, MFP1501
ASSIGNMENT 2
Instructions
First, sign and include the honesty declaration on the last page of this Assessment. If you are
typing your assessment, you can make this declaration your first page, followed by your cover
page. If you are writing by hand, save it as a PDF and combine it with the rest of your
assessment after scanning.
Question 1
Jacob and Willis (2003) outline hierarchical phases through which multiplicative
thinking develops, which include one-to-one counting, additive composition, many-to-
one counting, and multiplicative relations. Discuss each phase to show how best you
understand it. N.B. It should not be the same. Be creative.
One-to-one counting: The Explorer Phase
In this phase, children are like explorers setting foot on a new land of numbers. They see
each number as a unique landmark, counting them one by one. Just as explorers mark their
path with each step, these learners mark their understanding with each counted object.
However, much like explorers initially focus on individual trees rather than the forest, these
children perceive numbers individually rather than seeing the relationships between them. To
guide them into this new territory, educators act as experienced navigators, showing them
that rearranging the landscape doesn't change its essence. Through engaging activities,
children discover that no matter how the objects are arranged, the total count remains the
same, akin to finding different routes to the same destination.
Additive composition: The Architect Phase
As children advance, they transition into the role of architects, constructing their
understanding of numbers like builders laying bricks. They now grasp that numbers can be
rearranged without altering the total, similar to designing a building with interchangeable
components. Yet, their focus remains on the individual components rather than the structure
as a whole. Educators serve as mentors, guiding them to see beyond the bricks to the
blueprint that unites them. Through hands-on activities, children learn to see the relationships
between groups, shifting from simply adding components to understanding the
interconnectedness of the whole structure.
Many-to-one counting: The Conductor Phase
Now, children step into the role of conductors, orchestrating the symphony of numbers with
finesse. Like a skilled conductor leading an ensemble, they can simultaneously keep track of
multiple elements, guiding them towards harmony. They understand that numbers can be
grouped and counted efficiently, much like orchestrating different sections of an orchestra to
create a unified melody. However, they may still struggle to switch between different
compositions, much like a conductor navigating between musical pieces. Educators act as
maestros, teaching children to seamlessly transition between different numerical
ASSIGNMENT 2
Instructions
First, sign and include the honesty declaration on the last page of this Assessment. If you are
typing your assessment, you can make this declaration your first page, followed by your cover
page. If you are writing by hand, save it as a PDF and combine it with the rest of your
assessment after scanning.
Question 1
Jacob and Willis (2003) outline hierarchical phases through which multiplicative
thinking develops, which include one-to-one counting, additive composition, many-to-
one counting, and multiplicative relations. Discuss each phase to show how best you
understand it. N.B. It should not be the same. Be creative.
One-to-one counting: The Explorer Phase
In this phase, children are like explorers setting foot on a new land of numbers. They see
each number as a unique landmark, counting them one by one. Just as explorers mark their
path with each step, these learners mark their understanding with each counted object.
However, much like explorers initially focus on individual trees rather than the forest, these
children perceive numbers individually rather than seeing the relationships between them. To
guide them into this new territory, educators act as experienced navigators, showing them
that rearranging the landscape doesn't change its essence. Through engaging activities,
children discover that no matter how the objects are arranged, the total count remains the
same, akin to finding different routes to the same destination.
Additive composition: The Architect Phase
As children advance, they transition into the role of architects, constructing their
understanding of numbers like builders laying bricks. They now grasp that numbers can be
rearranged without altering the total, similar to designing a building with interchangeable
components. Yet, their focus remains on the individual components rather than the structure
as a whole. Educators serve as mentors, guiding them to see beyond the bricks to the
blueprint that unites them. Through hands-on activities, children learn to see the relationships
between groups, shifting from simply adding components to understanding the
interconnectedness of the whole structure.
Many-to-one counting: The Conductor Phase
Now, children step into the role of conductors, orchestrating the symphony of numbers with
finesse. Like a skilled conductor leading an ensemble, they can simultaneously keep track of
multiple elements, guiding them towards harmony. They understand that numbers can be
grouped and counted efficiently, much like orchestrating different sections of an orchestra to
create a unified melody. However, they may still struggle to switch between different
compositions, much like a conductor navigating between musical pieces. Educators act as
maestros, teaching children to seamlessly transition between different numerical
