As learners grow from lower grades to higher grades, the level of performance in mathematics will depend on their ability to understand the growing number of digits from two figures to higher figures. As children grow in understanding numbers, they need to understand the place-value groups further to develop strategies on separating quantity. Using groups of tens to represent quantities is a challenging process that requires an understanding of place-values. The integration of new and difficult construct concepts of having to group quantity by tens is the primary purpose of the whole-number place-value concept after understanding counting.
Counting a number like 73 requires further ability to group the number into the same quantities of tens and the leftovers. Learners can develop an understanding of groupings through demonstration of the counting ones and treating every digit as a separate group. Instructors can integrate base-ten groupings by ensuring that learners understand how to count a number as singles and groups differently. Association of the base-ten language and the grouping language helps the learners understand every digit's place values from a range of numbers.
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A grouping scheme is used to write the base-ten numbers where students can then associate the groupings of tens and ones and, therefore, record individual digits with their place values. The connection between counting and grouping numbers results from language development (Browning & Beauford, 2012) . Through individual counts of digits, a learner builds a sense of single matches in numbers, thus associating the respective place values. Group models are used in building the base-ten models for ones, tens, hundreds, and thousands. Proportional material is relevant in checking for the ten within numbers and equate to the one piece in the columns of digit arrangements.
Learners achieve the groupings by arranging objects such as cubes, cups, and bundles of sticks. The introduction of tens language results to the ability of learners to match the objects and generate meaningful phrases such as groups of hundreds and thousands (Brickwedde, 2018) . Learners use pre-grouped models such as understanding that a 10 is group of ones, and groups of tens makes up hundreds while hundreds makes up thousands. Students at their early stages use little ten-frames to generate reasoning about numbers. The model is essential as it shows the distance from one group to the next decade. However, a learner must have prior knowledge of the groupable models to understand the pre-grouped models.
Another important aspect to understand is the non-proportional models. In these models ten is not physically associated with 10 times larger than the normal one in counting. This models helps students to enhance their understanding of the place values in the normal learning. Example of non-proportional models is the use of abacus with same size of beads in different columns. Students need some practice on putting amounts in groups before understanding the base-ten grouping. The best way to teach place values is to have learners understand that grouping 10 can make up to 100 and 100 can be grouped to make up 100s. Therefore, the basic building foundation of the whole-number place-value concept is the counting process. Learners should first understand the counting of individual numbers. Later, the learner is introduced to a grouping of quantity from 10s, 100s, and so on (Brickwedde, 2018) . After the learner can group the numbers and separate the numbers, it is possible to generate the idea of place values based on understanding the total value of digits. The decomposition of complex numbers into simple numbers requires sufficient knowledge of groupings, which corresponds to getting the place value of a given digit within a number.
References
Browning, S., & Beauford, J. (2012). Language and Number Values: The Influence of Number Names on Children’s Understanding of Place Values. Investigations In Mathematics Learning , 4 (2), 1-24. https://doi.org/10.1080/24727466.2012.11790310
Brickwedde, J. (2018). Place Value as a Rate of Ten. Teaching Children Mathematics , 25 (1), 30. https://doi.org/10.5951/teacchilmath.25.1.0030
