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MFP1501 Assignment 2 Due 18 June 2024
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MFP1501 Assignment 2 Due 18 June 2024
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MFP1501ASSIGNMENT 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
,arrangements, enabling them to conduct their mathematical symphony with confidence and
precision.
Multiplicative relations: The Mastermind Phase
In this final phase, children ascend to the role of masterminds, wielding their deep
understanding of numbers with expertise. Like master strategists on a chessboard, they
anticipate the consequences of each numerical move, seeing the interconnectedness of every
piece. They recognize that every numerical scenario involves three key elements, akin to
analyzing the intricate dynamics of a complex strategy. Educators act as mentors, guiding
children to unlock the full potential of their numerical prowess. Through engaging challenges
and explorations, children develop a profound understanding of the relationships between
numbers, enabling them to navigate the mathematical landscape with mastery and finesse.
Question 2
In the Foundation Phase, multiplication is commonly introduced as repeated addition,
that is, situations where several groups of the same size need to be added together.
We usually ask questions such as: “How big is each group or how many groups?
Provide five examples which are different from those in the study guide.
Shopping Spree in Africa Mall:
Kaylin went shopping and bought 3 packs of gum, with 4 gums in each pack. How many
gums did Kaylin buy in total?
A Pizza Party at Rocklands:
At a party, there are 5 pizzas, and each pizza is cut into 8 slices. How many pizza slices are
there in total?
Bookshelves:
A library has 6 shelves, and each shelf can hold 10 books. How many books can the library
hold in total?
Candy Distribution:
There are 8 bags of candies, and each bag contains 12 candies. How many candies are
there in total?
Joubiez School Supplies:
Ms. Jacobs bought 9 packs of markers, with 6 markers in each pack. How many markers did
the teacher buy in total?
, Question 3
You can teach doubling in the Foundation Phase in various ways. These approaches
depend on the grade level you teach or what learners can or cannot do. It is important
always to be responsive to your learners' cognitive level. It would be best if you always were
moving learners to a more abstract level but using concrete apparatus to scaffold these
moves. There are also a variety of diagrams for teaching doubling apart from using body
parts as resources.
3.1 Identify two diagrams that you can use to teach doubling to the Foundation Phase.
Pyramid Format:
Spider Web Format:
3.2 Motivate how you will use each diagram. Do not copy from the study guide
Pyramid Format:
The pyramid format is a simple yet effective diagram that can be used to teach doubling in
the Foundation Phase. The pyramid starts with a single number at the top, representing the
original value to be doubled. Beneath it are two numbers, each representing the doubled
value of the original number? This pattern continues downwards, with each subsequent row
representing the doubling of the previous row's numbers.
Motivation:
Start with small numbers, such as 1 or 2, at the top of the pyramid to introduce the concept
of doubling.
As learners progress, gradually increase the complexity by introducing larger numbers.
Allow learners to actively participate by filling in the empty blocks of the pyramid, promoting
engagement and reinforcement of the doubling concept.
Use colorful visuals and manipulatives to make the pyramid format visually appealing and
interactive, enhancing understanding and retention.
Spider Web Format:
The spider web format is a more advanced diagram that can be introduced to Grade 2 and
Grade 3 learners. In this format, the instruction or original number is placed in the center
circle, while the doubled values are written in the blocks on the outside circle, radiating
outwards like a spider's web.
Motivation:
Introduce the spider web format as a challenging and engaging activity for learners who
have mastered basic doubling concepts.
Encourage learners to think critically and strategically as they determine the doubled values
for a given number.
Use the spider web format as a visual aid during group discussions or classroom
presentations, facilitating collaborative learning and peer interaction.
Provide opportunities for learners to create their own spider web diagrams, fostering
creativity and ownership of learning
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