Embedded Files
Definitions
Definitions
array: Rows x columns
rows: Horizontal sections of an array
columns: Vertical sections of an array
2D shape: A flat figure with an outline or form
square un. : A unit of area - square inches, square centimeters, etc.
unit square: 1 unit by 1 unit square
side length: The straight line distances between two points
tiling: To cover an area without gaps or overlaps
area model: A model for multiplication that relates rectangular arrays to area
area : The space inside of a 2D shape
Tiling and Grids
Tiling and Grids
Grids
Grids
In the beginning of learning about area, students use grid paper to SEE the square units that create the area of a shape. Students learn they can just COUNT the square inside the shape to find the area.
In the beginning of learning about area, students use grid paper to SEE the square units that create the area of a shape. Students learn they can just COUNT the square inside the shape to find the area.
We also discuss how you can count the length and the width of the shape and use those numbers to create a multiplication equation to find the area.
We also discuss how you can count the length and the width of the shape and use those numbers to create a multiplication equation to find the area.
Tiling
Tiling
Tiling is similar to grids, but students create the "grid" using square tiles. Students then count how many units long and wide the shape is and use those units to multiply and find the area.
Tiling is similar to grids, but students create the "grid" using square tiles. Students then count how many units long and wide the shape is and use those units to multiply and find the area.
Students check their answer by counting the number of total tiles to create the shape.
Students check their answer by counting the number of total tiles to create the shape.
length x width
length x width
Multiplication & Area
Multiplication & Area
Students learn the more efficient way to find the area of a rectangle/square is to multiply the units of the length and width.
Students learn the more efficient way to find the area of a rectangle/square is to multiply the units of the length and width.
Irregular Shapes
Irregular Shapes
Irregular shapes are shapes that do not have all equal sides, or do not follow the regular look of a particular shape. Most of the irregular shapes third graders see when finding area are irregular hexagons (6 sided shapes).
Shape A: 2 x 5
Shape B: 3 x 3
Final equation:
(2 x 5) + (3 x 3)
10 + 9
19 sq. cm
Decompose to find area
Decompose to find area
When finding the area of irregular shapes, student can use the DECOMPOSING strategy. In the strategy students decompose the irregular shape into smaller rectangular shapes.
When finding the area of irregular shapes, student can use the DECOMPOSING strategy. In the strategy students decompose the irregular shape into smaller rectangular shapes.
Students then find the area of each smaller shape using L x W.
Students then find the area of each smaller shape using L x W.
Lastly, students add the areas of the smaller shapes to find the total area of the irregular shape.
Lastly, students add the areas of the smaller shapes to find the total area of the irregular shape.
Both strategies produce the same answer.
_________________________
_________________________
Composed shape: 5 x 5
Extra shape: 3 x 2
Final equation:
(5 x 5) - (3 x 2)
25 - 6
19 sq. cm
compose to find area
compose to find area
When finding the area of irregular shapes, student can use the COMPOSING strategy. In the strategy students compose the irregular shape by creating one LARGE rectangular shape.
When finding the area of irregular shapes, student can use the COMPOSING strategy. In the strategy students compose the irregular shape by creating one LARGE rectangular shape.
Students find find the area of that composed shape using L x W.
Students find find the area of that composed shape using L x W.
Lastly, students then find the area of the extra shape/piece and subtract that area from the composed area, to find the area of the irregular shape.
Lastly, students then find the area of the extra shape/piece and subtract that area from the composed area, to find the area of the irregular shape.
Both strategies produce the same answer.
Missing Sides
Missing Sides
Unknown Side Length given the area
Unknown Side Length given the area
When students are given one side length and the area, there are two strategies.
When students are given one side length and the area, there are two strategies.
1. Division (32 ÷ 4 = 8)
2. Unknown Factor (4 x ____ = 32)
Missing Side lengths on irregular shapes
Missing Side lengths on irregular shapes
When students are NOT given the area and need to find the missing side length, they use the fact family or number bond strategy.
RED: 4 + ____ = 9
BLUE: 5 + ____ = 11
After students have found the missing sides, they can solve for the area.
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