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In this lesson, students will discover the relationships between area & perimeter as they relate to quadrilaterals and other shapes.
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Click and watch this teacher preparation video to help you understand how to teach this lesson. Here is a YouTube link of the teacher video for your reference: https://youtu.be/yr9ddiNX5Sw
Start Here: Teacher Preparation Video
By the end of the lesson, students will:
Construct several rectangles using a specific number of blocks
Construct several rectangles with a specific perimeter
Construct several rectangles with a specific perimeter and have to calculate the area of each rectangle
Construct several rectangles with a specific area and have to calculate the perimeter of each rectangle
Construct two rectangles with a specific area. These two rectangles have to be those with the maximum and minimum perimeter
Construct at least 3 figures (everything but rectangles) with a specific number of blocks and have to calculate the perimeter of each figure
Construct adjacent figures with two type of block. They need to calculate the perimeter and the area of each distinct figure and then the perimeter and the area of the entire figure, writing on a board their viewpoints
Communication
Creativity
Critical thinking
The Geometry World is divided in nine areas and in each area there are 8 geometry assignments written on posters. In each area could work at the same time three students for a total of 27 students. The game mode should be left in survival mode (the world file is already set in survival mode) and the time should be always set to day (/time set day command) by the op user, avoiding monsters and so on, because students are invited to share the few resources they find in every chest.
At first students have to build simple rectangles without considering any kind of calculation
On the next assignments students have to build specific rectangles with specific perimeters or areas
Students have to build all possible rectangles having specific perimeters and need to calculate their areas
Students have to build only two rectangles those with the maximum and minimum perimeter
Students have to calculate the perimeter of figures that aren't rectangles
Students have to build figures formed by two different rectangles and calculate the perimeter and the area of every figures, expressing also their consideration about the sum of perimeters and areas of adjacent figures
Students have to share the area where they are building their rectangles because it's quite limited and tight
Students are able to describe what is a perimeter
Students are able to describe what is an area
Students are able to identify different figures with the same area or the same perimeters
Students are able to describe that figures with the same area can have different perimeters
Students are able to share their working areas with others building vertical rectangles instead of horizontal ones
Students are able to describe adjacent figures have a total area that is the sum of each figure. That is not the same for the perimeter calculation.
Curriculum Extensions
Students can be invited to measure their classroom and calculate the perimeter and the area
Students can be invited to build their classroom and introduced to the concept of volume
Check out the Tips & Tricks video playlist that will help you and your students better use Minecraft: Education Edition in the classroom:
https://youtube.com/playlist?list=PLkh9rrdH-ARER03ojhFYtmoFDVuACYJLa
More videos added periodically so make sure you check often for more content!
Click and watch the student pause and play video with your class, pausing and playing as needed. This will help your students understand how to navigate through this lesson and Minecraft world and complete the activities located within them. Enjoy!
Check out the YouTube link of this video for your reference: https://youtu.be/RAWMwjggPlU
Student 'Pause & Play' Video
Shape and Space
Demonstrate an understanding of area of regular and irregular 2-D shapes by:
• recognizing that area is measured in square units
• selecting and justifying referents for the units cm2 or m2
• estimating area, using referents for cm2 or m2
• determining and recording area (cm2 or m2 )
• constructing different rectangles for a given area (cm2 or m2 ) in order to demonstrate that many different rectangles may have the same area.
Shape and Space
Design and construct different rectangles, given either perimeter or area, or both (whole numbers), and make generalizations
Applied Design
Prototyping
Outline a general plan, identifying tools and materials
Construct a first version of the product, making changes to tools, materials, and procedures as needed
Record iterations of prototyping
Testing
Test the product
Gather peer feedback and inspiration
Make changes and test again, repeating until satisfied with the product
Making
Construct the final product, incorporating planned change
Perimeter of regular and irregular shapes
Closed shapes have area and perimeter that can be described, measured, and compared.
Applied Design
Prototyping
Outline a general plan, identifying tools and materials
Construct a first version of the product, making changes to tools, materials, and procedures as needed
Record iterations of prototyping
Testing
Test the product
Gather peer feedback and inspiration
Make changes and test again, repeating until satisfied with the product
Making
Construct the final product, incorporating planned change
Perimeter of regular and irregular shapes
Closed shapes have area and perimeter that can be described, measured, and compared.
Area
E2.5 use the row and column structure of an array to measure the areas of rectangles and to show that the area of any rectangle can be found by multiplying its side lengths
E2.6 apply the formula for the area of a rectangle to find the unknown measurement when given two of the three
Shape and Space Strand
g) Determine the area of a regular 2-D shape and explain the strategy used.
h) Determine the area of an irregular 2-D shape and explain the strategy used.
i) Construct a rectangle with a given area.
Shape and Space Strand
a. Construct (concretely or pictorially) and record the dimensions of two or more rectangles with a specified perimeter and select, with justification, the dimensions that would be most appropriate in a particular situation (e.g., a rectangle is to have a perimeter of 18 units, what are the dimensions of the possible rectangles, which rectangle would be most appropriate if the rectangle is to be the base of a shoe box or a dog pen).
b. Critique the statement “A rectangle with dimensions of 1 cm by 8 cm is different from a rectangle with dimensions of 8 cm by 1 cm”. (Note: Any dimensions could be used to demonstrate the idea of orientation and point of view.)
c. Construct (concretely or pictorially) and record the dimensions of as many rectangles as possible with a specified area and select, with justification, the rectangle that would be most appropriate in a particular situation (e.g., a rectangle is to have an area of 24 units², what are the dimensions of the possible rectangles, which rectangle would be most appropriate if the rectangle is to fence off the largest garden possible or be the base of a box on a shelf that is 10 units by 8 units).
d. Critique the statement: “A rectangle with dimensions of 3 cm by 4 cm is different from a rectangle with dimensions of 2 cm by 5 cm”. (Note: Any dimensions with the same perimeter could be used to demonstrate the idea of same perimeter not necessarily resulting in the same area or shape of the rectangle).
e. Generalize patterns discovered through the exploration of the areas of rectangles with the same perimeter and through the exploration of the perimeters of rectangles with the same area (e.g., greater areas do not imply greater perimeters and vice versa, the rectangle for a situation closest to a square will have the greatest area, or the rectangle with the smallest width for a given perimeter will have the smallest area)will have the greatest area, or the rectangle with the smallest width for a given perimeter will have the smallest area)
Shape and Space
Demonstrate an understanding of perimeter of regular and irregular shapes by
- estimating perimeter using referents for centimetre or metre
- measuring and recording perimeter (cm, m)
- constructing different shapes for a given perimeter (cm, m) to demonstrate that many shapes are possible for a perimeter [C, ME, PS, R, V
Shape and Space
Design and construct different rectangles given either perimeter or area, or both (whole numbers), and draw conclusions.
Estimates and measures surface area
using unconventional units
using conventional units
Calculates the perimeter of plane figures
SS3
determining and recording area
constructing different rectangles for a given area (cm2 or m2 ) in order to demonstrate that many different rectangles may have the same area
SS1
Design and construct different rectangles, given either perimeter or area, or both (whole numbers), and make generalizations.
Measurement
determine the area of regular and irregular 2-D shapes in square centimetres and square metres
recognize and demonstrate that different rectangles can have the same inside space (area)
recognize and demonstrate that for any given area, many different rectangles are possible
draw rectangles for a given area
solve problems involving area
Measurement
draw rectangles for a given perimeter (distance around the outside)
draw rectangles for a given area
recognize and demonstrate that different objects can have the same area (inside space)
recognize and demonstrate that objects with the same area can have different perimeters (distance around the outside)
determine the shape that will result in the least or the greatest area for a given perimeter
estimate and measure area in square centimetres and square metres
solve simple problems involving the perimeter and/or area of polygons
SS3 Demonstrate an understanding of area of regular and irregular 2-D shapes by:
• recognizing that area is measured in square units
• selecting and justifying referents for the units cm² or m²
• estimating area, using referents for cm² or m²
• determining and recording area (cm² or m²
5SS1 Design and construct different rectangles, given either perimeter or area, or both (whole numbers), and make generalizations.
Shape and Space
determining and recording area
constructing different rectangles for a given area (cm2 or m2 ) in order to demonstrate that many different rectangles may have the same area.
Shape and Space
SS2 - Design and construct different rectangles, given either perimeter or area, or both (whole numbers), and make generalizations.