MFP1501
Assignment 2
(COMPLETE
ANSWERS)
2024 - 18 June
2024
CONTACT:
, 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. (20)
Certainly! Let's explore each phase of multiplicative thinking development in a creative way:
1. One-to-One Counting: Imagine you're in a magical forest, and you come across a row of
colorful mushrooms. Each mushroom represents a different creature in the forest. As you
count them one by one, you realize that each creature has its own unique identity, much
like the individual numbers you're assigning to them. This phase is like laying the
groundwork, where you're establishing a connection between each entity and a number,
forming the basis of multiplication.
2. Additive Composition: Now, picture yourself in a bustling marketplace filled with
vendors selling various fruits. You're tasked with creating baskets of fruit for customers.
You start by adding apples, then oranges, and finally bananas to each basket. Each basket
represents a sum of individual fruits. As you compose these baskets, you're essentially
adding together the quantities of different items. This phase involves combining
individual counts to form larger sums, paving the way for understanding multiplication as
repeated addition.
3. Many-to-One Counting: Transport yourself to a colorful coral reef teeming with marine
life. Here, different species of fish swim together in groups, each group forming a unique
ecosystem within the reef. You observe that while each species is distinct, they can be
counted together as part of a larger community. In this phase, you're moving beyond
counting individual items and instead counting groups of items as a single entity, laying
the groundwork for understanding multiplication as groups of equal sets.
4. Multiplicative Relations: Finally, envision yourself as an explorer in a vast desert,
where you stumble upon ancient ruins with intricate patterns etched into the sandstone
walls. Each pattern represents a mathematical relationship, where certain symbols interact
with each other in specific ways. These multiplicative relationships reveal how numbers
can interact to produce outcomes greater than mere addition. You start to see how
quantities can be scaled up or down through multiplication, unlocking the deeper
connections between numbers and their operations.
In essence, each phase of multiplicative thinking development takes you on a journey through
different landscapes, from the simplicity of individual counting to the complexity of
multiplicative relationships, gradually building your understanding of how numbers interact and
relate to each other in the realm of multiplication.
Assignment 2
(COMPLETE
ANSWERS)
2024 - 18 June
2024
CONTACT:
, 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. (20)
Certainly! Let's explore each phase of multiplicative thinking development in a creative way:
1. One-to-One Counting: Imagine you're in a magical forest, and you come across a row of
colorful mushrooms. Each mushroom represents a different creature in the forest. As you
count them one by one, you realize that each creature has its own unique identity, much
like the individual numbers you're assigning to them. This phase is like laying the
groundwork, where you're establishing a connection between each entity and a number,
forming the basis of multiplication.
2. Additive Composition: Now, picture yourself in a bustling marketplace filled with
vendors selling various fruits. You're tasked with creating baskets of fruit for customers.
You start by adding apples, then oranges, and finally bananas to each basket. Each basket
represents a sum of individual fruits. As you compose these baskets, you're essentially
adding together the quantities of different items. This phase involves combining
individual counts to form larger sums, paving the way for understanding multiplication as
repeated addition.
3. Many-to-One Counting: Transport yourself to a colorful coral reef teeming with marine
life. Here, different species of fish swim together in groups, each group forming a unique
ecosystem within the reef. You observe that while each species is distinct, they can be
counted together as part of a larger community. In this phase, you're moving beyond
counting individual items and instead counting groups of items as a single entity, laying
the groundwork for understanding multiplication as groups of equal sets.
4. Multiplicative Relations: Finally, envision yourself as an explorer in a vast desert,
where you stumble upon ancient ruins with intricate patterns etched into the sandstone
walls. Each pattern represents a mathematical relationship, where certain symbols interact
with each other in specific ways. These multiplicative relationships reveal how numbers
can interact to produce outcomes greater than mere addition. You start to see how
quantities can be scaled up or down through multiplication, unlocking the deeper
connections between numbers and their operations.
In essence, each phase of multiplicative thinking development takes you on a journey through
different landscapes, from the simplicity of individual counting to the complexity of
multiplicative relationships, gradually building your understanding of how numbers interact and
relate to each other in the realm of multiplication.
