MTE1501 Assignment
4 (COMPLETE
ANSWERS) 2025 -
DUE 31 August 2025
FOR ASSISTANCE CONTACT
EMAIL:
,Definitions and Examples
A polygon is a two-dimensional shape with straight sides. The sides are connected to form a closed
figure. An example is the face of a stop sign.
A polyhedron is a three-dimensional solid with flat polygonal faces, straight edges, and vertices. An
example is a die.
A spatial object is a three-dimensional object that occupies space and has depth, width, and height.
An example is a soccer ball.
A 2-D shape is a flat shape that has only two dimensions: length and width. An example is the
shadow cast by a building on a sunny day.
Comparing Geometric Shapes
Shape Faces Edges Vertices
Cube 6 12 8
Rectangular Prism 6 12 8
Rectangular Pyramid 5 8 5
Export to Sheets
Geometric Shape Diagrams
Van Hiele's Levels of Geometric Thought
Van Hiele's levels describe a hierarchy of how students understand geometry, from simple
recognition to complex formal proofs. Learners must progress through the levels sequentially.
• Level 0: Visualization. At this level, learners identify shapes based on their overall
appearance. They don't recognize the properties of the shapes.
o Question/Task: "Can you pick out all the triangles from this pile of shapes?"
• Level 1: Analysis. Learners start to identify the properties of shapes (e.g., a square has four
equal sides and four right angles) but don't see the relationships between different shapes.
o Question/Task: "What do all these rectangles have in common?"
• Level 2: Informal Deduction/Abstraction. Learners can recognize the relationships between
properties and classes of shapes. They understand that a square is also a rectangle and a
rhombus.
o Question/Task: "If a square has four equal sides and a rhombus has four equal sides,
why is every square a rhombus, but not every rhombus a square?"
, Misconception in Area Calculation
The learner's calculation of 4×3×3×5×3=540cm2 for the area of the L-shape is incorrect. The errors
are:
• Incorrect Formula Application: The learner multiplied all the given dimensions together, as if
calculating the volume of a 3-D object, rather than finding the area of a 2-D shape.
• Lack of Decomposition: The learner didn't break down the complex L-shape into simpler
rectangles, which is the correct method for finding the area of this shape.
• Incorrect Units: The final answer uses cm2 which is the correct unit for area, but the
calculation method is flawed.
To correct this using a constructivist approach, I would guide the learner to discover the correct
method themselves. I'd provide them with a grid paper representation of the L-shape and ask them
to count the squares inside. This would visually demonstrate that area is the space inside a shape.
Then, I'd ask, "Is there an easier way to count all these squares without counting one by one?" This
would prompt them to see that they can split the shape into two rectangles, find the area of each,
and then add them together. I would ask questions like: "Can you cut this shape into two rectangles?
What are the dimensions of the two new rectangles? Can you find the area of each of those
rectangles? What do you do with those two areas to find the total area of the L-shape?" This method
allows the learner to construct their own understanding of decomposing complex shapes to calculate
area.
Mathematics Activity: "Building a Class Garden"
• Curriculum Topic: Measurement: Perimeter and Area
• Expected Learning Outcomes:
o Learners will be able to calculate the perimeter and area of squares and rectangles.
o Learners will be able to apply their knowledge of number operations (addition and
multiplication) in a geometric context.
o Learners will be able to solve real-world problems involving perimeter and area.
Detailed Description of the Activity
Title: The Class Garden Project
Instructions: The class is going to design a vegetable garden for the school. Each group of 4-5
learners will receive a plot of land to design. The "land" is a large piece of graph paper. Your task is to
design a garden layout using two different rectangular shapes for different types of vegetables (e.g.,
one for carrots and one for tomatoes). You must calculate the perimeter of the entire garden to
determine the amount of fencing needed and the total area to figure out how many vegetable
seedlings can be planted.
Materials:
• Large sheets of A3 graph paper
• Rulers and pencils
4 (COMPLETE
ANSWERS) 2025 -
DUE 31 August 2025
FOR ASSISTANCE CONTACT
EMAIL:
,Definitions and Examples
A polygon is a two-dimensional shape with straight sides. The sides are connected to form a closed
figure. An example is the face of a stop sign.
A polyhedron is a three-dimensional solid with flat polygonal faces, straight edges, and vertices. An
example is a die.
A spatial object is a three-dimensional object that occupies space and has depth, width, and height.
An example is a soccer ball.
A 2-D shape is a flat shape that has only two dimensions: length and width. An example is the
shadow cast by a building on a sunny day.
Comparing Geometric Shapes
Shape Faces Edges Vertices
Cube 6 12 8
Rectangular Prism 6 12 8
Rectangular Pyramid 5 8 5
Export to Sheets
Geometric Shape Diagrams
Van Hiele's Levels of Geometric Thought
Van Hiele's levels describe a hierarchy of how students understand geometry, from simple
recognition to complex formal proofs. Learners must progress through the levels sequentially.
• Level 0: Visualization. At this level, learners identify shapes based on their overall
appearance. They don't recognize the properties of the shapes.
o Question/Task: "Can you pick out all the triangles from this pile of shapes?"
• Level 1: Analysis. Learners start to identify the properties of shapes (e.g., a square has four
equal sides and four right angles) but don't see the relationships between different shapes.
o Question/Task: "What do all these rectangles have in common?"
• Level 2: Informal Deduction/Abstraction. Learners can recognize the relationships between
properties and classes of shapes. They understand that a square is also a rectangle and a
rhombus.
o Question/Task: "If a square has four equal sides and a rhombus has four equal sides,
why is every square a rhombus, but not every rhombus a square?"
, Misconception in Area Calculation
The learner's calculation of 4×3×3×5×3=540cm2 for the area of the L-shape is incorrect. The errors
are:
• Incorrect Formula Application: The learner multiplied all the given dimensions together, as if
calculating the volume of a 3-D object, rather than finding the area of a 2-D shape.
• Lack of Decomposition: The learner didn't break down the complex L-shape into simpler
rectangles, which is the correct method for finding the area of this shape.
• Incorrect Units: The final answer uses cm2 which is the correct unit for area, but the
calculation method is flawed.
To correct this using a constructivist approach, I would guide the learner to discover the correct
method themselves. I'd provide them with a grid paper representation of the L-shape and ask them
to count the squares inside. This would visually demonstrate that area is the space inside a shape.
Then, I'd ask, "Is there an easier way to count all these squares without counting one by one?" This
would prompt them to see that they can split the shape into two rectangles, find the area of each,
and then add them together. I would ask questions like: "Can you cut this shape into two rectangles?
What are the dimensions of the two new rectangles? Can you find the area of each of those
rectangles? What do you do with those two areas to find the total area of the L-shape?" This method
allows the learner to construct their own understanding of decomposing complex shapes to calculate
area.
Mathematics Activity: "Building a Class Garden"
• Curriculum Topic: Measurement: Perimeter and Area
• Expected Learning Outcomes:
o Learners will be able to calculate the perimeter and area of squares and rectangles.
o Learners will be able to apply their knowledge of number operations (addition and
multiplication) in a geometric context.
o Learners will be able to solve real-world problems involving perimeter and area.
Detailed Description of the Activity
Title: The Class Garden Project
Instructions: The class is going to design a vegetable garden for the school. Each group of 4-5
learners will receive a plot of land to design. The "land" is a large piece of graph paper. Your task is to
design a garden layout using two different rectangular shapes for different types of vegetables (e.g.,
one for carrots and one for tomatoes). You must calculate the perimeter of the entire garden to
determine the amount of fencing needed and the total area to figure out how many vegetable
seedlings can be planted.
Materials:
• Large sheets of A3 graph paper
• Rulers and pencils
