[Date]
MFP1501
Assignment 2 2024 -
18 June 2024
QUESTIONS AND ANSWERS
,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).
Educational Activity: A teacher could use arrays or grids to visually demonstrate
multiplication. For instance, showing a 3 by 4 grid of dots helps children visualize
3 x 4 = 12. This method helps them see the structure and pattern in multiplication.
MFP1501
Assignment 2 2024 -
18 June 2024
QUESTIONS AND ANSWERS
,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).
Educational Activity: A teacher could use arrays or grids to visually demonstrate
multiplication. For instance, showing a 3 by 4 grid of dots helps children visualize
3 x 4 = 12. This method helps them see the structure and pattern in multiplication.
