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Product No. 4132 Textbook Price: $99.00

Staff Developer's Guide: Investigations in Number, Data, and Space (CD-ROM)


Mathematics Topic:
Application Areas:
Staff Development
Adobe Acrobat

| © October 2003 | Bridges to Classroom Mathematics | Books 1, 2 & 3 on one CD-Rom |

Includes: 16 Workshop Sessions / 50 Unit Guides / 2 Videos

Bridges Sessions Specific to Investigations in Number, Data, and Space


These sessions are intended to familiarize teachers with the mathematical content and pedagogy of the Investigations curriculum. All sessions are 2 hours, except as noted.



The Role of Games
in Investigations
Participants work with number games from different grade levels of Investigations.They play the games with an eye toward recognizing the underlying mathematics, and the way in which teachers: 1) "talk mathematics" with children as game play proceeds; 2) use games for assesment purposes; 3) adapt games to challenge children at different levels. Participants discuss the mathematical learning that is addressed through Investigations games.


Investigations Overview and Structure of an Investigations Unit

After staff and participants introduce themselves, the leader explains the goals and pedagogy of the Investigations curriculum and the structure and purpose of the units. Participants then work in grade level groups with each reviewing an individual unit, looking at the introductory material and the components of an investigation and a session, and reading teacher notes, dialogue boxes, and assessments.


Routines and Ten-Minute Math in Investigations

The leader explains how Classroom Routines (K-grade 2) and Ten-Minute Math (grades 3-5) fit into the Investigations curriculum, and their uses in supporting practice in arithmetic and also in geometry and data analysis. Then participants try a number of the activities: Today's Number, Broken Calculator, Visual Images of Number, Nearest Answer, Estimation Game, and Collecting Data. 


Addition and Subtraction in Investigations

(3 hours)

In this session participants look closely at how students develop strategies to combine and compare amounts. They use mental strategies to solve addition and subtraction problems and generalize these strategies to discover what is happening mathematically in each one. Then they try out strategies that may not be as familiar to them. Participants look at activities from kindergarten through grade 5 and discuss the knowledge of number and operations that is developed through this number strand. The role of speed and efficiency in computation is discussed in regard to addition and subtraction.


Multiplication and Division in Investigations
Part 1

This is the first of two sessions on multiplication and division in Investigations. It focuses on the early grades of Investigations, but also includes mental arithmetic and counting around which are done throughout the grades. Participants look at the development of multiplication and division in grades K-2. Participants first consider how multiplication and division problems can be interpreted. Then they look at samples of children's work from grades 1 and 2 that show students using counting and adding to solve multiplication and division story problems. They see a variety of other multiplication and division tasks in K-2 Investigations and discuss what knowledge their solutions require. Participants then do some mathematics for themselves: mental arithmetic and counting around to look at how knowledge of landmark numbers and patterns in the multiplication tables provide foundation for multiplication and division.

Optional Video:
"Quick Image Dots" (grade 1); "Counting Around the Class" (grade 2)


Multiplication and Division in Investigations
Part 2

(2.5 - 3 hours)

This is the second of two sessions on multiplication and division in Investigations. Participants try activities from grades 3-5 that support students' understanding of the operations of multiplication and division: factoring numbers, and using arrays and cluster problems. They look at the work of fourth and fifth grade students to consider the role that knowledge of the number system and operations can play in students' computational strategies.


2-D Geometry in Investigations

(Allow an extra 30 minutes for optional GeoLogo.)

Participants first brainstorm uses of geometry. Then they look at work in area through the grades. They do activities from grades K-2 using pattern blocks, activities from grade 3 using triangles and squares, and from grade 4 using geoboards. If computers are available, participants explore the GeoLogo Shapes software. 


3-D Geometry in Investigations Participants build their own skills in 3-D geometry as they examine problems using materials that kindergarten through grade 5 students use in Investigations.They examine and describe 3-dimensional shapes while focusing on specific attributes of these shapes and how they relate to one another. Participants explore the connections between two- and three-dimensional shapes by building shapes based on drawings, diagrams, and written instructions. They see an overview of the geometry units in Investigations.


Fractions in Investigations


Participants split rectangular "brownies" into equal shares and discuss different approaches. Then they assess student work on a similar problem. They decide what percents are equivalent to various common fractions and compare fractions to the landmarks, one half and one whole. They work in groups to show a number of different ways to compare fractions or to do a computation problem. They see an overview of the fractions units and consider the importance of geometrical thinking in working with fractions. 

Optional Video episode: "Comparing Fractions" (grade 4)


Data in Investigations

In this session, an introduction to goals for learning about data is presented. Participants collect data about how many roofs each has lived under, represent the data in a line plot and describe and interpret their data. In small groups, participants list games they played as children, form categories to sort them, and talk about criteria for effective categorization. They discuss the use of various measures of typicality.


Roots of Algebra in Investigations

Participants work with problems from Investigations that require them to reason about quantities whose value they do not know, but about which they have some information. They consider how to represent these quantities symbolically. They investigate how basic properties of the number system (e.g. commutative and associative properties) appear in student work as early as first grade. They also use coordinate graphs to explore properties of rectangles.




Math of Change in Investigations Participants are introduced to the Math of Change as a strand in mathematics, and look at possible explanations for a graph of change over time. Then they do activities from units from grades 2-5. They find different combinations of changes that have the same net change. They make a time line through a day and interpret graphs of plant growth to consider the issue of representing elapsed time with a regular time scale. In the final activity, they make tables and graphs to fit a story of changing speed of motion along a straight line and discuss similarities between graphs and between tables that fit the same stories.


Choice Time,
grade 1

(with video)

In this session participants are introduced to the important role of Choice Time in the Investigations curriculum. This session is designed around the videotape "Choice Time, grade 1" in which students are engaged in three mathematically related activities. Teachers reflect on their own experience with Choice Time, both in and outside of math classes. Participants try out the activities themselves and then discuss the mathematics that students will be engaged in as they participate in these activities. Participants consider the role of the teacher and the role of students during Choice Time, how the teacher can use Choice Time for assessment, and the value of Choice Time for the students. 


Choice Time,
grade 4

(with video)

Participants view a videotape of Choice Time in a fourth grade class. They discuss the issues involved in planning for Choice Time, such as selecting an appropriate range of activities and in setting expectations for students. They consider the use of Choice Time in the Investigations curriculum and theteacher's and students' roles during choice time. Participants then do two of the Choice Time activities and talk about the important mathematical ideas in the activities, the procedures or content that might require clarification and intervention during the session, and the ways in which they might modify the games to challenge children at different levels.


Assessment in Investigations,
grade 2

(with video)

Participants explore an approach to assessment emphasized in reform curricula. After viewing the video, "Assesment in Investigations" (grade 2) and student work, participants discuss criteria to determine the understanding of knowledge of several students. A second grade teacher discusses ways she assesses students and how her teaching is informed by observation and evaluation of student work. Participants consider the strengths and challenges of this and other approaches to assessment. A brief overview is provided of the types of support for assessment offered in Investigations. 


Assessment in Investigations,
grade 4

(with video)
The session begins with a brief discussion of types of assessment that students typically encounter in mathematics, and what teachers can learn about their students from each. Next, participants look through samples of student work on a multiplication problem, and view a video clip,"Assesment in Investigations" (grade 4)in which a teacher observes and talks with her students as they work on the problem and explains how she drew on her observations to help inform her analysis of their papers. Following the video, participants look again at the students' work and discuss how this kind of assessment can be used to gather information for grading. Finally, a brief overview is provided of the types of support for assessment offered in Investigations.


Computers in Investigations

This session contains three parts to introduce teachers to three pieces of software in Investigations: Shapes Software, GeoLogo, and Trips. It is expected that leaders will choose two of the three to do in a 2-hour session. 


Preparing Investigations Students for
External Tests

In this session participants consider ways to prepare students for external tests in ways that are in concert with the Investigations curriculum. They consider how to prepare students to recognize vocabulary, computational formats, and other problem presentations so that they can make sense of what is asked and still answer the problems in their own way. They evaluate students' work on open-ended problems.


Videos of Investigations Classroom Episodes The following video clips can be used with Investigations sessions or independently:
"Quick Image Dots" (grade 1);
"Pencil Subtraction" (grade 1);
"Capture 5" (grade 2);
"Counting Around the Class" (grade 2);
"Division with Remainders" (grade 3);
"Comparing Fractions" (grade 4);
"Fraction Track Game" (grade 5).