as proportionality when converting inches to feet and visualizing congruent parts. The major strands are:

• Visualizing and reasoning about shapes—classifying and sorting shapes, partitioning shapes into equal shares, composition and decomposition of shapes, recognizing symmetry, classifying two-dimensional figures
• Measuring dimensions and angles—ordering objects by length, using appropriate tools, unit conversion, a dynamic understanding of area and perimeter, volume, angle measurement

## Fractions and Decimals (3-6)

Developing competence in fractions and decimals involves a number of concepts that precede operations on these numbers. The major strands are:

• Fraction meaning— naming and representing fractions, equal shares, fractions as division, equivalence, magnitude
• Operations on fractions— conceptual foundations for each operation
• Decimal meaning— link to fractions, base ten, magnitude
• Operations on decimals— conceptual foundation for each operation, number sense

## Ratios and Proportions (6-8)

Ratios are a significant shift for students because of the relationship between quantities. They can be part-to-part or partto- whole relationships. This module tackles misconceptions that students exhibit as they move into ratios and proportional thinking. The major strands are:

• Complexity of proportional thinking —the importance of multiplicative thinking, definitions of ratios and proportion
• Problem solving and visual representations— models (tables, double number lines, tape diagrams), researchbased problem-solving strategies
• Connections to other middle school domains— geometry, statistics, algebra

## Algebraic Thinking (6-8)

Traditional instruction focuses almost exclusively on teaching students procedures. This module presents a rich picture of algebraic thinking, connecting algebra to math in earlier grades. The major strands are:

• Making generalizations —finding the algebra in arithmetic, making inductions from patterns, determining the truth value math statements
• Rules, properties, and procedures—a conceptual understanding of integers and operations on integers, visual representations of expressions and equations
• Problem solving— making sense of functions, researchbased approaches for algebraic problem solving