On the campus of

# AIMS Math Professional Development

The following are the types of one-day math professional development workshops AIMS offers. Each day covers three grade levels. Our PD Facilitators will engage teachers in hands-on math activities using manipulatives. The goal is to share ways teachers can help students build a strong conceptual understanding of mathematics. Our materials are both content and concept rich, incorporating the knowledge and practices students need, to be able to communicate well mathematically. They help students with understanding concept development in mathematics in a certain domain or for the goals set by standards.

## Math Topics

Math Practices: K-2, 3-5, and 6-8
The Mathematical Practices describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. We have chosen lessons that allow teachers to specifically focus on the eight Mathematical Practices Standards at the appropriate levels found in the Common Core State Standards for Mathematics.

Operations and Algebraic Thinking: K-2 and 3-5, 6-8
Algebra is a powerful set of tools for representing situations, analyzing mathematical relationships, making generalizations and solving problems. We must develop algebraic thinking across the grades so students will incorporate algebraic techniques into their broader mathematical thinking. Lessons chosen for these days will give the attending teachers techniques that help students develop an algebraic sense.

Number and Operations Base 10: K-2 and 3-5
Base-ten is our most common number language. Students must come to:

• understand the place-value structure of the base-ten number system
• represent and compare whole numbers and decimals
• explore numbers less than zero by extending the number line

AIMS lessons will be used to give teachers added experiences they can implement in to their classroom teaching to help students develop a better command of our Base-ten number system.

Number and Operations Fractions: 3-5
Fractions are developed and explored in the intermediate grades. Teachers are responsible for building student understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers. They must share models, benchmarks, and equivalent forms to judge the size of fractions, and help students be able to recognize and generate equivalent forms of commonly used fractions, decimals, and percents. This workshop focuses on ways teachers can help students achieve the fraction knowledge and understanding they need.

Measurement and Data: K-2 and 3-5
Development of measurement for primary students focuses on recognizing attributes of length, volume, weight, area, and time. They should be able to compare and order objects according to these attributes. Understanding how to measure using nonstandard and standard units is an essential skill as well as selecting an appropriate unit and tool for the attribute being measured.
Intermediate students must:

• understand size of angle
• becoming familiar with standard units in the customary and metric systems
• understand that measurements are approximations
• realize how differences in units affect precision
• explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.

This workshop focuses on ways teachers can help students achieve the goals for measurement and data.

Geometry: K-2 and 3-5
Geometry expectations for Kindergarten through 2nd grade are for students to recognize, name, build, draw, compare, and sort two- and three-dimensional shapes, describe attributes and parts of two- and three-dimensional shapes, and to investigate and predict the results of putting together and taking apart two- and three-dimensional shapes. In the intermediate grades 3-5, students will add the skills of identifying, comparing, and analyzing attributes of two- and three-dimensional shapes. They will develop vocabulary to describe the attributes, classifying two- and three-dimensional shapes according to their properties. They will develop definitions of classes of shapes such as triangles and pyramids, investigating, describing, and reasoning about the results of subdividing, combining, and transforming shapes, and exploring congruence and similarity. AIMS lessons will be used in this workshop to share ideas and ways a teacher can meet the Geometry expectations for the primary and intermediate grades.

Geometry: 6-8
Geometry goals for 6th-8th grade students are to precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties. To understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects. To create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. This workshop focuses on ways teachers can help students achieve the geometry knowledge and understanding they need.

The Number System: 6-8
A middle school student should be able to work flexibly with fractions, decimals, and percents to solve problems, as well as compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line. They should also develop meaning for percents greater than 100 and less than, develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation, use factors, multiples, prime factorization, and relative prime numbers to solve problems, and develop meaning for integers and represent and compare quantities with them. AIMS lessons will be used in this workshop to share ideas and ways a teacher can come closer to meeting the rigorous goals for understanding the number system that we put on middle school students.

Ratios and Proportional Relationships: 6-8
A focus of mathematics in the middle grades is the ratio, proportion, and function strand. Experience the growth and development of this strand in grades 6–8 by engaging in a sequence of lessons. Start with a hands-on lesson that highlights different approaches to and representations for the important concepts of ratio. Continue with lessons involving unit ratios, equivalent ratios, and methods of creating and solving proportions. Wrap up your work with a lesson that highlights the connection between proportions and the key concept of function. The session will also model different formative assessments and important pedagogical moves for use in implementing the lessons.

Statistics and Probability: 6-8
In grades 6–8 students should be able to formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population, and select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter-plots. This workshop will utilize AIMS activities to help model and show classroom teachers additional ways of accomplishing these goals.

Expressions, Equations and Functions: 6-8
In grades 6-8, students need to be able to solve real-life mathematical problems using numerical and algebraic expressions and equations while applying and extending previous understandings of arithmetic to algebraic expressions. Their reasoning skills will be utilized while solving one or more variable equations and inequalities. They will need to understand the connections between proportional relationships, lines, and linear equations, and also leads to a need for understanding functions. Using hands-on AIMS lessons educators will discover and learn other ways to promote the needed skills for understanding expressions, equations and functions for 6th thru 8th grade students.