MFP1501
ASSIGNMENT 2 2024
- 18 JUNE 2024
QUESTIONS WITH COMPLETE ANSWERS
[DATE]
[Company address]
,MFP1501 Assignment 2 2024 - 18 June 2024
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)
One-to-One Counting
Description: One-to-one counting is the foundational phase where children learn to count
objects one at a time. Each object is paired with a single counting word, ensuring a direct
correspondence between the number of items and the number words.
Example: Imagine a child playing with blocks. As they place each block into a box, they count
aloud: "one, two, three, four, five." This phase focuses on the child's ability to correctly assign
one number to each object, ensuring an accurate count.
Educational Activity: A teacher might use a counting book where children have to count the
number of animals on each page. This reinforces the concept of one-to-one correspondence as
they point to each animal and say the corresponding number.
Significance: This phase is crucial because it establishes the basic understanding of numbers and
counting, which is necessary for more complex mathematical concepts. Without mastering one-
to-one counting, a child would struggle with higher-level arithmetic.
Additive Composition
Description: Additive composition involves understanding that numbers can be broken down
into parts and recombined. Children learn that numbers are composed of smaller numbers added
together.
Example: Consider a child who has 7 apples. They realize that this total can be broken down
into 3 apples and 4 apples, or 5 apples and 2 apples, and still add up to 7.
, Educational Activity: A teacher might provide a set of 10 blocks and ask the children to find all
the different ways to group the blocks into two piles. For instance, 1+9, 2+8, 3+7, etc. This
exercise helps children see the flexibility of numbers and the various ways they can be
combined.
Significance: Additive composition is essential for understanding more complex operations like
addition and subtraction. It helps children see the relationships between numbers and prepares
them for multiplication and division.
Many-to-One Counting
Description: Many-to-one counting, also known as skip counting, involves counting objects in
groups or sets rather than individually. This phase introduces the concept of multiplication as
repeated addition.
Example: A child counting by twos might count: "2, 4, 6, 8, 10," instead of counting each
number individually. This method groups numbers into sets of two.
Educational Activity: A teacher might use a number line and ask children to place markers at
intervals of 5. By doing so, children practice counting by fives (5, 10, 15, 20, etc.), reinforcing
the idea of grouping.
Significance: Many-to-one counting is a stepping stone to understanding multiplication. It helps
children grasp the concept of adding equal groups together, which is fundamental to more
advanced mathematical operations.
Multiplicative Relations
Description: Multiplicative relations involve understanding the relationships between numbers
in terms of multiplication and division. Children learn to see numbers as factors and products,
understanding that multiplication is not just repeated addition, but a relationship between
quantities.
Example: A child might understand that 3 groups of 4 apples (3 x 4) equal 12 apples.
Conversely, they can also comprehend that dividing 12 apples into 3 groups gives 4 apples per
group (12 ÷ 3 = 4).
ASSIGNMENT 2 2024
- 18 JUNE 2024
QUESTIONS WITH COMPLETE ANSWERS
[DATE]
[Company address]
,MFP1501 Assignment 2 2024 - 18 June 2024
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)
One-to-One Counting
Description: One-to-one counting is the foundational phase where children learn to count
objects one at a time. Each object is paired with a single counting word, ensuring a direct
correspondence between the number of items and the number words.
Example: Imagine a child playing with blocks. As they place each block into a box, they count
aloud: "one, two, three, four, five." This phase focuses on the child's ability to correctly assign
one number to each object, ensuring an accurate count.
Educational Activity: A teacher might use a counting book where children have to count the
number of animals on each page. This reinforces the concept of one-to-one correspondence as
they point to each animal and say the corresponding number.
Significance: This phase is crucial because it establishes the basic understanding of numbers and
counting, which is necessary for more complex mathematical concepts. Without mastering one-
to-one counting, a child would struggle with higher-level arithmetic.
Additive Composition
Description: Additive composition involves understanding that numbers can be broken down
into parts and recombined. Children learn that numbers are composed of smaller numbers added
together.
Example: Consider a child who has 7 apples. They realize that this total can be broken down
into 3 apples and 4 apples, or 5 apples and 2 apples, and still add up to 7.
, Educational Activity: A teacher might provide a set of 10 blocks and ask the children to find all
the different ways to group the blocks into two piles. For instance, 1+9, 2+8, 3+7, etc. This
exercise helps children see the flexibility of numbers and the various ways they can be
combined.
Significance: Additive composition is essential for understanding more complex operations like
addition and subtraction. It helps children see the relationships between numbers and prepares
them for multiplication and division.
Many-to-One Counting
Description: Many-to-one counting, also known as skip counting, involves counting objects in
groups or sets rather than individually. This phase introduces the concept of multiplication as
repeated addition.
Example: A child counting by twos might count: "2, 4, 6, 8, 10," instead of counting each
number individually. This method groups numbers into sets of two.
Educational Activity: A teacher might use a number line and ask children to place markers at
intervals of 5. By doing so, children practice counting by fives (5, 10, 15, 20, etc.), reinforcing
the idea of grouping.
Significance: Many-to-one counting is a stepping stone to understanding multiplication. It helps
children grasp the concept of adding equal groups together, which is fundamental to more
advanced mathematical operations.
Multiplicative Relations
Description: Multiplicative relations involve understanding the relationships between numbers
in terms of multiplication and division. Children learn to see numbers as factors and products,
understanding that multiplication is not just repeated addition, but a relationship between
quantities.
Example: A child might understand that 3 groups of 4 apples (3 x 4) equal 12 apples.
Conversely, they can also comprehend that dividing 12 apples into 3 groups gives 4 apples per
group (12 ÷ 3 = 4).
