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MFP1501
Assignment 2
2024 - 18 June
2024
QUESTIONS WITH DETAILED ANSWERS
,MFP1501 Assignment 2 2024 - 18 June 2024
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
MFP1501 Assignment 2 2024 - 18 June 2024
, MFP1501 Assignment 2 2024 - 18 June 2024
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.
MFP1501 Assignment 2 2024 - 18 June 2024
MFP1501
Assignment 2
2024 - 18 June
2024
QUESTIONS WITH DETAILED ANSWERS
,MFP1501 Assignment 2 2024 - 18 June 2024
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
MFP1501 Assignment 2 2024 - 18 June 2024
, MFP1501 Assignment 2 2024 - 18 June 2024
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.
MFP1501 Assignment 2 2024 - 18 June 2024
