Shapes | Geo-Logo | Tumbling Tetrominoes | Trips
Other Software: Table Top Jr. | Table Top Sr.
Also see: Units with Software
The Investigations curriculum (1998, 2004, and 2006 editions) incorporates technology in one or more units at each grade level. Four software programs were developed specifically for the Investigations curriculum, in order to enhance students' learning. These software programs are used in the 2-D geometry units at each grade, as well as in some of the units on measuring, data, and change. The use of computers enables students to approach and visualize mathematical situations in new ways. They can construct and manipulate geometric shapes, see objects move according to rules they specify, and turn, flip, and repeat a pattern (P1-8 and 1-9 of any Investigations units).
Investigations software programs include: Shapes, Geo-Logo,Tumbling Tetrominoes, and Trips. Students use Shapes (grades K-2) and Tumbling Tetrominoes (grade 3), to explore symmetry, pattern, rotation and reflection, area, and characteristics of 2-D shapes. Geo-Logo (grades 2-5) is used to investigate rotation and reflection, coordinate geometry, the properties of 2-D shapes, and angles. Trips (grade 5) engages students in a mathematical exploration of motion. Students conduct experiments and interpret data presented in graphs and tables.
Two additional software programs, Table Top Jr. and Table Top Sr., are recommended as optional software programs for Investigations users. Both programs were developed at TERC, and are available for purchase through Sunburst.
For more on the use of software in Investigations, see the essay "Technology in the Curriculum" on P. 1-8 and 1-9 of any unit. More detailed information about each program follows, as well as descriptions of the math ideas students encounter in their work with the software, in the units that use it (Units with Software).
The Shapes software helps children develop their ability to visualize shapes and motions, and the affects of those motions, and to begin to think about the attributes of shapes. Shapes does this by supporting young students as they: explore the pattern block shapes and the variety of relationships among them; compose and decompose shapes in different ways; think about what parts of shapes fit together; become more aware of geometric motions (such as flips, turns, and slides); and investigate topics like patterns (and the units that form them), area, and symmetry. Shapes takes manipulatives already familiar to students--pattern blocks and/or tangrams--and extends what students can do with these shapes. Students can create many copies of the shapes and use computer tools to move, combine, and duplicate these shapes to make pictures and designs and to solve problems. Unlike work with actual blocks, students have access to an unlimited supply of shapes, and can save their work in order to develop ideas and projects over time.
Geo-Logo is a special version of Logo that emphasizes the construction of geometric paths and figures. Geo-Logo provides an environment in which students create and modify geometric figures, use mathematical language, measure parts of figures or paths, and work with coordinate systems--all by communicating with a turtle in a geometry-oriented language. (For example, to draw a square the turtle must walk so many steps, make a 90 degree turn, and then repeat this process three more times.)
In Tumbling Tetrominoes, students use the three basic geometric motions (slides, flips, and turns) to place tetrominoes (five different arrangements of four squares) within a larger rectangle, with the goal being to leave as few empty spaces as possible.
Trips is a computer program designed for the mathematical exploration of motion. Students control the movement of two people who walk along parallel tracks, in order to investigate relationships involving change and motion. Students can define the initial position, direction, and speed of both people. Students see the data for each trip displayed along number lines that label the tracks (0-100), in a table that records position changing over time, and in a graph that shows position vs. time or step size vs. time. (NCTM's Illuminations website, designed to 'illuminate' the new NCTM Principles and Standards for School Mathematics, presents an online activity using the TRIPS software.)
Additional Recommended Software
Tabletop Jr. and Tabletop Sr. are tools that give students the power to categorize and measure, organize and arrange, represent and interpret, and graph and analyze data. These programs offer a new way to interact with data and information by animating data and creating engaging visual environments. They help students develop skills fundamental for data analysis and essential for literacy in an information age.
Units with Software
Curriculum Unit: Making Shapes and Building Blocks (Exploring Geometry)
Software Title: Shapes
In Kindergarten, children are developing their ability to recognize, describe, and name shapes, and are beginning to relate shapes to each other. One way students do this is by using the Shapes software to explore the pattern block shapes and relationships among them. They also think about geometric motions--such as rotations--as they turn shapes to make designs, copy designs made with actual blocks, and fill in outlines of pictures that are provided. They also develop their visual and spatial sense as they play Quick Images, an activity in which students briefly see an image of a few shapes and then work to build an exact copy.
Curriculum Unit: Quilt Squares and Block Towns (2-D and 3-D Geometry)
Software Title: Shapes
In first grade, students continue to use Shapes to think about attributes of the pattern block shapes and relationships among them. They also explore the idea that one shape can be made in a variety of ways, using a variety of different shapes. They use motions such as flips and turns to create designs with pattern blocks, and to fill provided outlines in as many different ways as possible. They begin to think about the idea of a unit as they design quilt squares using squares and triangles, which are repeated to create a quilt pattern.
Mathematical Thinking at Grade 2 (Introduction)
Shapes, Halves, and Symmetry (Geometry and Fractions)
Software Title: Shapes
In these two second grade units, students continue their work with Shapes. Designing pictures and solving shape puzzles encourages children to think about how shapes fit together, how certain shapes fit into particular spaces, and what it means to completely fill a given space. In this way students encounter beginning ideas about area. As they consider different ways to fill the same shape, think about the fewest possible blocks that would fill a particular space, and predict how many green triangles (the smallest pieces) would fill the same shape, they are also exploring the idea of a unit of area. Students also use Shapes to explore attributes of rectangles, made from rows (or columns) of squares. Finally, they investigate symmetry by creating symmetrical designs with pattern blocks and Computer Mirrors.
Curriculum Unit: Does It Walk, Crawl, or Swim? (Sorting and Classifying Data)
Software Title: Tabletop Jr.
(Note: The recommended software is optional, and is not included with this unit.) This unit focuses on collecting, organizing, representing and analyzing a variety of kinds of data. As an extension to the activities presented in the unit, Tabletop Jr. is recommended. This software engages primary students in sorting, organizing and graphing data. Students can create free-form arrangements of data, or organize them in a variety of ways. Students can create their own data sets or work with ones provided.
Curriculum Unit: How Long? How Far? (Measuring)
Software Title: Geo-Logo
Students use Geo-Logo to explore measurement ideas such as how many steps it takes to get to a particular object, and how the size of a pace affects the number of steps. They also explore paths and turns (angles) as they try to find the most efficient route through a maze. Finally, students think about how to use the commands they have learned -- commands that send the turtle forward and back, or make it turn to the left and right -- to make the turtle draw a particular shape.
Curriculum Unit: Flips, Turns, and Area (2-D Geometry)
Software Title: Tumbling Tetrominoes
In Tumbling Tetrominoes, students use the three basic geometric motions--slides, flips, and turns--to place tetrominoes (five different arrangements of four squares) within a larger rectangle, with the goal being to leave as few empty spaces as possible. Students also play Tumbling Tetrominoes using rectangles of various sizes. As they discuss how differently shaped rectangle gameboards affect the play of the game, they explore ideas about conservation of area and strategies for covering areas.
Curriculum Unit: Turtle Paths (2-D Geometry)
Software Title: Geo-Logo
Students consider geometry and measurement ideas such as how the size of a unit is related to the number of units in a measured distance as they use Geo-Logo commands to direct a turtle through maze-like floor plans to retrieve toys or food. As students write procedures to draw shapes, students explore the attributes of shapes like equilateral triangles and rectangles. They also use what they know about shapes and their attributes to find missing measures of particular shapes, and to make rectangles with a given perimeter. Students combine many of these ideas while designing and carrying out a Geo Logo project
Curriculum Unit: Sunken Ships and Grid Patterns (2-D Geometry)
Software Title: Geo-Logo
Students investigate the four quadrants of the coordinate grid system by playing Sunken Ships, a game similar to Battleship, and by designing a symmetrical bulletin board. They explore paths in the coordinate grid system by finding the shortest path a taxi could take to stop at five different houses and return home. Students also undertake an in-depth study of rectangles and their attributes: how would you write a procedure to draw a rectangle? what commands are repeated in all of these procedures? what would happen if we turned the turtle 45° before drawing the rectangle? Students finish the unit by making a complex pattern on the computer using many of these commands.
Curriculum Unit: Picturing Polygons (2-D Geometry)
Software Title: Geo-Logo
Students think about the attributes of polygons as write Geo-Logo procedures that make regular and other polygons and as they try to construct shapes according to given properties (e.g. a quadrilateral with no equal sides and two right angles). They further investigate the coordinate grid system as they draw polygons that span all four quadrants. Finally, students consider special classes of polygons when they look at mystery polygons to decide if they are regular or not, and when they write procedures to draw similar rectangles and houses.
Curriculum Unit: Patterns of Changes (Tables and Graphs)
Software Title: Trips
Students explore speed, distance, time, and relationships among them--important ideas in the mathematics of change--as they plan trips for two people who move along parallel tracks. Students plan ways to coordinate speed and distance so that, for example, one beats the other by a particularly large or small margin, or so they tie. The software, called Trips, provides lists of their positions and graphs of their distance over time.
Curriculum Unit: Data: Kids, Cats, and Ads (Statistics)
Software Title: Tabletop Sr.
(Note: The recommended software is optional, and is not included with this unit.) This unit focuses on collecting, graphing and interpreting data. Tabletop Sr. is recommended as an optional piece of software for comparing, sorting and representing data. The program provides information about the weight, length, age, gender, and eye, pad, and fur color of a data set of cats, the same as those in the unit, and also allows students to enter their own cat data into the set. Students can also use Tabletop Sr. to conduct a survey of their own, combine the data into a single database, ask questions about the data, and develop representations for displaying it.