MFP1501
Assignment 2 2024
Detailed Solutions, References & Explanations
Unique number:
Due Date: 18 June 202
QUESTION 1
One-to-One Counting
In the initial phase of one-to-one counting, children are primarily concerned with answering
the "how many" question by counting objects individually. They count in ones, which
indicates that they have a basic understanding of cardinality—the concept that a number
represents a specific quantity. However, the idea of grouping objects to make counting
more efficient or to understand multiplication and division remains foreign to them. At this
stage, even if they can recite numbers in sequences of 2s, 3s, or 5s, they revert back to
one-to-one counting when asked to determine the number of objects in a group. Their
understanding is limited to seeing counting as a temporary procedure rather than a
permanent indicator of the total quantity in a collection.
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QUESTION 1
One-to-One Counting
In the initial phase of one-to-one counting, children are primarily concerned with
answering the "how many" question by counting objects individually. They count in
ones, which indicates that they have a basic understanding of cardinality—the concept
that a number represents a specific quantity. However, the idea of grouping objects to
make counting more efficient or to understand multiplication and division remains
foreign to them. At this stage, even if they can recite numbers in sequences of 2s, 3s,
or 5s, they revert back to one-to-one counting when asked to determine the number
of objects in a group. Their understanding is limited to seeing counting as a temporary
procedure rather than a permanent indicator of the total quantity in a collection.
Application: To help children in this phase understand multiplicative concepts,
teachers could design activities that show different representations of the same total
number. For example, showing that 3 groups of 2 objects is the same as 2 groups of
3 objects helps to introduce the principle of commutativity. Using array diagrams to
visually organize collections of objects in rows and columns can also aid in this
understanding. This method makes connections to skip counting, helping children
transition from seeing counting as a temporary task to understanding it as a stable
indicator of quantity.
Additive Composition
In the second phase, known as additive composition, children start to grasp that a
quantity remains the same even if it is rearranged or counted in different ways. Here,
they begin to connect counting with the concepts of skip counting and repeated
addition. However, they often need to physically lay out objects in groups before they
can skip count or use repeated addition to find the total number. At this stage, they
understand multiplication as repeated addition but do not yet recognize the inverse
relationship between multiplication and division.
Disclaimer
Extreme care has been used to create this document, however the contents are provided “as is” without
any representations or warranties, express or implied. The author assumes no liability as a result of
reliance and use of the contents of this document. This document is to be used for comparison, research
and reference purposes ONLY. No part of this document may be reproduced, resold or transmitted in any
form or by any means.
, +27 67 171 1739
Application: Effective activities for children in this phase might include exercises
where they need to describe multiplicative situations using arrays. For instance, asking
them to count the number of rows and the number of items in each row without finding
the total fosters their ability to conceptualize groups and group sizes. Encouraging
children to count groups simultaneously with the number of items in each group will
further enhance their understanding of both multiplication and division.
Many-to-One Counting
In the many-to-one counting phase, children are proficient in keeping track of both the
number of groups and the total number of objects in each group. They have developed
the ability to double count: they can count repetitions of a group while simultaneously
keeping track of the number of groups, effectively managing both the multiplicand (size
of the group) and the multiplier (number of groups). However, their understanding of
multiplication and division remains separate and not fully integrated. They struggle to
use the inverse relationship between these operations consistently.
Application: One way to strengthen their understanding is by providing problems that
explicitly require the use of the inverse relationship. For example, asking them to solve
"3 x ? = 12" or "? x 4 = 12" helps them understand that identifying the unknown quantity
determines whether the problem involves multiplication or division. Activities that
require identifying the number of items in each group, the number of groups, and the
total across various scenarios will enhance their ability to transition smoothly between
multiplication and division concepts.
Multiplicative Relations
In the final phase, multiplicative relations, children have a comprehensive
understanding of the multiplicative structure. They know that multiplicative situations
involve groups of equal size (multiplicand), the number of such groups (multiplier), and
the total amount (product). They are adept at coordinating these aspects for both
multiplication and division problems before counting. At this point, they can easily
Disclaimer
Extreme care has been used to create this document, however the contents are provided “as is” without
any representations or warranties, express or implied. The author assumes no liability as a result of
reliance and use of the contents of this document. This document is to be used for comparison, research
and reference purposes ONLY. No part of this document may be reproduced, resold or transmitted in any
form or by any means.
