What are the groupable models and the pregrouped/Trading models of base-ten concept?
How are they different?
I have been searching for a definition for these terms but my efforts deem unsuccessful. Could u asset me plzz.
In base 10, blocks of one can be combined to make blocks of length ten, then the strings of ten can be grouped to make a block of 100. The individual blocks are groupable, but a block of lenght ten is called pregrouped, and can be traded for ten individual blocks.
These blocks, or some in rod form, were popular in the sixties, and seventies, as manipulatives for number sense, but research has been clear that that they fail to help children understand number structure and number operations, albeit they understood the trading game well.
Groupable: can be combined to make units of 10 or 100
Pregrouped: blocks or rods precombined in length 10
Trading model: A block of length 10 which can be traded for ten individual blocks.
The terms "groupable models" and "pregrouped/trading models" are commonly used in mathematics education, specifically when teaching the base-ten concept.
Groupable models refer to manipulatives or visual representations that can be grouped together to aid in understanding place value and regrouping. These models are typically used to represent numbers using base-ten blocks or other similar tools. Base-ten blocks include units (ones), rods (tens), flats (hundreds), and cubes (thousands). By physically manipulating these blocks, students can group and regroup them to better comprehend the base-ten system. For example, if they have 15 ones, they can group 10 of them together to form one rod (representing ten) and have 5 leftover ones.
On the other hand, pregrouped or trading models are visual representations where groups have already been formed to represent larger place values. These models incorporate the concept of regrouping or trading, where a certain quantity from a larger place value is exchanged for smaller units of a smaller place value. For instance, pregrouped models might include bundles of ten units, blocks representing hundreds, or sets of ten rods. Instead of needing to combine individual units to create larger numbers (as in groupable models), pregrouped models already show groups.
In summary, the key difference lies in the stage of grouping: groupable models require students to actively group individual units together, while pregrouped models already have groups formed. Groupable models are typically used when first introducing the base-ten concept, providing a concrete representation for building understanding. Pregrouped or trading models are used to further develop students' understanding of place value and the concept of regrouping.
I believe there may be some confusion with the terms you mentioned, as they do not correspond to common mathematical concepts related to base-ten. However, I can provide you with an explanation of the base-ten concept and grouping in mathematics.
The base-ten concept is a fundamental concept in our number system, where each place value position is ten times the value of the position to its right. In base-ten, the numbers 0-9 are used, and once you reach 9 in a particular place value, you carry over to the next place value by adding 1.
Grouping in mathematics refers to a strategy used to simplify calculations by regrouping numbers. This can be done by combining or splitting numbers to make calculations easier. Grouping is commonly used when performing addition, subtraction, multiplication, and division. It allows for easier mental calculations or breaks down complex problems into smaller, more manageable steps.
However, the terms "groupable models" and "pregrouped/Trading models" are not commonly used mathematical terms. It's possible that they may refer to specific teaching methods or curriculum materials used in a particular educational context. To provide more accurate information, I would need additional context or clarification on where these terms are being used.