The objective of this first program is to engage students in the activities of packing and unpacking to build a sense of place value and ten as a composite unit. Students can ask the computer to generate a random number of candies, estimate how many were produced, and then pack them up to facilitate the task of counting to verify their estimates. Other activities might include packing and unpacking specified amounts of candies to show that these transformations do not change initial number of candies produced.
Click to see an animated GIF file for generating random candies and packing them up.
The objective of this second program is to help students develop ways to symbolize their packing and unpacking activities. This microworld contains two linked representation systems: graphical icons, and numeric symbols. If students make a change in one system (e.g., pack up 10 candies) this action is then represented as a "cross out" on the inventory form. Conversely, students can operate on the numerals and see these changes be reflected in the icons. This program also enables users to study the concept of place value in more depth by changing the "packing rule" to specify the number of candies packed in each roll and the number of rolls in each box.
Click to see an animated GIF file for unpacking a box and updating the inventory form.
Click to see similar animation in base 8.
The objective of this third program is to help students develop a conceptual understanding of the algorithms for addition and subtraction. In the example shown, there were initially 500 candies (packed in 5 boxes). A customer asked to purchase 145 candies (1 box, 4 rolls, and 5 pieces). Since there were 0 rolls and 0 pieces in the storeroom, this request required the students to unpack a box and a roll. As with the second microworld, these actions could be performed using either the graphics or the numeric symbols. When using the numeric symbols, the program supports multiple approaches such as starting from the left (the boxes), starting from the right (the pieces), or unpacking boxes and rolls after they have been subtracted (as shown in the example below). Thus, although the program is designed to help students understand the conventional algorithm, it also supports their attempts to invent other, equally viable algorithms for exploration.
Click to see an animated GIF file in which this transaction is illustrated.
This final version of the software was developed for teacher training. The progam allows the users to change the "packing rule" so that any number of rolls and candies (from 1-10) can be packed at one time. This activity is designed to support the development of further imagery for place value in different bases. Many pre and inservice teachers who have used this program have indicated that they developed insights regarding:
If you would like to obtain a copy of this program and accompanying activity sheets, click as indicated below:
Activity 1: Estimating in different bases
Activity 2: Drawing different ways to arrange candies
Activity 3: Concepts of place value numeration
Click to download a copy of this program.
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