Adding and Subtracting with Place Value Materials
|One type of place value material involves four types of objects. Each object happens to correspond to a dimension (geometry dimension):|
|The ones place is represented by a small cube, also referred to as a unit. [corresponds to a geometric point that has 0 dimension - no width, length, or height]|
|The tens place is represented by ten of these small cubes joined together, thus forming a stick. [corresponds to a geometric line that has 1 dimension - length]|
|The hundreds place is represented by ten sticks joined together, thus forming a flat. [corresponds to a geometric plane that has 2 dimensions - length and width]|
|The thousands place is represented by ten flats joined together, thus forming a large cube. [corresponds to a geometric solid that has 3 dimensions - length, width and height]|
The above place value materials do not allow us to represent the 10 000 place and beyond, because that would involve geometric objects that have four dimensions and more.
These place value materials are similar to an absolute numeration system because no matter which way you arrange the four types of PV materials (unit, stick, flat, cube) the count represented by the materials stays the same. This is different from a place value system where switching the digits changes the value of the numeral (e.g. 23 is different from 32). Yet we use these materials as model for place value. You need to understand that a model is NOT the real thing; it only tries to be the real thing (e.g. I would not fly in a model of an airplane).
|These place value materials can be used to develop place value understanding. For a grade 2 example, refer to:|
|Grade 2 Place Value|
|What numeral would the following place value materials represent?|
|Place value materials can be useful for helping children understand addition and subtraction.|
Place value materials can be useful for helping children understand addition. You build each number, then trade as needed, combine (put together) the materials, and lastly determine what numeral they represent.
Here is an example for 231 + 79.
|Step 1: Building 231.|
|Step 2: Building 79.|
|Step 3: Combining.|
|Step 4: Trading.|
|These materials represent the answer of 310 after the trading is done.|
Place value materials can be useful for helping children understand subtraction. The 'take away' meaning of subtraction best serves this purpose (if you use the "comparison" meaning of subtraction, you would have to build two sets and match them, where the answer is the unmatched stuff).
Suppose you wanted to use the place value materials to do: 231 - 65. You would build 231 with the place value materials and then remove 65.
Step 1 - Building 231
Step 2 - Removing 65
|There are not enough ones (small cubes/units) and tens (sticks) available for removing. You will have to trade 1 hundred (flat) for 10 tens (sticks) and 1 ten (stick) for 10 ones (small cubes/units).
The trading would look as follows:
|Removing 65 is now possible. Remove 6 tens (sticks) and 5 ones (units).|
|These materials represent 166, the answer to 231 - 65.|
|How would you use the place value materials to do 3105 -1878?|